From fe1c5c2f4d5622e878a03b2332de22812ff29c03 Mon Sep 17 00:00:00 2001
From: Anthony Damico <ajdamico@gmail.com>
Date: Tue, 7 Nov 2023 14:28:43 -0500
Subject: [PATCH] remove the progress()

---
 docs/1.1-install.html                         |   2 +-
 docs/1.2-survey.html                          |   2 +-
 docs/1.3-usage-examples.html                  |   2 +-
 ...1.4-the-current-population-survey-cps.html | 473 +++-------------
 docs/2-var.html                               |   2 +-
 docs/2.1-lin.html                             |   2 +-
 ...replication-based-variance-estimation.html |  66 +--
 ...ariance-estimation-for-decompositions.html |   2 +-
 docs/3-poverty.html                           |   2 +-
 ...-at-risk-of-poverty-threshold-svyarpt.html | 264 ++++-----
 .../3.2-at-risk-of-poverty-ratio-svyarpr.html | 470 ++++++++--------
 ...-relative-median-income-ratio-svyrmir.html | 282 +++++-----
 ...4-relative-median-poverty-gap-svyrmpg.html | 264 ++++-----
 ...-risk-of-poverty-threshold-svypoormed.html | 266 ++++-----
 ...reer-thorbecke-class-svyfgt-svyfgtdec.html | 504 +++++++++---------
 ...-poverty-measure-svywatts-svywattsdec.html | 462 ++++++++--------
 docs/4-inequality.html                        |   2 +-
 ...ich-inequality-measure-should-be-used.html |   2 +-
 docs/4.10-entropy-based-measures.html         |   2 +-
 ...py-and-decomposition-svygei-svygeidec.html | 162 +++---
 ...-and-decomposition-svyjdiv-svyjdivdec.html | 212 ++++----
 docs/4.2-the-gender-pay-gap-svygpg.html       | 266 ++++-----
 docs/4.3-quintile-share-ratio-svyqsr.html     | 264 ++++-----
 docs/4.4-lorenz-curve-based-measures.html     |   2 +-
 docs/4.5-lorenz-curve-svylorenz.html          | 112 ++--
 docs/4.6-gini-index-svygini.html              | 256 ++++-----
 docs/4.7-zenga-index-svyzenga.html            | 304 +++++------
 ...ocial-welfare-function-based-measures.html |   2 +-
 docs/4.9-atkinson-index-svyatk.html           | 116 ++--
 docs/404.html                                 |   2 +-
 docs/5-richness.html                          |   2 +-
 docs/5.1-richness-measures-svyrich.html       | 364 ++++++-------
 docs/6-multidimensional-poverty.html          |   2 +-
 docs/6.1-example-calculation.html             |   2 +-
 docs/7-covariance-matrix.html                 |  50 +-
 docs/7.1-example-calculation-1.html           | 118 ++--
 docs/index.html                               |   4 +-
 37 files changed, 2494 insertions(+), 2817 deletions(-)

diff --git a/docs/1.1-install.html b/docs/1.1-install.html
index aa3b715..27ab5ce 100644
--- a/docs/1.1-install.html
+++ b/docs/1.1-install.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
diff --git a/docs/1.2-survey.html b/docs/1.2-survey.html
index 8605db3..f3b5d20 100644
--- a/docs/1.2-survey.html
+++ b/docs/1.2-survey.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
diff --git a/docs/1.3-usage-examples.html b/docs/1.3-usage-examples.html
index 0f37f79..10b9d35 100644
--- a/docs/1.3-usage-examples.html
+++ b/docs/1.3-usage-examples.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
diff --git a/docs/1.4-the-current-population-survey-cps.html b/docs/1.4-the-current-population-survey-cps.html
index b0b4fb9..6b0ba05 100644
--- a/docs/1.4-the-current-population-survey-cps.html
+++ b/docs/1.4-the-current-population-survey-cps.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -263,429 +263,106 @@ <h2><span class="header-section-number">1.4</span> The Current Population Survey
 <span id="cb27-5"><a href="1.4-the-current-population-survey-cps.html#cb27-5" tabindex="-1"></a>this_url <span class="ot">&lt;-</span></span>
 <span id="cb27-6"><a href="1.4-the-current-population-survey-cps.html#cb27-6" tabindex="-1"></a>  <span class="st">&quot;https://www2.census.gov/programs-surveys/cps/datasets/2023/march/asecpub23sas.zip&quot;</span></span>
 <span id="cb27-7"><a href="1.4-the-current-population-survey-cps.html#cb27-7" tabindex="-1"></a></span>
-<span id="cb27-8"><a href="1.4-the-current-population-survey-cps.html#cb27-8" tabindex="-1"></a><span class="fu">GET</span>(this_url , <span class="fu">write_disk</span>(tf) , <span class="fu">progress</span>())</span></code></pre></div>
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+<span id="cb27-8"><a href="1.4-the-current-population-survey-cps.html#cb27-8" tabindex="-1"></a><span class="fu">GET</span>(this_url , <span class="fu">write_disk</span>(tf))</span></code></pre></div>
 <pre><code>## Response [https://www2.census.gov/programs-surveys/cps/datasets/2023/march/asecpub23sas.zip]
-##   Date: 2023-11-04 20:12
+##   Date: 2023-11-07 18:12
 ##   Status: 200
 ##   Content-Type: application/zip
 ##   Size: 176 MB
-## &lt;ON DISK&gt;  C:\Users\anthonyd\AppData\Local\Temp\RtmpEPzxb7\file5368225b1a46</code></pre>
-<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb30-1"><a href="1.4-the-current-population-survey-cps.html#cb30-1" tabindex="-1"></a>unzipped_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> <span class="fu">tempdir</span>())</span></code></pre></div>
+## &lt;ON DISK&gt;  C:\Users\AnthonyD\AppData\Local\Temp\RtmpKOLV87\file3350197b5f3f</code></pre>
+<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="1.4-the-current-population-survey-cps.html#cb29-1" tabindex="-1"></a>unzipped_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> <span class="fu">tempdir</span>())</span></code></pre></div>
 <p>Import all four files:</p>
-<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb31-1"><a href="1.4-the-current-population-survey-cps.html#cb31-1" tabindex="-1"></a><span class="fu">library</span>(haven)</span>
-<span id="cb31-2"><a href="1.4-the-current-population-survey-cps.html#cb31-2" tabindex="-1"></a></span>
-<span id="cb31-3"><a href="1.4-the-current-population-survey-cps.html#cb31-3" tabindex="-1"></a>four_tbl <span class="ot">&lt;-</span> <span class="fu">lapply</span>(unzipped_files , read_sas)</span>
-<span id="cb31-4"><a href="1.4-the-current-population-survey-cps.html#cb31-4" tabindex="-1"></a></span>
-<span id="cb31-5"><a href="1.4-the-current-population-survey-cps.html#cb31-5" tabindex="-1"></a>four_df <span class="ot">&lt;-</span> <span class="fu">lapply</span>(four_tbl , data.frame)</span>
-<span id="cb31-6"><a href="1.4-the-current-population-survey-cps.html#cb31-6" tabindex="-1"></a></span>
-<span id="cb31-7"><a href="1.4-the-current-population-survey-cps.html#cb31-7" tabindex="-1"></a>four_df <span class="ot">&lt;-</span></span>
-<span id="cb31-8"><a href="1.4-the-current-population-survey-cps.html#cb31-8" tabindex="-1"></a>  <span class="fu">lapply</span>(four_df , <span class="cf">function</span>(w) {</span>
-<span id="cb31-9"><a href="1.4-the-current-population-survey-cps.html#cb31-9" tabindex="-1"></a>    <span class="fu">names</span>(w) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(w))</span>
-<span id="cb31-10"><a href="1.4-the-current-population-survey-cps.html#cb31-10" tabindex="-1"></a>    w</span>
-<span id="cb31-11"><a href="1.4-the-current-population-survey-cps.html#cb31-11" tabindex="-1"></a>  })</span>
-<span id="cb31-12"><a href="1.4-the-current-population-survey-cps.html#cb31-12" tabindex="-1"></a></span>
-<span id="cb31-13"><a href="1.4-the-current-population-survey-cps.html#cb31-13" tabindex="-1"></a>household_df <span class="ot">&lt;-</span></span>
-<span id="cb31-14"><a href="1.4-the-current-population-survey-cps.html#cb31-14" tabindex="-1"></a>  four_df[[<span class="fu">grep</span>(<span class="st">&#39;hhpub&#39;</span> , <span class="fu">basename</span>(unzipped_files))]]</span>
-<span id="cb31-15"><a href="1.4-the-current-population-survey-cps.html#cb31-15" tabindex="-1"></a>family_df <span class="ot">&lt;-</span></span>
-<span id="cb31-16"><a href="1.4-the-current-population-survey-cps.html#cb31-16" tabindex="-1"></a>  four_df[[<span class="fu">grep</span>(<span class="st">&#39;ffpub&#39;</span> , <span class="fu">basename</span>(unzipped_files))]]</span>
-<span id="cb31-17"><a href="1.4-the-current-population-survey-cps.html#cb31-17" tabindex="-1"></a>person_df <span class="ot">&lt;-</span></span>
-<span id="cb31-18"><a href="1.4-the-current-population-survey-cps.html#cb31-18" tabindex="-1"></a>  four_df[[<span class="fu">grep</span>(<span class="st">&#39;pppub&#39;</span> , <span class="fu">basename</span>(unzipped_files))]]</span>
-<span id="cb31-19"><a href="1.4-the-current-population-survey-cps.html#cb31-19" tabindex="-1"></a>repwgts_df <span class="ot">&lt;-</span></span>
-<span id="cb31-20"><a href="1.4-the-current-population-survey-cps.html#cb31-20" tabindex="-1"></a>  four_df[[<span class="fu">grep</span>(<span class="st">&#39;repwgt&#39;</span> , <span class="fu">basename</span>(unzipped_files))]]</span></code></pre></div>
+<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb30-1"><a href="1.4-the-current-population-survey-cps.html#cb30-1" tabindex="-1"></a><span class="fu">library</span>(haven)</span>
+<span id="cb30-2"><a href="1.4-the-current-population-survey-cps.html#cb30-2" tabindex="-1"></a></span>
+<span id="cb30-3"><a href="1.4-the-current-population-survey-cps.html#cb30-3" tabindex="-1"></a>four_tbl <span class="ot">&lt;-</span> <span class="fu">lapply</span>(unzipped_files , read_sas)</span>
+<span id="cb30-4"><a href="1.4-the-current-population-survey-cps.html#cb30-4" tabindex="-1"></a></span>
+<span id="cb30-5"><a href="1.4-the-current-population-survey-cps.html#cb30-5" tabindex="-1"></a>four_df <span class="ot">&lt;-</span> <span class="fu">lapply</span>(four_tbl , data.frame)</span>
+<span id="cb30-6"><a href="1.4-the-current-population-survey-cps.html#cb30-6" tabindex="-1"></a></span>
+<span id="cb30-7"><a href="1.4-the-current-population-survey-cps.html#cb30-7" tabindex="-1"></a>four_df <span class="ot">&lt;-</span></span>
+<span id="cb30-8"><a href="1.4-the-current-population-survey-cps.html#cb30-8" tabindex="-1"></a>  <span class="fu">lapply</span>(four_df , <span class="cf">function</span>(w) {</span>
+<span id="cb30-9"><a href="1.4-the-current-population-survey-cps.html#cb30-9" tabindex="-1"></a>    <span class="fu">names</span>(w) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(w))</span>
+<span id="cb30-10"><a href="1.4-the-current-population-survey-cps.html#cb30-10" tabindex="-1"></a>    w</span>
+<span id="cb30-11"><a href="1.4-the-current-population-survey-cps.html#cb30-11" tabindex="-1"></a>  })</span>
+<span id="cb30-12"><a href="1.4-the-current-population-survey-cps.html#cb30-12" tabindex="-1"></a></span>
+<span id="cb30-13"><a href="1.4-the-current-population-survey-cps.html#cb30-13" tabindex="-1"></a>household_df <span class="ot">&lt;-</span></span>
+<span id="cb30-14"><a href="1.4-the-current-population-survey-cps.html#cb30-14" tabindex="-1"></a>  four_df[[<span class="fu">grep</span>(<span class="st">&#39;hhpub&#39;</span> , <span class="fu">basename</span>(unzipped_files))]]</span>
+<span id="cb30-15"><a href="1.4-the-current-population-survey-cps.html#cb30-15" tabindex="-1"></a>family_df <span class="ot">&lt;-</span></span>
+<span id="cb30-16"><a href="1.4-the-current-population-survey-cps.html#cb30-16" tabindex="-1"></a>  four_df[[<span class="fu">grep</span>(<span class="st">&#39;ffpub&#39;</span> , <span class="fu">basename</span>(unzipped_files))]]</span>
+<span id="cb30-17"><a href="1.4-the-current-population-survey-cps.html#cb30-17" tabindex="-1"></a>person_df <span class="ot">&lt;-</span></span>
+<span id="cb30-18"><a href="1.4-the-current-population-survey-cps.html#cb30-18" tabindex="-1"></a>  four_df[[<span class="fu">grep</span>(<span class="st">&#39;pppub&#39;</span> , <span class="fu">basename</span>(unzipped_files))]]</span>
+<span id="cb30-19"><a href="1.4-the-current-population-survey-cps.html#cb30-19" tabindex="-1"></a>repwgts_df <span class="ot">&lt;-</span></span>
+<span id="cb30-20"><a href="1.4-the-current-population-survey-cps.html#cb30-20" tabindex="-1"></a>  four_df[[<span class="fu">grep</span>(<span class="st">&#39;repwgt&#39;</span> , <span class="fu">basename</span>(unzipped_files))]]</span></code></pre></div>
 <p>Divide weights:</p>
-<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb32-1"><a href="1.4-the-current-population-survey-cps.html#cb32-1" tabindex="-1"></a>household_df[, <span class="st">&#39;hsup_wgt&#39;</span>] <span class="ot">&lt;-</span> household_df[, <span class="st">&#39;hsup_wgt&#39;</span>] <span class="sc">/</span> <span class="dv">100</span></span>
-<span id="cb32-2"><a href="1.4-the-current-population-survey-cps.html#cb32-2" tabindex="-1"></a>family_df[, <span class="st">&#39;fsup_wgt&#39;</span>] <span class="ot">&lt;-</span> family_df[, <span class="st">&#39;fsup_wgt&#39;</span>] <span class="sc">/</span> <span class="dv">100</span></span>
-<span id="cb32-3"><a href="1.4-the-current-population-survey-cps.html#cb32-3" tabindex="-1"></a><span class="cf">for</span> (j <span class="cf">in</span> <span class="fu">c</span>(<span class="st">&#39;marsupwt&#39;</span> , <span class="st">&#39;a_ernlwt&#39;</span> , <span class="st">&#39;a_fnlwgt&#39;</span>))</span>
-<span id="cb32-4"><a href="1.4-the-current-population-survey-cps.html#cb32-4" tabindex="-1"></a>  person_df[, j] <span class="ot">&lt;-</span> person_df[, j] <span class="sc">/</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb31-1"><a href="1.4-the-current-population-survey-cps.html#cb31-1" tabindex="-1"></a>household_df[, <span class="st">&#39;hsup_wgt&#39;</span>] <span class="ot">&lt;-</span> household_df[, <span class="st">&#39;hsup_wgt&#39;</span>] <span class="sc">/</span> <span class="dv">100</span></span>
+<span id="cb31-2"><a href="1.4-the-current-population-survey-cps.html#cb31-2" tabindex="-1"></a>family_df[, <span class="st">&#39;fsup_wgt&#39;</span>] <span class="ot">&lt;-</span> family_df[, <span class="st">&#39;fsup_wgt&#39;</span>] <span class="sc">/</span> <span class="dv">100</span></span>
+<span id="cb31-3"><a href="1.4-the-current-population-survey-cps.html#cb31-3" tabindex="-1"></a><span class="cf">for</span> (j <span class="cf">in</span> <span class="fu">c</span>(<span class="st">&#39;marsupwt&#39;</span> , <span class="st">&#39;a_ernlwt&#39;</span> , <span class="st">&#39;a_fnlwgt&#39;</span>))</span>
+<span id="cb31-4"><a href="1.4-the-current-population-survey-cps.html#cb31-4" tabindex="-1"></a>  person_df[, j] <span class="ot">&lt;-</span> person_df[, j] <span class="sc">/</span> <span class="dv">100</span></span></code></pre></div>
 <p>Merge these four files:</p>
-<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb33-1"><a href="1.4-the-current-population-survey-cps.html#cb33-1" tabindex="-1"></a><span class="fu">names</span>(family_df)[<span class="fu">names</span>(family_df) <span class="sc">==</span> <span class="st">&#39;fh_seq&#39;</span>] <span class="ot">&lt;-</span> <span class="st">&#39;h_seq&#39;</span></span>
-<span id="cb33-2"><a href="1.4-the-current-population-survey-cps.html#cb33-2" tabindex="-1"></a><span class="fu">names</span>(person_df)[<span class="fu">names</span>(person_df) <span class="sc">==</span> <span class="st">&#39;ph_seq&#39;</span>] <span class="ot">&lt;-</span> <span class="st">&#39;h_seq&#39;</span></span>
-<span id="cb33-3"><a href="1.4-the-current-population-survey-cps.html#cb33-3" tabindex="-1"></a><span class="fu">names</span>(person_df)[<span class="fu">names</span>(person_df) <span class="sc">==</span> <span class="st">&#39;phf_seq&#39;</span>] <span class="ot">&lt;-</span> <span class="st">&#39;ffpos&#39;</span></span>
-<span id="cb33-4"><a href="1.4-the-current-population-survey-cps.html#cb33-4" tabindex="-1"></a></span>
-<span id="cb33-5"><a href="1.4-the-current-population-survey-cps.html#cb33-5" tabindex="-1"></a>hh_fm_df <span class="ot">&lt;-</span> <span class="fu">merge</span>(household_df , family_df)</span>
-<span id="cb33-6"><a href="1.4-the-current-population-survey-cps.html#cb33-6" tabindex="-1"></a>hh_fm_pr_df <span class="ot">&lt;-</span> <span class="fu">merge</span>(hh_fm_df , person_df)</span>
-<span id="cb33-7"><a href="1.4-the-current-population-survey-cps.html#cb33-7" tabindex="-1"></a>cps_df <span class="ot">&lt;-</span> <span class="fu">merge</span>(hh_fm_pr_df , repwgts_df)</span>
-<span id="cb33-8"><a href="1.4-the-current-population-survey-cps.html#cb33-8" tabindex="-1"></a></span>
-<span id="cb33-9"><a href="1.4-the-current-population-survey-cps.html#cb33-9" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">nrow</span>(cps_df) <span class="sc">==</span> <span class="fu">nrow</span>(person_df))</span></code></pre></div>
+<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb32-1"><a href="1.4-the-current-population-survey-cps.html#cb32-1" tabindex="-1"></a><span class="fu">names</span>(family_df)[<span class="fu">names</span>(family_df) <span class="sc">==</span> <span class="st">&#39;fh_seq&#39;</span>] <span class="ot">&lt;-</span> <span class="st">&#39;h_seq&#39;</span></span>
+<span id="cb32-2"><a href="1.4-the-current-population-survey-cps.html#cb32-2" tabindex="-1"></a><span class="fu">names</span>(person_df)[<span class="fu">names</span>(person_df) <span class="sc">==</span> <span class="st">&#39;ph_seq&#39;</span>] <span class="ot">&lt;-</span> <span class="st">&#39;h_seq&#39;</span></span>
+<span id="cb32-3"><a href="1.4-the-current-population-survey-cps.html#cb32-3" tabindex="-1"></a><span class="fu">names</span>(person_df)[<span class="fu">names</span>(person_df) <span class="sc">==</span> <span class="st">&#39;phf_seq&#39;</span>] <span class="ot">&lt;-</span> <span class="st">&#39;ffpos&#39;</span></span>
+<span id="cb32-4"><a href="1.4-the-current-population-survey-cps.html#cb32-4" tabindex="-1"></a></span>
+<span id="cb32-5"><a href="1.4-the-current-population-survey-cps.html#cb32-5" tabindex="-1"></a>hh_fm_df <span class="ot">&lt;-</span> <span class="fu">merge</span>(household_df , family_df)</span>
+<span id="cb32-6"><a href="1.4-the-current-population-survey-cps.html#cb32-6" tabindex="-1"></a>hh_fm_pr_df <span class="ot">&lt;-</span> <span class="fu">merge</span>(hh_fm_df , person_df)</span>
+<span id="cb32-7"><a href="1.4-the-current-population-survey-cps.html#cb32-7" tabindex="-1"></a>cps_df <span class="ot">&lt;-</span> <span class="fu">merge</span>(hh_fm_pr_df , repwgts_df)</span>
+<span id="cb32-8"><a href="1.4-the-current-population-survey-cps.html#cb32-8" tabindex="-1"></a></span>
+<span id="cb32-9"><a href="1.4-the-current-population-survey-cps.html#cb32-9" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">nrow</span>(cps_df) <span class="sc">==</span> <span class="fu">nrow</span>(person_df))</span></code></pre></div>
 <p>Construct a complex sample survey design:</p>
-<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb34-1"><a href="1.4-the-current-population-survey-cps.html#cb34-1" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb34-2"><a href="1.4-the-current-population-survey-cps.html#cb34-2" tabindex="-1"></a></span>
-<span id="cb34-3"><a href="1.4-the-current-population-survey-cps.html#cb34-3" tabindex="-1"></a>cps_design <span class="ot">&lt;-</span></span>
-<span id="cb34-4"><a href="1.4-the-current-population-survey-cps.html#cb34-4" tabindex="-1"></a>  <span class="fu">svrepdesign</span>(</span>
-<span id="cb34-5"><a href="1.4-the-current-population-survey-cps.html#cb34-5" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> marsupwt ,</span>
-<span id="cb34-6"><a href="1.4-the-current-population-survey-cps.html#cb34-6" tabindex="-1"></a>    <span class="at">repweights =</span> <span class="st">&quot;pwwgt[1-9]&quot;</span> ,</span>
-<span id="cb34-7"><a href="1.4-the-current-population-survey-cps.html#cb34-7" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;Fay&quot;</span> ,</span>
-<span id="cb34-8"><a href="1.4-the-current-population-survey-cps.html#cb34-8" tabindex="-1"></a>    <span class="at">rho =</span> (<span class="dv">1</span> <span class="sc">-</span> <span class="dv">1</span> <span class="sc">/</span> <span class="fu">sqrt</span>(<span class="dv">4</span>)) ,</span>
-<span id="cb34-9"><a href="1.4-the-current-population-survey-cps.html#cb34-9" tabindex="-1"></a>    <span class="at">data =</span> cps_df ,</span>
-<span id="cb34-10"><a href="1.4-the-current-population-survey-cps.html#cb34-10" tabindex="-1"></a>    <span class="at">combined.weights =</span> <span class="cn">TRUE</span> ,</span>
-<span id="cb34-11"><a href="1.4-the-current-population-survey-cps.html#cb34-11" tabindex="-1"></a>    <span class="at">mse =</span> <span class="cn">TRUE</span></span>
-<span id="cb34-12"><a href="1.4-the-current-population-survey-cps.html#cb34-12" tabindex="-1"></a>  )</span></code></pre></div>
+<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb33-1"><a href="1.4-the-current-population-survey-cps.html#cb33-1" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb33-2"><a href="1.4-the-current-population-survey-cps.html#cb33-2" tabindex="-1"></a></span>
+<span id="cb33-3"><a href="1.4-the-current-population-survey-cps.html#cb33-3" tabindex="-1"></a>cps_design <span class="ot">&lt;-</span></span>
+<span id="cb33-4"><a href="1.4-the-current-population-survey-cps.html#cb33-4" tabindex="-1"></a>  <span class="fu">svrepdesign</span>(</span>
+<span id="cb33-5"><a href="1.4-the-current-population-survey-cps.html#cb33-5" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> marsupwt ,</span>
+<span id="cb33-6"><a href="1.4-the-current-population-survey-cps.html#cb33-6" tabindex="-1"></a>    <span class="at">repweights =</span> <span class="st">&quot;pwwgt[1-9]&quot;</span> ,</span>
+<span id="cb33-7"><a href="1.4-the-current-population-survey-cps.html#cb33-7" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;Fay&quot;</span> ,</span>
+<span id="cb33-8"><a href="1.4-the-current-population-survey-cps.html#cb33-8" tabindex="-1"></a>    <span class="at">rho =</span> (<span class="dv">1</span> <span class="sc">-</span> <span class="dv">1</span> <span class="sc">/</span> <span class="fu">sqrt</span>(<span class="dv">4</span>)) ,</span>
+<span id="cb33-9"><a href="1.4-the-current-population-survey-cps.html#cb33-9" tabindex="-1"></a>    <span class="at">data =</span> cps_df ,</span>
+<span id="cb33-10"><a href="1.4-the-current-population-survey-cps.html#cb33-10" tabindex="-1"></a>    <span class="at">combined.weights =</span> <span class="cn">TRUE</span> ,</span>
+<span id="cb33-11"><a href="1.4-the-current-population-survey-cps.html#cb33-11" tabindex="-1"></a>    <span class="at">mse =</span> <span class="cn">TRUE</span></span>
+<span id="cb33-12"><a href="1.4-the-current-population-survey-cps.html#cb33-12" tabindex="-1"></a>  )</span></code></pre></div>
 <p>Run the <code>convey_prep()</code> function on the full design:</p>
-<div class="sourceCode" id="cb35"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb35-1"><a href="1.4-the-current-population-survey-cps.html#cb35-1" tabindex="-1"></a>cps_design <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(cps_design)</span></code></pre></div>
+<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb34-1"><a href="1.4-the-current-population-survey-cps.html#cb34-1" tabindex="-1"></a>cps_design <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(cps_design)</span></code></pre></div>
 <div id="household-level-analysis-of-the-cps" class="section level3" number="1.4.1">
 <h3><span class="header-section-number">1.4.1</span> Household-level Analysis of the CPS</h3>
 <p>Limit the CPS person-level design to the household reference person, then calculate the gini coefficient with total household income:</p>
-<div class="sourceCode" id="cb36"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb36-1"><a href="1.4-the-current-population-survey-cps.html#cb36-1" tabindex="-1"></a>cps_household_design <span class="ot">&lt;-</span> <span class="fu">subset</span>(cps_design , a_exprrp <span class="sc">%in%</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">2</span>)</span>
-<span id="cb36-2"><a href="1.4-the-current-population-survey-cps.html#cb36-2" tabindex="-1"></a></span>
-<span id="cb36-3"><a href="1.4-the-current-population-survey-cps.html#cb36-3" tabindex="-1"></a>(cps_household_gini <span class="ot">&lt;-</span> <span class="fu">svygini</span>(<span class="sc">~</span> htotval , cps_household_design))</span></code></pre></div>
+<div class="sourceCode" id="cb35"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb35-1"><a href="1.4-the-current-population-survey-cps.html#cb35-1" tabindex="-1"></a>cps_household_design <span class="ot">&lt;-</span> <span class="fu">subset</span>(cps_design , a_exprrp <span class="sc">%in%</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">2</span>)</span>
+<span id="cb35-2"><a href="1.4-the-current-population-survey-cps.html#cb35-2" tabindex="-1"></a></span>
+<span id="cb35-3"><a href="1.4-the-current-population-survey-cps.html#cb35-3" tabindex="-1"></a>(cps_household_gini <span class="ot">&lt;-</span> <span class="fu">svygini</span>(<span class="sc">~</span> htotval , cps_household_design))</span></code></pre></div>
 <pre><code>##            gini    SE
 ## htotval 0.48846 0.002</code></pre>
-<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb38-1"><a href="1.4-the-current-population-survey-cps.html#cb38-1" tabindex="-1"></a><span class="co"># match 2022 household gini coefficient</span></span>
-<span id="cb38-2"><a href="1.4-the-current-population-survey-cps.html#cb38-2" tabindex="-1"></a><span class="co"># https://www2.census.gov/programs-surveys/cps/tables/time-series/historical-income-households/h04.xlsx</span></span>
-<span id="cb38-3"><a href="1.4-the-current-population-survey-cps.html#cb38-3" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(cps_household_gini) , <span class="dv">3</span>) <span class="sc">==</span> <span class="fl">0.488</span>)</span>
-<span id="cb38-4"><a href="1.4-the-current-population-survey-cps.html#cb38-4" tabindex="-1"></a></span>
-<span id="cb38-5"><a href="1.4-the-current-population-survey-cps.html#cb38-5" tabindex="-1"></a><span class="co"># match 2022 household gini margin of error</span></span>
-<span id="cb38-6"><a href="1.4-the-current-population-survey-cps.html#cb38-6" tabindex="-1"></a><span class="co"># https://www.census.gov/content/dam/Census/newsroom/press-kits/2023/iphi/20230912-iphi-slides-income.pdf#page=13</span></span>
-<span id="cb38-7"><a href="1.4-the-current-population-survey-cps.html#cb38-7" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
-<span id="cb38-8"><a href="1.4-the-current-population-survey-cps.html#cb38-8" tabindex="-1"></a>  <span class="fu">coef</span>(cps_household_gini) <span class="sc">-</span> <span class="fu">confint</span>(cps_household_gini , <span class="at">level =</span> <span class="fl">0.9</span>)[<span class="dv">1</span>] ,</span>
-<span id="cb38-9"><a href="1.4-the-current-population-survey-cps.html#cb38-9" tabindex="-1"></a>  <span class="dv">4</span></span>
-<span id="cb38-10"><a href="1.4-the-current-population-survey-cps.html#cb38-10" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.0033</span>) </span></code></pre></div>
+<div class="sourceCode" id="cb37"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb37-1"><a href="1.4-the-current-population-survey-cps.html#cb37-1" tabindex="-1"></a><span class="co"># match 2022 household gini coefficient</span></span>
+<span id="cb37-2"><a href="1.4-the-current-population-survey-cps.html#cb37-2" tabindex="-1"></a><span class="co"># https://www2.census.gov/programs-surveys/cps/tables/time-series/historical-income-households/h04.xlsx</span></span>
+<span id="cb37-3"><a href="1.4-the-current-population-survey-cps.html#cb37-3" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(cps_household_gini) , <span class="dv">3</span>) <span class="sc">==</span> <span class="fl">0.488</span>)</span>
+<span id="cb37-4"><a href="1.4-the-current-population-survey-cps.html#cb37-4" tabindex="-1"></a></span>
+<span id="cb37-5"><a href="1.4-the-current-population-survey-cps.html#cb37-5" tabindex="-1"></a><span class="co"># match 2022 household gini margin of error</span></span>
+<span id="cb37-6"><a href="1.4-the-current-population-survey-cps.html#cb37-6" tabindex="-1"></a><span class="co"># https://www.census.gov/content/dam/Census/newsroom/press-kits/2023/iphi/20230912-iphi-slides-income.pdf#page=13</span></span>
+<span id="cb37-7"><a href="1.4-the-current-population-survey-cps.html#cb37-7" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
+<span id="cb37-8"><a href="1.4-the-current-population-survey-cps.html#cb37-8" tabindex="-1"></a>  <span class="fu">coef</span>(cps_household_gini) <span class="sc">-</span> <span class="fu">confint</span>(cps_household_gini , <span class="at">level =</span> <span class="fl">0.9</span>)[<span class="dv">1</span>] ,</span>
+<span id="cb37-9"><a href="1.4-the-current-population-survey-cps.html#cb37-9" tabindex="-1"></a>  <span class="dv">4</span></span>
+<span id="cb37-10"><a href="1.4-the-current-population-survey-cps.html#cb37-10" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.0033</span>) </span></code></pre></div>
 </div>
 <div id="family-level-analysis-of-the-cps" class="section level3" number="1.4.2">
 <h3><span class="header-section-number">1.4.2</span> Family-level Analysis of the CPS</h3>
 <p>Limit the CPS person-level design to the family reference person of primary families, then calculate the gini coefficient with total family income:</p>
-<div class="sourceCode" id="cb39"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb39-1"><a href="1.4-the-current-population-survey-cps.html#cb39-1" tabindex="-1"></a>cps_family_design <span class="ot">&lt;-</span></span>
-<span id="cb39-2"><a href="1.4-the-current-population-survey-cps.html#cb39-2" tabindex="-1"></a>  <span class="fu">subset</span>(cps_design , a_famrel <span class="sc">%in%</span> <span class="dv">1</span> <span class="sc">&amp;</span> a_famtyp <span class="sc">%in%</span> <span class="dv">1</span>)</span>
-<span id="cb39-3"><a href="1.4-the-current-population-survey-cps.html#cb39-3" tabindex="-1"></a></span>
-<span id="cb39-4"><a href="1.4-the-current-population-survey-cps.html#cb39-4" tabindex="-1"></a>(cps_family_gini <span class="ot">&lt;-</span> <span class="fu">svygini</span>(<span class="sc">~</span> ftotval , cps_family_design))</span></code></pre></div>
+<div class="sourceCode" id="cb38"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb38-1"><a href="1.4-the-current-population-survey-cps.html#cb38-1" tabindex="-1"></a>cps_family_design <span class="ot">&lt;-</span></span>
+<span id="cb38-2"><a href="1.4-the-current-population-survey-cps.html#cb38-2" tabindex="-1"></a>  <span class="fu">subset</span>(cps_design , a_famrel <span class="sc">%in%</span> <span class="dv">1</span> <span class="sc">&amp;</span> a_famtyp <span class="sc">%in%</span> <span class="dv">1</span>)</span>
+<span id="cb38-3"><a href="1.4-the-current-population-survey-cps.html#cb38-3" tabindex="-1"></a></span>
+<span id="cb38-4"><a href="1.4-the-current-population-survey-cps.html#cb38-4" tabindex="-1"></a>(cps_family_gini <span class="ot">&lt;-</span> <span class="fu">svygini</span>(<span class="sc">~</span> ftotval , cps_family_design))</span></code></pre></div>
 <pre><code>##            gini     SE
 ## ftotval 0.45816 0.0023</code></pre>
-<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb41-1"><a href="1.4-the-current-population-survey-cps.html#cb41-1" tabindex="-1"></a><span class="co"># match 2022 family gini coefficient</span></span>
-<span id="cb41-2"><a href="1.4-the-current-population-survey-cps.html#cb41-2" tabindex="-1"></a><span class="co"># https://www2.census.gov/programs-surveys/cps/tables/time-series/historical-income-families/f04.xlsx</span></span>
-<span id="cb41-3"><a href="1.4-the-current-population-survey-cps.html#cb41-3" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(cps_family_gini) , <span class="dv">3</span>) <span class="sc">==</span> <span class="fl">0.458</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb40"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb40-1"><a href="1.4-the-current-population-survey-cps.html#cb40-1" tabindex="-1"></a><span class="co"># match 2022 family gini coefficient</span></span>
+<span id="cb40-2"><a href="1.4-the-current-population-survey-cps.html#cb40-2" tabindex="-1"></a><span class="co"># https://www2.census.gov/programs-surveys/cps/tables/time-series/historical-income-families/f04.xlsx</span></span>
+<span id="cb40-3"><a href="1.4-the-current-population-survey-cps.html#cb40-3" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(cps_family_gini) , <span class="dv">3</span>) <span class="sc">==</span> <span class="fl">0.458</span>)</span></code></pre></div>
 </div>
 <div id="full-time-full-year-worker-analysis-of-the-cps" class="section level3" number="1.4.3">
 <h3><span class="header-section-number">1.4.3</span> Full-time Full Year Worker Analysis of the CPS</h3>
 <p>Limit the CPS person-level design to full-time, full year workers, then calculate the gini coefficient with both total personal income and then total earnings:</p>
-<div class="sourceCode" id="cb42"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb42-1"><a href="1.4-the-current-population-survey-cps.html#cb42-1" tabindex="-1"></a>cps_ftfy_worker_design <span class="ot">&lt;-</span> <span class="fu">subset</span>(cps_design , wewkrs <span class="sc">%in%</span> <span class="dv">1</span>)</span>
-<span id="cb42-2"><a href="1.4-the-current-population-survey-cps.html#cb42-2" tabindex="-1"></a></span>
-<span id="cb42-3"><a href="1.4-the-current-population-survey-cps.html#cb42-3" tabindex="-1"></a><span class="fu">svygini</span>(<span class="sc">~</span> ptotval , cps_ftfy_worker_design)</span></code></pre></div>
+<div class="sourceCode" id="cb41"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb41-1"><a href="1.4-the-current-population-survey-cps.html#cb41-1" tabindex="-1"></a>cps_ftfy_worker_design <span class="ot">&lt;-</span> <span class="fu">subset</span>(cps_design , wewkrs <span class="sc">%in%</span> <span class="dv">1</span>)</span>
+<span id="cb41-2"><a href="1.4-the-current-population-survey-cps.html#cb41-2" tabindex="-1"></a></span>
+<span id="cb41-3"><a href="1.4-the-current-population-survey-cps.html#cb41-3" tabindex="-1"></a><span class="fu">svygini</span>(<span class="sc">~</span> ptotval , cps_ftfy_worker_design)</span></code></pre></div>
 <pre><code>##            gini     SE
 ## ptotval 0.41809 0.0025</code></pre>
-<div class="sourceCode" id="cb44"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb44-1"><a href="1.4-the-current-population-survey-cps.html#cb44-1" tabindex="-1"></a><span class="fu">svygini</span>(<span class="sc">~</span> pearnval , cps_ftfy_worker_design)</span></code></pre></div>
+<div class="sourceCode" id="cb43"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb43-1"><a href="1.4-the-current-population-survey-cps.html#cb43-1" tabindex="-1"></a><span class="fu">svygini</span>(<span class="sc">~</span> pearnval , cps_ftfy_worker_design)</span></code></pre></div>
 <pre><code>##           gini     SE
 ## pearnval 0.412 0.0026</code></pre>
 
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 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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+<meta name="date" content="2023-11-07" />
 
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@@ -258,34 +258,34 @@ <h2><span class="header-section-number">2.2</span> Replication-Based Variance Es
 <p>The function <code>bootVar</code> from the <code>laeken</code> library <span class="citation">(<label for="tufte-mn-12" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-12" class="margin-toggle">Alfons and Templ 2013<span class="marginnote">Alfons, Andreas, and Matthias Templ. 2013. <span>“Estimation of Social Exclusion Indicators from Complex Surveys: The <span>R</span> Package <span class="nocase">laeken</span>.”</span> <em>Journal of Statistical Software</em> 54 (15): 1–25. <a href="http://www.jstatsoft.org/v54/i15/">http://www.jstatsoft.org/v54/i15/</a>.</span>)</span>, also uses the bootstrap method to estimate variances.</p>
 <div id="replication-design-example" class="section level3" number="2.2.1">
 <h3><span class="header-section-number">2.2.1</span> Replication Design Example</h3>
-<div class="sourceCode" id="cb46"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb46-1"><a href="2.2-replication-based-variance-estimation.html#cb46-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
-<span id="cb46-2"><a href="2.2-replication-based-variance-estimation.html#cb46-2" tabindex="-1"></a><span class="fu">library</span>( survey )</span>
-<span id="cb46-3"><a href="2.2-replication-based-variance-estimation.html#cb46-3" tabindex="-1"></a><span class="fu">library</span>( convey )</span>
-<span id="cb46-4"><a href="2.2-replication-based-variance-estimation.html#cb46-4" tabindex="-1"></a><span class="fu">library</span>( laeken ) <span class="co"># for the dataset</span></span>
-<span id="cb46-5"><a href="2.2-replication-based-variance-estimation.html#cb46-5" tabindex="-1"></a></span>
-<span id="cb46-6"><a href="2.2-replication-based-variance-estimation.html#cb46-6" tabindex="-1"></a><span class="co"># get laeken eusilc data</span></span>
-<span id="cb46-7"><a href="2.2-replication-based-variance-estimation.html#cb46-7" tabindex="-1"></a><span class="fu">data</span>( eusilc ) ; <span class="fu">names</span>( eusilc ) <span class="ot">&lt;-</span> <span class="fu">tolower</span>( <span class="fu">names</span>( eusilc ) )</span>
-<span id="cb46-8"><a href="2.2-replication-based-variance-estimation.html#cb46-8" tabindex="-1"></a></span>
-<span id="cb46-9"><a href="2.2-replication-based-variance-estimation.html#cb46-9" tabindex="-1"></a><span class="co"># survey design object for TSL/ifluence function variance estimation</span></span>
-<span id="cb46-10"><a href="2.2-replication-based-variance-estimation.html#cb46-10" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="at">ids =</span> <span class="sc">~</span>rb030 , <span class="at">strata =</span> <span class="sc">~</span>db040 ,  <span class="at">weights =</span> <span class="sc">~</span>rb050 , <span class="at">data =</span> eusilc )</span>
-<span id="cb46-11"><a href="2.2-replication-based-variance-estimation.html#cb46-11" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>( des_eusilc )</span>
-<span id="cb46-12"><a href="2.2-replication-based-variance-estimation.html#cb46-12" tabindex="-1"></a></span>
-<span id="cb46-13"><a href="2.2-replication-based-variance-estimation.html#cb46-13" tabindex="-1"></a><span class="co"># influence function SE estimate for the gini index</span></span>
-<span id="cb46-14"><a href="2.2-replication-based-variance-estimation.html#cb46-14" tabindex="-1"></a>convey<span class="sc">:::</span><span class="fu">svygini.survey.design</span>( <span class="sc">~</span>eqincome , <span class="at">design =</span> des_eusilc )</span></code></pre></div>
+<div class="sourceCode" id="cb45"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb45-1"><a href="2.2-replication-based-variance-estimation.html#cb45-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
+<span id="cb45-2"><a href="2.2-replication-based-variance-estimation.html#cb45-2" tabindex="-1"></a><span class="fu">library</span>( survey )</span>
+<span id="cb45-3"><a href="2.2-replication-based-variance-estimation.html#cb45-3" tabindex="-1"></a><span class="fu">library</span>( convey )</span>
+<span id="cb45-4"><a href="2.2-replication-based-variance-estimation.html#cb45-4" tabindex="-1"></a><span class="fu">library</span>( laeken ) <span class="co"># for the dataset</span></span>
+<span id="cb45-5"><a href="2.2-replication-based-variance-estimation.html#cb45-5" tabindex="-1"></a></span>
+<span id="cb45-6"><a href="2.2-replication-based-variance-estimation.html#cb45-6" tabindex="-1"></a><span class="co"># get laeken eusilc data</span></span>
+<span id="cb45-7"><a href="2.2-replication-based-variance-estimation.html#cb45-7" tabindex="-1"></a><span class="fu">data</span>( eusilc ) ; <span class="fu">names</span>( eusilc ) <span class="ot">&lt;-</span> <span class="fu">tolower</span>( <span class="fu">names</span>( eusilc ) )</span>
+<span id="cb45-8"><a href="2.2-replication-based-variance-estimation.html#cb45-8" tabindex="-1"></a></span>
+<span id="cb45-9"><a href="2.2-replication-based-variance-estimation.html#cb45-9" tabindex="-1"></a><span class="co"># survey design object for TSL/ifluence function variance estimation</span></span>
+<span id="cb45-10"><a href="2.2-replication-based-variance-estimation.html#cb45-10" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="at">ids =</span> <span class="sc">~</span>rb030 , <span class="at">strata =</span> <span class="sc">~</span>db040 ,  <span class="at">weights =</span> <span class="sc">~</span>rb050 , <span class="at">data =</span> eusilc )</span>
+<span id="cb45-11"><a href="2.2-replication-based-variance-estimation.html#cb45-11" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>( des_eusilc )</span>
+<span id="cb45-12"><a href="2.2-replication-based-variance-estimation.html#cb45-12" tabindex="-1"></a></span>
+<span id="cb45-13"><a href="2.2-replication-based-variance-estimation.html#cb45-13" tabindex="-1"></a><span class="co"># influence function SE estimate for the gini index</span></span>
+<span id="cb45-14"><a href="2.2-replication-based-variance-estimation.html#cb45-14" tabindex="-1"></a>convey<span class="sc">:::</span><span class="fu">svygini.survey.design</span>( <span class="sc">~</span>eqincome , <span class="at">design =</span> des_eusilc )</span></code></pre></div>
 <pre><code>##             gini     SE
 ## eqincome 0.26497 0.0019</code></pre>
-<div class="sourceCode" id="cb48"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb48-1"><a href="2.2-replication-based-variance-estimation.html#cb48-1" tabindex="-1"></a><span class="co"># create survey design object for replicate-based variance estimation</span></span>
-<span id="cb48-2"><a href="2.2-replication-based-variance-estimation.html#cb48-2" tabindex="-1"></a>des_eusilc_rep <span class="ot">&lt;-</span> <span class="fu">as.svrepdesign</span>( des_eusilc , <span class="at">type =</span> <span class="st">&quot;bootstrap&quot;</span> )</span>
-<span id="cb48-3"><a href="2.2-replication-based-variance-estimation.html#cb48-3" tabindex="-1"></a>des_eusilc_rep <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>( des_eusilc_rep )</span>
-<span id="cb48-4"><a href="2.2-replication-based-variance-estimation.html#cb48-4" tabindex="-1"></a></span>
-<span id="cb48-5"><a href="2.2-replication-based-variance-estimation.html#cb48-5" tabindex="-1"></a><span class="co"># replicate-based (bootstrao) SE estimate for the gini index</span></span>
-<span id="cb48-6"><a href="2.2-replication-based-variance-estimation.html#cb48-6" tabindex="-1"></a><span class="co"># with option to keep replicates</span></span>
-<span id="cb48-7"><a href="2.2-replication-based-variance-estimation.html#cb48-7" tabindex="-1"></a>( gini.repstat <span class="ot">&lt;-</span> convey<span class="sc">:::</span><span class="fu">svygini.svyrep.design</span>( <span class="sc">~</span>eqincome , <span class="at">design =</span> des_eusilc_rep , <span class="at">return.replicates =</span> <span class="cn">TRUE</span> ) )</span></code></pre></div>
+<div class="sourceCode" id="cb47"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb47-1"><a href="2.2-replication-based-variance-estimation.html#cb47-1" tabindex="-1"></a><span class="co"># create survey design object for replicate-based variance estimation</span></span>
+<span id="cb47-2"><a href="2.2-replication-based-variance-estimation.html#cb47-2" tabindex="-1"></a>des_eusilc_rep <span class="ot">&lt;-</span> <span class="fu">as.svrepdesign</span>( des_eusilc , <span class="at">type =</span> <span class="st">&quot;bootstrap&quot;</span> )</span>
+<span id="cb47-3"><a href="2.2-replication-based-variance-estimation.html#cb47-3" tabindex="-1"></a>des_eusilc_rep <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>( des_eusilc_rep )</span>
+<span id="cb47-4"><a href="2.2-replication-based-variance-estimation.html#cb47-4" tabindex="-1"></a></span>
+<span id="cb47-5"><a href="2.2-replication-based-variance-estimation.html#cb47-5" tabindex="-1"></a><span class="co"># replicate-based (bootstrao) SE estimate for the gini index</span></span>
+<span id="cb47-6"><a href="2.2-replication-based-variance-estimation.html#cb47-6" tabindex="-1"></a><span class="co"># with option to keep replicates</span></span>
+<span id="cb47-7"><a href="2.2-replication-based-variance-estimation.html#cb47-7" tabindex="-1"></a>( gini.repstat <span class="ot">&lt;-</span> convey<span class="sc">:::</span><span class="fu">svygini.svyrep.design</span>( <span class="sc">~</span>eqincome , <span class="at">design =</span> des_eusilc_rep , <span class="at">return.replicates =</span> <span class="cn">TRUE</span> ) )</span></code></pre></div>
 <pre><code>##             gini     SE
 ## eqincome 0.26497 0.0022</code></pre>
 <p>To understand how that variance is estimated, we can look at the replicates:</p>
-<div class="sourceCode" id="cb50"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb50-1"><a href="2.2-replication-based-variance-estimation.html#cb50-1" tabindex="-1"></a><span class="co"># collect gini bootstrap replicates</span></span>
-<span id="cb50-2"><a href="2.2-replication-based-variance-estimation.html#cb50-2" tabindex="-1"></a>( gini.reps <span class="ot">&lt;-</span> gini.repstat<span class="sc">$</span>replicates )</span></code></pre></div>
+<div class="sourceCode" id="cb49"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb49-1"><a href="2.2-replication-based-variance-estimation.html#cb49-1" tabindex="-1"></a><span class="co"># collect gini bootstrap replicates</span></span>
+<span id="cb49-2"><a href="2.2-replication-based-variance-estimation.html#cb49-2" tabindex="-1"></a>( gini.reps <span class="ot">&lt;-</span> gini.repstat<span class="sc">$</span>replicates )</span></code></pre></div>
 <pre><code>##  [1] 0.2628816 0.2653672 0.2663951 0.2646311 0.2660021 0.2648396 0.2633737
 ##  [8] 0.2611656 0.2613233 0.2647174 0.2638256 0.2621616 0.2646830 0.2587950
 ## [15] 0.2642947 0.2651559 0.2663231 0.2673018 0.2687169 0.2671058 0.2654078
@@ -302,16 +302,16 @@ <h3><span class="header-section-number">2.2.1</span> Replication Design Example<
 ## attr(,&quot;mse&quot;)
 ## [1] FALSE</code></pre>
 <p>These are resampling (bootstrap) replicates. With them, we can look at the variance of these replicates to get an estimate the gini estimator’s variance:</p>
-<div class="sourceCode" id="cb52"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb52-1"><a href="2.2-replication-based-variance-estimation.html#cb52-1" tabindex="-1"></a><span class="co"># variance estimate</span></span>
-<span id="cb52-2"><a href="2.2-replication-based-variance-estimation.html#cb52-2" tabindex="-1"></a>des.scale <span class="ot">&lt;-</span> des_eusilc_rep<span class="sc">$</span>scale</span>
-<span id="cb52-3"><a href="2.2-replication-based-variance-estimation.html#cb52-3" tabindex="-1"></a>meantheta <span class="ot">&lt;-</span> <span class="fu">mean</span>( gini.reps )[[<span class="dv">1</span>]]</span>
-<span id="cb52-4"><a href="2.2-replication-based-variance-estimation.html#cb52-4" tabindex="-1"></a>v <span class="ot">&lt;-</span> <span class="fu">sum</span>( ( gini.reps <span class="sc">-</span> meantheta )<span class="sc">^</span><span class="dv">2</span> ) <span class="sc">*</span> des.scale</span>
-<span id="cb52-5"><a href="2.2-replication-based-variance-estimation.html#cb52-5" tabindex="-1"></a></span>
-<span id="cb52-6"><a href="2.2-replication-based-variance-estimation.html#cb52-6" tabindex="-1"></a><span class="co"># SE estimate</span></span>
-<span id="cb52-7"><a href="2.2-replication-based-variance-estimation.html#cb52-7" tabindex="-1"></a>( gini.se <span class="ot">&lt;-</span> ( <span class="fu">sqrt</span>( v ) ) )</span></code></pre></div>
+<div class="sourceCode" id="cb51"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb51-1"><a href="2.2-replication-based-variance-estimation.html#cb51-1" tabindex="-1"></a><span class="co"># variance estimate</span></span>
+<span id="cb51-2"><a href="2.2-replication-based-variance-estimation.html#cb51-2" tabindex="-1"></a>des.scale <span class="ot">&lt;-</span> des_eusilc_rep<span class="sc">$</span>scale</span>
+<span id="cb51-3"><a href="2.2-replication-based-variance-estimation.html#cb51-3" tabindex="-1"></a>meantheta <span class="ot">&lt;-</span> <span class="fu">mean</span>( gini.reps )[[<span class="dv">1</span>]]</span>
+<span id="cb51-4"><a href="2.2-replication-based-variance-estimation.html#cb51-4" tabindex="-1"></a>v <span class="ot">&lt;-</span> <span class="fu">sum</span>( ( gini.reps <span class="sc">-</span> meantheta )<span class="sc">^</span><span class="dv">2</span> ) <span class="sc">*</span> des.scale</span>
+<span id="cb51-5"><a href="2.2-replication-based-variance-estimation.html#cb51-5" tabindex="-1"></a></span>
+<span id="cb51-6"><a href="2.2-replication-based-variance-estimation.html#cb51-6" tabindex="-1"></a><span class="co"># SE estimate</span></span>
+<span id="cb51-7"><a href="2.2-replication-based-variance-estimation.html#cb51-7" tabindex="-1"></a>( gini.se <span class="ot">&lt;-</span> ( <span class="fu">sqrt</span>( v ) ) )</span></code></pre></div>
 <pre><code>## [1] 0.002226009</code></pre>
-<div class="sourceCode" id="cb54"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb54-1"><a href="2.2-replication-based-variance-estimation.html#cb54-1" tabindex="-1"></a><span class="co"># compare estimates</span></span>
-<span id="cb54-2"><a href="2.2-replication-based-variance-estimation.html#cb54-2" tabindex="-1"></a><span class="fu">identical</span>( gini.se , <span class="fu">SE</span>( gini.repstat )[[<span class="dv">1</span>]] )</span></code></pre></div>
+<div class="sourceCode" id="cb53"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb53-1"><a href="2.2-replication-based-variance-estimation.html#cb53-1" tabindex="-1"></a><span class="co"># compare estimates</span></span>
+<span id="cb53-2"><a href="2.2-replication-based-variance-estimation.html#cb53-2" tabindex="-1"></a><span class="fu">identical</span>( gini.se , <span class="fu">SE</span>( gini.repstat )[[<span class="dv">1</span>]] )</span></code></pre></div>
 <pre><code>## [1] TRUE</code></pre>
 </div>
 </div>
diff --git a/docs/2.3-variance-estimation-for-decompositions.html b/docs/2.3-variance-estimation-for-decompositions.html
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 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
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+++ b/docs/3.1-at-risk-of-poverty-threshold-svyarpt.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
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@@ -253,13 +253,13 @@
 <div class="col-sm-12">
 <div id="at-risk-of-poverty-threshold-svyarpt" class="section level2" number="3.1">
 <h2><span class="header-section-number">3.1</span> At Risk of Poverty Threshold (svyarpt)</h2>
-<div class="sourceCode" id="cb56"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb56-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-1" tabindex="-1"></a>✔️ commonly used by statistical agencies <span class="cf">in</span> the european union working group on statistics on income <span class="sc">&amp;</span> living <span class="fu">conditions</span> (eurostat)</span>
-<span id="cb56-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-2" tabindex="-1"></a>✔️ not tied to the inflation rate nor to a basket of goods or consumable products</span>
-<span id="cb56-3"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-3" tabindex="-1"></a>✔️ generic calculation that can be broadly applied to different nations or regions</span>
-<span id="cb56-4"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-4" tabindex="-1"></a>✔️ easy to understand<span class="sc">:</span> defaults to <span class="dv">60</span>% of median income</span>
-<span id="cb56-5"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-5" tabindex="-1"></a>❌ the <span class="dv">60</span>% of median income used <span class="cf">in</span> ARPT might appear arbitrary <span class="cf">for</span> non<span class="sc">-</span>EU analyses</span>
-<span id="cb56-6"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-6" tabindex="-1"></a>❌ does not account <span class="cf">for</span> the intensity<span class="sc">/</span>severity of poverty</span>
-<span id="cb56-7"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-7" tabindex="-1"></a>❌ not really a poverty measure, but an estimated poverty threshold<span class="sc">/</span>poverty line</span></code></pre></div>
+<div class="sourceCode" id="cb55"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb55-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb55-1" tabindex="-1"></a>✔️ commonly used by statistical agencies <span class="cf">in</span> the european union working group on statistics on income <span class="sc">&amp;</span> living <span class="fu">conditions</span> (eurostat)</span>
+<span id="cb55-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb55-2" tabindex="-1"></a>✔️ not tied to the inflation rate nor to a basket of goods or consumable products</span>
+<span id="cb55-3"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb55-3" tabindex="-1"></a>✔️ generic calculation that can be broadly applied to different nations or regions</span>
+<span id="cb55-4"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb55-4" tabindex="-1"></a>✔️ easy to understand<span class="sc">:</span> defaults to <span class="dv">60</span>% of median income</span>
+<span id="cb55-5"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb55-5" tabindex="-1"></a>❌ the <span class="dv">60</span>% of median income used <span class="cf">in</span> ARPT might appear arbitrary <span class="cf">for</span> non<span class="sc">-</span>EU analyses</span>
+<span id="cb55-6"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb55-6" tabindex="-1"></a>❌ does not account <span class="cf">for</span> the intensity<span class="sc">/</span>severity of poverty</span>
+<span id="cb55-7"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb55-7" tabindex="-1"></a>❌ not really a poverty measure, but an estimated poverty threshold<span class="sc">/</span>poverty line</span></code></pre></div>
 <p>The at-risk-of-poverty threshold (ARPT) is a measure used to define the people whose incomes imply a low standard of living in comparison to the general living standards. Even though some people are not below the effective poverty line, those below the ARPT can be considered “almost deprived”.</p>
 <p>This measure is defined as <span class="math inline">\(0.6\)</span> times the median income for the entire population:</p>
 <p><span class="math display">\[
@@ -271,142 +271,142 @@ <h2><span class="header-section-number">3.1</span> At Risk of Poverty Threshold
 <h3><span class="header-section-number">3.1.1</span> Replication Example</h3>
 <p>The R <code>vardpoor</code> package <span class="citation">(<label for="tufte-mn-25" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-25" class="margin-toggle">Breidaks, Liberts, and Ivanova 2016<span class="marginnote">Breidaks, Juris, Martins Liberts, and Santa Ivanova. 2016. <span>“Vardpoor: Estimation of Indicators on Social Exclusion and Poverty and Its Linearization, Variance Estimation.”</span> Riga, Latvia: CSB.</span>)</span>, created by researchers at the Central Statistical Bureau of Latvia, includes an ARPT coefficient calculation using the ultimate cluster method. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb57"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb57-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb57-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb57-3"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-3" tabindex="-1"></a></span>
-<span id="cb57-4"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb57-5"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb57-6"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-6" tabindex="-1"></a></span>
-<span id="cb57-7"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb57-8"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
-<span id="cb57-9"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-9" tabindex="-1"></a></span>
-<span id="cb57-10"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-10" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
-<span id="cb57-11"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
-<span id="cb57-12"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-12" tabindex="-1"></a></span>
-<span id="cb57-13"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
-<span id="cb57-14"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
-<span id="cb57-15"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-15" tabindex="-1"></a></span>
-<span id="cb57-16"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
-<span id="cb57-17"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
-<span id="cb57-18"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-18" tabindex="-1"></a></span>
-<span id="cb57-19"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
-<span id="cb57-20"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
-<span id="cb57-21"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-21" tabindex="-1"></a></span>
-<span id="cb57-22"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-22" tabindex="-1"></a><span class="co"># calculate the arpt coefficient</span></span>
-<span id="cb57-23"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
-<span id="cb57-24"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-24" tabindex="-1"></a>varpoord_arpt_calculation <span class="ot">&lt;-</span></span>
-<span id="cb57-25"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
-<span id="cb57-26"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
-<span id="cb57-27"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
-<span id="cb57-28"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-28" tabindex="-1"></a>    </span>
-<span id="cb57-29"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
-<span id="cb57-30"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
-<span id="cb57-31"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-31" tabindex="-1"></a>    </span>
-<span id="cb57-32"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb57-33"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb57-34"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-34" tabindex="-1"></a>    </span>
-<span id="cb57-35"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb57-36"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb57-37"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-37" tabindex="-1"></a>    </span>
-<span id="cb57-38"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
-<span id="cb57-39"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
-<span id="cb57-40"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-40" tabindex="-1"></a>    </span>
-<span id="cb57-41"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
-<span id="cb57-42"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-42" tabindex="-1"></a>    </span>
-<span id="cb57-43"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
-<span id="cb57-44"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
-<span id="cb57-45"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-45" tabindex="-1"></a>    </span>
-<span id="cb57-46"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
-<span id="cb57-47"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
-<span id="cb57-48"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-48" tabindex="-1"></a>    </span>
-<span id="cb57-49"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-49" tabindex="-1"></a>    <span class="co"># arpt coefficient function</span></span>
-<span id="cb57-50"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linarpt&quot;</span>,</span>
-<span id="cb57-51"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-51" tabindex="-1"></a>    </span>
-<span id="cb57-52"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
-<span id="cb57-53"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
-<span id="cb57-54"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-54" tabindex="-1"></a>  )</span>
-<span id="cb57-55"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-55" tabindex="-1"></a></span>
-<span id="cb57-56"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-56" tabindex="-1"></a></span>
-<span id="cb57-57"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-57" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb57-58"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-58" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
-<span id="cb57-59"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-59" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
-<span id="cb57-60"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-60" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb57-61"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-61" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb57-62"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-62" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb57-63"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-63" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb57-64"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-64" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
-<span id="cb57-65"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-65" tabindex="-1"></a>  )</span>
-<span id="cb57-66"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-66" tabindex="-1"></a></span>
-<span id="cb57-67"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-67" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
-<span id="cb57-68"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-68" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
-<span id="cb57-69"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-69" tabindex="-1"></a></span>
-<span id="cb57-70"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-70" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
-<span id="cb57-71"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb57-71" tabindex="-1"></a>varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
+<div class="sourceCode" id="cb56"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb56-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb56-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb56-3"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-3" tabindex="-1"></a></span>
+<span id="cb56-4"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb56-5"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb56-6"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-6" tabindex="-1"></a></span>
+<span id="cb56-7"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb56-8"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
+<span id="cb56-9"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-9" tabindex="-1"></a></span>
+<span id="cb56-10"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-10" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
+<span id="cb56-11"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
+<span id="cb56-12"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-12" tabindex="-1"></a></span>
+<span id="cb56-13"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
+<span id="cb56-14"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
+<span id="cb56-15"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-15" tabindex="-1"></a></span>
+<span id="cb56-16"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
+<span id="cb56-17"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
+<span id="cb56-18"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-18" tabindex="-1"></a></span>
+<span id="cb56-19"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
+<span id="cb56-20"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
+<span id="cb56-21"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-21" tabindex="-1"></a></span>
+<span id="cb56-22"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-22" tabindex="-1"></a><span class="co"># calculate the arpt coefficient</span></span>
+<span id="cb56-23"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
+<span id="cb56-24"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-24" tabindex="-1"></a>varpoord_arpt_calculation <span class="ot">&lt;-</span></span>
+<span id="cb56-25"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
+<span id="cb56-26"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
+<span id="cb56-27"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
+<span id="cb56-28"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-28" tabindex="-1"></a>    </span>
+<span id="cb56-29"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
+<span id="cb56-30"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
+<span id="cb56-31"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-31" tabindex="-1"></a>    </span>
+<span id="cb56-32"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb56-33"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb56-34"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-34" tabindex="-1"></a>    </span>
+<span id="cb56-35"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb56-36"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb56-37"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-37" tabindex="-1"></a>    </span>
+<span id="cb56-38"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
+<span id="cb56-39"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
+<span id="cb56-40"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-40" tabindex="-1"></a>    </span>
+<span id="cb56-41"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
+<span id="cb56-42"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-42" tabindex="-1"></a>    </span>
+<span id="cb56-43"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
+<span id="cb56-44"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
+<span id="cb56-45"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-45" tabindex="-1"></a>    </span>
+<span id="cb56-46"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
+<span id="cb56-47"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
+<span id="cb56-48"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-48" tabindex="-1"></a>    </span>
+<span id="cb56-49"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-49" tabindex="-1"></a>    <span class="co"># arpt coefficient function</span></span>
+<span id="cb56-50"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linarpt&quot;</span>,</span>
+<span id="cb56-51"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-51" tabindex="-1"></a>    </span>
+<span id="cb56-52"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
+<span id="cb56-53"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
+<span id="cb56-54"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-54" tabindex="-1"></a>  )</span>
+<span id="cb56-55"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-55" tabindex="-1"></a></span>
+<span id="cb56-56"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-56" tabindex="-1"></a></span>
+<span id="cb56-57"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-57" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb56-58"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-58" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
+<span id="cb56-59"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-59" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
+<span id="cb56-60"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-60" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb56-61"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-61" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb56-62"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-62" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb56-63"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-63" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb56-64"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-64" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
+<span id="cb56-65"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-65" tabindex="-1"></a>  )</span>
+<span id="cb56-66"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-66" tabindex="-1"></a></span>
+<span id="cb56-67"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-67" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
+<span id="cb56-68"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-68" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
+<span id="cb56-69"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-69" tabindex="-1"></a></span>
+<span id="cb56-70"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-70" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
+<span id="cb56-71"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb56-71" tabindex="-1"></a>varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
 <pre><code>## [1] 10859.24</code></pre>
-<div class="sourceCode" id="cb59"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb59-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb59-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
+<div class="sourceCode" id="cb58"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb58-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb58-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
 <pre><code>## eqincome 
 ## 10859.24</code></pre>
-<div class="sourceCode" id="cb61"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb61-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb61-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
-<span id="cb61-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb61-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
-<span id="cb61-3"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb61-3" tabindex="-1"></a>lin_arpt_varpoord <span class="ot">&lt;-</span> varpoord_arpt_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_arpt</span>
-<span id="cb61-4"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb61-4" tabindex="-1"></a><span class="co"># convey</span></span>
-<span id="cb61-5"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb61-5" tabindex="-1"></a>lin_arpt_convey <span class="ot">&lt;-</span> <span class="fu">attr</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc), <span class="st">&quot;lin&quot;</span>)</span>
-<span id="cb61-6"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb61-6" tabindex="-1"></a></span>
-<span id="cb61-7"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb61-7" tabindex="-1"></a><span class="co"># check equality</span></span>
-<span id="cb61-8"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb61-8" tabindex="-1"></a><span class="fu">all.equal</span>(lin_arpt_varpoord, lin_arpt_convey)</span></code></pre></div>
+<div class="sourceCode" id="cb60"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb60-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb60-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
+<span id="cb60-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb60-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
+<span id="cb60-3"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb60-3" tabindex="-1"></a>lin_arpt_varpoord <span class="ot">&lt;-</span> varpoord_arpt_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_arpt</span>
+<span id="cb60-4"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb60-4" tabindex="-1"></a><span class="co"># convey</span></span>
+<span id="cb60-5"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb60-5" tabindex="-1"></a>lin_arpt_convey <span class="ot">&lt;-</span> <span class="fu">attr</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc), <span class="st">&quot;lin&quot;</span>)</span>
+<span id="cb60-6"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb60-6" tabindex="-1"></a></span>
+<span id="cb60-7"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb60-7" tabindex="-1"></a><span class="co"># check equality</span></span>
+<span id="cb60-8"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb60-8" tabindex="-1"></a><span class="fu">all.equal</span>(lin_arpt_varpoord, lin_arpt_convey)</span></code></pre></div>
 <pre><code>## [1] TRUE</code></pre>
-<div class="sourceCode" id="cb63"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb63-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb63-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
-<span id="cb63-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb63-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb62"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb62-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb62-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
+<span id="cb62-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb62-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
 <pre><code>##          eqincome
 ## eqincome 2564.027</code></pre>
-<div class="sourceCode" id="cb65"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb65-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb65-1" tabindex="-1"></a>varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb64"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb64-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb64-1" tabindex="-1"></a>varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 2559.442</code></pre>
-<div class="sourceCode" id="cb67"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb67-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb67-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
-<span id="cb67-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb67-2" tabindex="-1"></a>varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb66"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb66-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb66-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
+<span id="cb66-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb66-2" tabindex="-1"></a>varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 50.59093</code></pre>
-<div class="sourceCode" id="cb69"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb69-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb69-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
+<div class="sourceCode" id="cb68"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb68-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb68-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
 <pre><code>##          eqincome
 ## eqincome 50.63622</code></pre>
 <p>The variance estimate is computed by using the approximation defined in <a href="2-var.html#var">2</a>, while the linearized variable <span class="math inline">\(z\)</span> is defined by <a href="2.1-lin.html#lin">2.1</a>. The functions <code>convey::svyarpt</code> and <code>vardpoor::linarpt</code> produce the same linearized variable <span class="math inline">\(z\)</span>.</p>
 <p>However, the measures of uncertainty do not line up, because <code>library(vardpoor)</code> defaults to an ultimate cluster method that can be replicated with an alternative setup of the <code>survey.design</code> object.</p>
-<div class="sourceCode" id="cb71"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb71-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
-<span id="cb71-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
-<span id="cb71-3"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
-<span id="cb71-4"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-4" tabindex="-1"></a></span>
-<span id="cb71-5"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
-<span id="cb71-6"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
-<span id="cb71-7"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-7" tabindex="-1"></a></span>
-<span id="cb71-8"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
-<span id="cb71-9"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
-<span id="cb71-10"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-10" tabindex="-1"></a></span>
-<span id="cb71-11"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb71-12"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
-<span id="cb71-13"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb71-14"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb71-15"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb71-16"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb71-17"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb71-18"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
-<span id="cb71-19"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
-<span id="cb71-20"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-20" tabindex="-1"></a>  )</span>
-<span id="cb71-21"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-21" tabindex="-1"></a></span>
-<span id="cb71-22"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
-<span id="cb71-23"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb71-24"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
-<span id="cb71-25"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-25" tabindex="-1"></a></span>
-<span id="cb71-26"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-26" tabindex="-1"></a></span>
-<span id="cb71-27"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-27" tabindex="-1"></a></span>
-<span id="cb71-28"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-28" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb71-29"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-29" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
-<span id="cb71-30"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-30" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>)[<span class="dv">1</span>] ,</span>
-<span id="cb71-31"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-31" tabindex="-1"></a>  varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span>
-<span id="cb71-32"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-32" tabindex="-1"></a>))</span>
-<span id="cb71-33"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-33" tabindex="-1"></a></span>
-<span id="cb71-34"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-34" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb71-35"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-35" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se ,</span>
-<span id="cb71-36"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-36" tabindex="-1"></a>                    <span class="fu">SE</span>(</span>
-<span id="cb71-37"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-37" tabindex="-1"></a>                      <span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster)</span>
-<span id="cb71-38"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb71-38" tabindex="-1"></a>                    )[<span class="dv">1</span>]))</span></code></pre></div>
+<div class="sourceCode" id="cb70"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb70-1"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
+<span id="cb70-2"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
+<span id="cb70-3"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
+<span id="cb70-4"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-4" tabindex="-1"></a></span>
+<span id="cb70-5"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
+<span id="cb70-6"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
+<span id="cb70-7"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-7" tabindex="-1"></a></span>
+<span id="cb70-8"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
+<span id="cb70-9"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
+<span id="cb70-10"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-10" tabindex="-1"></a></span>
+<span id="cb70-11"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb70-12"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
+<span id="cb70-13"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb70-14"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb70-15"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb70-16"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb70-17"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb70-18"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
+<span id="cb70-19"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
+<span id="cb70-20"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-20" tabindex="-1"></a>  )</span>
+<span id="cb70-21"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-21" tabindex="-1"></a></span>
+<span id="cb70-22"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
+<span id="cb70-23"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb70-24"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
+<span id="cb70-25"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-25" tabindex="-1"></a></span>
+<span id="cb70-26"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-26" tabindex="-1"></a></span>
+<span id="cb70-27"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-27" tabindex="-1"></a></span>
+<span id="cb70-28"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-28" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb70-29"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-29" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
+<span id="cb70-30"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-30" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>)[<span class="dv">1</span>] ,</span>
+<span id="cb70-31"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-31" tabindex="-1"></a>  varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span>
+<span id="cb70-32"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-32" tabindex="-1"></a>))</span>
+<span id="cb70-33"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-33" tabindex="-1"></a></span>
+<span id="cb70-34"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-34" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb70-35"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-35" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(varpoord_arpt_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se ,</span>
+<span id="cb70-36"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-36" tabindex="-1"></a>                    <span class="fu">SE</span>(</span>
+<span id="cb70-37"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-37" tabindex="-1"></a>                      <span class="fu">svyarpt</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster)</span>
+<span id="cb70-38"><a href="3.1-at-risk-of-poverty-threshold-svyarpt.html#cb70-38" tabindex="-1"></a>                    )[<span class="dv">1</span>]))</span></code></pre></div>
 <p>For additional usage examples of <code>svyarpt</code>, type <code>?convey::svyarpt</code> in the R console.</p>
 </div>
 </div>
diff --git a/docs/3.2-at-risk-of-poverty-ratio-svyarpr.html b/docs/3.2-at-risk-of-poverty-ratio-svyarpr.html
index cce552c..98d4a75 100644
--- a/docs/3.2-at-risk-of-poverty-ratio-svyarpr.html
+++ b/docs/3.2-at-risk-of-poverty-ratio-svyarpr.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,12 +253,12 @@
 <div class="col-sm-12">
 <div id="at-risk-of-poverty-ratio-svyarpr" class="section level2" number="3.2">
 <h2><span class="header-section-number">3.2</span> At Risk of Poverty Ratio (svyarpr)</h2>
-<div class="sourceCode" id="cb72"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb72-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-1" tabindex="-1"></a>✔️ EU standard like ARPT, easy to understand, interpret, and implement</span>
-<span id="cb72-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-2" tabindex="-1"></a>✔️ proportion of individuals below ARPT <span class="sc">--</span> a <span class="st">&quot;companion&quot;</span> <span class="cf">function</span> that uses <span class="fu">svyarpt</span>() internally</span>
-<span id="cb72-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-3" tabindex="-1"></a>✔️ measure is easy to understand</span>
-<span id="cb72-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-4" tabindex="-1"></a>❌ does not account <span class="cf">for</span> the intensity or inequality among the poor</span>
-<span id="cb72-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-5" tabindex="-1"></a>❌ not very common outside of the EU</span>
-<span id="cb72-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-6" tabindex="-1"></a>❌ just another name <span class="cf">for</span> the <span class="st">`</span><span class="at">svyfgt( g = 0 , thresh = &quot;relq&quot; )</span><span class="st">`</span></span></code></pre></div>
+<div class="sourceCode" id="cb71"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb71-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb71-1" tabindex="-1"></a>✔️ EU standard like ARPT, easy to understand, interpret, and implement</span>
+<span id="cb71-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb71-2" tabindex="-1"></a>✔️ proportion of individuals below ARPT <span class="sc">--</span> a <span class="st">&quot;companion&quot;</span> <span class="cf">function</span> that uses <span class="fu">svyarpt</span>() internally</span>
+<span id="cb71-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb71-3" tabindex="-1"></a>✔️ measure is easy to understand</span>
+<span id="cb71-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb71-4" tabindex="-1"></a>❌ does not account <span class="cf">for</span> the intensity or inequality among the poor</span>
+<span id="cb71-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb71-5" tabindex="-1"></a>❌ not very common outside of the EU</span>
+<span id="cb71-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb71-6" tabindex="-1"></a>❌ just another name <span class="cf">for</span> the <span class="st">`</span><span class="at">svyfgt( g = 0 , thresh = &quot;relq&quot; )</span><span class="st">`</span></span></code></pre></div>
 <p>The at-risk-of-poverty rate (ARPR) is the share of persons with an income below the at-risk-of-poverty threshold (ARPT). The logic behind this measure is that although most people below the ARPT cannot be considered “poor”, they are the ones most vulnerable to becoming poor in the event of a negative economic phenomenon like a recession.</p>
 <p>The ARPR is a composite estimate, taking into account both the sampling error in the proportion itself and that in the ARPT estimate. The details of the linearization of the ARPR are discussed by <span class="citation">Deville (<label for="tufte-mn-26" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-26" class="margin-toggle">1999<span class="marginnote">Deville, Jean-Claude. 1999. <span>“Variance Estimation for Complex Statistics and Estimators: Linearization and Residual Techniques.”</span> <em>Survey Methodology</em> 25 (2): 193–203. <a href="http://www.statcan.gc.ca/pub/12-001-x/1999002/article/4882-eng.pdf">http://www.statcan.gc.ca/pub/12-001-x/1999002/article/4882-eng.pdf</a>.</span>)</span> and <span class="citation">Osier (<label for="tufte-mn-27" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-27" class="margin-toggle">2009<span class="marginnote">Osier, Guillaume. 2009. <span>“Variance Estimation for Complex Indicators of Poverty and Inequality.”</span> <em>Journal of the European Survey Research Association</em> 3 (3): 167–95. <a href="http://ojs.ub.uni-konstanz.de/srm/article/view/369">http://ojs.ub.uni-konstanz.de/srm/article/view/369</a>.</span>)</span>.</p>
 <hr />
@@ -266,270 +266,270 @@ <h2><span class="header-section-number">3.2</span> At Risk of Poverty Ratio (svy
 <h3><span class="header-section-number">3.2.1</span> Replication Example</h3>
 <p>The R <code>vardpoor</code> package <span class="citation">(<label for="tufte-mn-28" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-28" class="margin-toggle">Breidaks, Liberts, and Ivanova 2016<span class="marginnote">Breidaks, Juris, Martins Liberts, and Santa Ivanova. 2016. <span>“Vardpoor: Estimation of Indicators on Social Exclusion and Poverty and Its Linearization, Variance Estimation.”</span> Riga, Latvia: CSB.</span>)</span>, created by researchers at the Central Statistical Bureau of Latvia, includes a ARPR coefficient calculation using the ultimate cluster method. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb73"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb73-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb73-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb73-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-3" tabindex="-1"></a></span>
-<span id="cb73-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb73-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb73-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-6" tabindex="-1"></a></span>
-<span id="cb73-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb73-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
-<span id="cb73-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-9" tabindex="-1"></a></span>
-<span id="cb73-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-10" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb73-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
-<span id="cb73-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-12" tabindex="-1"></a></span>
-<span id="cb73-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
-<span id="cb73-14"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
-<span id="cb73-15"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-15" tabindex="-1"></a></span>
-<span id="cb73-16"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
-<span id="cb73-17"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
-<span id="cb73-18"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-18" tabindex="-1"></a></span>
-<span id="cb73-19"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
-<span id="cb73-20"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
-<span id="cb73-21"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-21" tabindex="-1"></a></span>
-<span id="cb73-22"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-22" tabindex="-1"></a><span class="co"># calculate the arpr coefficient</span></span>
-<span id="cb73-23"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
-<span id="cb73-24"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-24" tabindex="-1"></a>varpoord_arpr_calculation <span class="ot">&lt;-</span></span>
-<span id="cb73-25"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
-<span id="cb73-26"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
-<span id="cb73-27"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
-<span id="cb73-28"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-28" tabindex="-1"></a>    </span>
-<span id="cb73-29"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
-<span id="cb73-30"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
-<span id="cb73-31"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-31" tabindex="-1"></a>    </span>
-<span id="cb73-32"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb73-33"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb73-34"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-34" tabindex="-1"></a>    </span>
-<span id="cb73-35"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb73-36"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb73-37"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-37" tabindex="-1"></a>    </span>
-<span id="cb73-38"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
-<span id="cb73-39"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
-<span id="cb73-40"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-40" tabindex="-1"></a>    </span>
-<span id="cb73-41"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
-<span id="cb73-42"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-42" tabindex="-1"></a>    </span>
-<span id="cb73-43"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
-<span id="cb73-44"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
-<span id="cb73-45"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-45" tabindex="-1"></a>    </span>
-<span id="cb73-46"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
-<span id="cb73-47"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
-<span id="cb73-48"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-48" tabindex="-1"></a>    </span>
-<span id="cb73-49"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-49" tabindex="-1"></a>    <span class="co"># arpr coefficient function</span></span>
-<span id="cb73-50"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linarpr&quot;</span>,</span>
-<span id="cb73-51"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-51" tabindex="-1"></a>    </span>
-<span id="cb73-52"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
-<span id="cb73-53"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
-<span id="cb73-54"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-54" tabindex="-1"></a>    </span>
-<span id="cb73-55"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-55" tabindex="-1"></a>  )</span>
-<span id="cb73-56"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-56" tabindex="-1"></a></span>
-<span id="cb73-57"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-57" tabindex="-1"></a></span>
-<span id="cb73-58"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-58" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb73-59"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-59" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
-<span id="cb73-60"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-60" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
-<span id="cb73-61"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-61" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb73-62"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-62" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb73-63"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-63" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb73-64"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-64" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb73-65"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-65" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
-<span id="cb73-66"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-66" tabindex="-1"></a>  )</span>
-<span id="cb73-67"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-67" tabindex="-1"></a></span>
-<span id="cb73-68"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-68" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
-<span id="cb73-69"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-69" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
-<span id="cb73-70"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-70" tabindex="-1"></a></span>
-<span id="cb73-71"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-71" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
-<span id="cb73-72"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb73-72" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
+<div class="sourceCode" id="cb72"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb72-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb72-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb72-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-3" tabindex="-1"></a></span>
+<span id="cb72-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb72-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb72-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-6" tabindex="-1"></a></span>
+<span id="cb72-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb72-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
+<span id="cb72-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-9" tabindex="-1"></a></span>
+<span id="cb72-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-10" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb72-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
+<span id="cb72-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-12" tabindex="-1"></a></span>
+<span id="cb72-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
+<span id="cb72-14"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
+<span id="cb72-15"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-15" tabindex="-1"></a></span>
+<span id="cb72-16"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
+<span id="cb72-17"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
+<span id="cb72-18"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-18" tabindex="-1"></a></span>
+<span id="cb72-19"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
+<span id="cb72-20"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
+<span id="cb72-21"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-21" tabindex="-1"></a></span>
+<span id="cb72-22"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-22" tabindex="-1"></a><span class="co"># calculate the arpr coefficient</span></span>
+<span id="cb72-23"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
+<span id="cb72-24"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-24" tabindex="-1"></a>varpoord_arpr_calculation <span class="ot">&lt;-</span></span>
+<span id="cb72-25"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
+<span id="cb72-26"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
+<span id="cb72-27"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
+<span id="cb72-28"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-28" tabindex="-1"></a>    </span>
+<span id="cb72-29"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
+<span id="cb72-30"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
+<span id="cb72-31"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-31" tabindex="-1"></a>    </span>
+<span id="cb72-32"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb72-33"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb72-34"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-34" tabindex="-1"></a>    </span>
+<span id="cb72-35"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb72-36"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb72-37"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-37" tabindex="-1"></a>    </span>
+<span id="cb72-38"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
+<span id="cb72-39"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
+<span id="cb72-40"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-40" tabindex="-1"></a>    </span>
+<span id="cb72-41"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
+<span id="cb72-42"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-42" tabindex="-1"></a>    </span>
+<span id="cb72-43"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
+<span id="cb72-44"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
+<span id="cb72-45"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-45" tabindex="-1"></a>    </span>
+<span id="cb72-46"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
+<span id="cb72-47"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
+<span id="cb72-48"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-48" tabindex="-1"></a>    </span>
+<span id="cb72-49"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-49" tabindex="-1"></a>    <span class="co"># arpr coefficient function</span></span>
+<span id="cb72-50"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linarpr&quot;</span>,</span>
+<span id="cb72-51"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-51" tabindex="-1"></a>    </span>
+<span id="cb72-52"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
+<span id="cb72-53"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
+<span id="cb72-54"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-54" tabindex="-1"></a>    </span>
+<span id="cb72-55"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-55" tabindex="-1"></a>  )</span>
+<span id="cb72-56"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-56" tabindex="-1"></a></span>
+<span id="cb72-57"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-57" tabindex="-1"></a></span>
+<span id="cb72-58"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-58" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb72-59"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-59" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
+<span id="cb72-60"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-60" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
+<span id="cb72-61"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-61" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb72-62"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-62" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb72-63"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-63" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb72-64"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-64" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb72-65"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-65" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
+<span id="cb72-66"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-66" tabindex="-1"></a>  )</span>
+<span id="cb72-67"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-67" tabindex="-1"></a></span>
+<span id="cb72-68"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-68" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
+<span id="cb72-69"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-69" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
+<span id="cb72-70"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-70" tabindex="-1"></a></span>
+<span id="cb72-71"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-71" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
+<span id="cb72-72"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb72-72" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
 <pre><code>## [1] 14.44422</code></pre>
-<div class="sourceCode" id="cb75"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb75-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb75-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb74"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb74-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb74-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>## eqincome 
 ## 14.44422</code></pre>
-<div class="sourceCode" id="cb77"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb77-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-1" tabindex="-1"></a><span class="co"># linearized variables do not match</span></span>
-<span id="cb77-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-2" tabindex="-1"></a><span class="co"># because Fprime is the derivative wrt</span></span>
-<span id="cb77-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-3" tabindex="-1"></a><span class="co"># to the estimated threshold, not the estimated quantile</span></span>
-<span id="cb77-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-4" tabindex="-1"></a><span class="co"># for more details, see</span></span>
-<span id="cb77-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-5" tabindex="-1"></a><span class="co"># https://github.com/ajdamico/convey/issues/372#issuecomment-1656264143</span></span>
-<span id="cb77-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-6" tabindex="-1"></a><span class="co">#</span></span>
-<span id="cb77-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-7" tabindex="-1"></a><span class="co"># vardpoor</span></span>
-<span id="cb77-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-8" tabindex="-1"></a>lin_arpr_varpoord <span class="ot">&lt;-</span> varpoord_arpr_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_arpr</span>
-<span id="cb77-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-9" tabindex="-1"></a><span class="co"># convey</span></span>
-<span id="cb77-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-10" tabindex="-1"></a>lin_arpr_convey <span class="ot">&lt;-</span> <span class="fu">attr</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc), <span class="st">&quot;lin&quot;</span>)</span>
-<span id="cb77-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-11" tabindex="-1"></a></span>
-<span id="cb77-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-12" tabindex="-1"></a><span class="co"># check equality</span></span>
-<span id="cb77-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb77-13" tabindex="-1"></a><span class="fu">all.equal</span>(lin_arpr_varpoord, <span class="dv">100</span> <span class="sc">*</span> lin_arpr_convey)</span></code></pre></div>
+<div class="sourceCode" id="cb76"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb76-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-1" tabindex="-1"></a><span class="co"># linearized variables do not match</span></span>
+<span id="cb76-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-2" tabindex="-1"></a><span class="co"># because Fprime is the derivative wrt</span></span>
+<span id="cb76-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-3" tabindex="-1"></a><span class="co"># to the estimated threshold, not the estimated quantile</span></span>
+<span id="cb76-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-4" tabindex="-1"></a><span class="co"># for more details, see</span></span>
+<span id="cb76-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-5" tabindex="-1"></a><span class="co"># https://github.com/ajdamico/convey/issues/372#issuecomment-1656264143</span></span>
+<span id="cb76-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-6" tabindex="-1"></a><span class="co">#</span></span>
+<span id="cb76-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-7" tabindex="-1"></a><span class="co"># vardpoor</span></span>
+<span id="cb76-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-8" tabindex="-1"></a>lin_arpr_varpoord <span class="ot">&lt;-</span> varpoord_arpr_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_arpr</span>
+<span id="cb76-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-9" tabindex="-1"></a><span class="co"># convey</span></span>
+<span id="cb76-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-10" tabindex="-1"></a>lin_arpr_convey <span class="ot">&lt;-</span> <span class="fu">attr</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc), <span class="st">&quot;lin&quot;</span>)</span>
+<span id="cb76-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-11" tabindex="-1"></a></span>
+<span id="cb76-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-12" tabindex="-1"></a><span class="co"># check equality</span></span>
+<span id="cb76-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb76-13" tabindex="-1"></a><span class="fu">all.equal</span>(lin_arpr_varpoord, <span class="dv">100</span> <span class="sc">*</span> lin_arpr_convey)</span></code></pre></div>
 <pre><code>## [1] &quot;Mean relative difference: 0.2264738&quot;</code></pre>
-<div class="sourceCode" id="cb79"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb79-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb79-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
-<span id="cb79-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb79-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
+<div class="sourceCode" id="cb78"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb78-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb78-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
+<span id="cb78-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb78-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
 <pre><code>##            eqincome
 ## eqincome 0.07599778</code></pre>
-<div class="sourceCode" id="cb81"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb81-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb81-1" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb80"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb80-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb80-1" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.08718569</code></pre>
-<div class="sourceCode" id="cb83"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb83-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb83-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
-<span id="cb83-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb83-2" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb82"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb82-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb82-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
+<span id="cb82-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb82-2" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.2952722</code></pre>
-<div class="sourceCode" id="cb85"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb85-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb85-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb84"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb84-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb84-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>##           eqincome
 ## eqincome 0.2756769</code></pre>
 <p>The variance estimate is computed by using the approximation defined in <a href="2-var.html#var">2</a>, while the linearized variable <span class="math inline">\(z\)</span> is defined by <a href="2.1-lin.html#lin">2.1</a>. The functions <code>convey::svyarpr</code> and <code>vardpoor::linarpr</code> produce the same linearized variable <span class="math inline">\(z\)</span>.</p>
 <p>However, the measures of uncertainty do not line up. One of the reasons is that <code>library(vardpoor)</code> defaults to an ultimate cluster method that can be replicated with an alternative setup of the <code>survey.design</code> object.</p>
-<div class="sourceCode" id="cb87"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb87-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
-<span id="cb87-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
-<span id="cb87-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
-<span id="cb87-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-4" tabindex="-1"></a></span>
-<span id="cb87-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
-<span id="cb87-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
-<span id="cb87-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-7" tabindex="-1"></a></span>
-<span id="cb87-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
-<span id="cb87-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
-<span id="cb87-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-10" tabindex="-1"></a></span>
-<span id="cb87-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb87-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
-<span id="cb87-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb87-14"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb87-15"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb87-16"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb87-17"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb87-18"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
-<span id="cb87-19"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
-<span id="cb87-20"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-20" tabindex="-1"></a>  )</span>
-<span id="cb87-21"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-21" tabindex="-1"></a></span>
-<span id="cb87-22"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
-<span id="cb87-23"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb87-24"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
-<span id="cb87-25"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-25" tabindex="-1"></a></span>
-<span id="cb87-26"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-26" tabindex="-1"></a><span class="co"># does not match</span></span>
-<span id="cb87-27"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb87-27" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
+<div class="sourceCode" id="cb86"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb86-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
+<span id="cb86-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
+<span id="cb86-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
+<span id="cb86-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-4" tabindex="-1"></a></span>
+<span id="cb86-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
+<span id="cb86-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
+<span id="cb86-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-7" tabindex="-1"></a></span>
+<span id="cb86-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
+<span id="cb86-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
+<span id="cb86-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-10" tabindex="-1"></a></span>
+<span id="cb86-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb86-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
+<span id="cb86-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb86-14"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb86-15"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb86-16"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb86-17"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb86-18"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
+<span id="cb86-19"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
+<span id="cb86-20"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-20" tabindex="-1"></a>  )</span>
+<span id="cb86-21"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-21" tabindex="-1"></a></span>
+<span id="cb86-22"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
+<span id="cb86-23"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb86-24"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
+<span id="cb86-25"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-25" tabindex="-1"></a></span>
+<span id="cb86-26"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-26" tabindex="-1"></a><span class="co"># does not match</span></span>
+<span id="cb86-27"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb86-27" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
 <pre><code>##            eqincome
 ## eqincome 0.07586194</code></pre>
-<div class="sourceCode" id="cb89"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb89-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb89-1" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb88"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb88-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb88-1" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.08718569</code></pre>
-<div class="sourceCode" id="cb91"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb91-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb91-1" tabindex="-1"></a><span class="co"># does not match</span></span>
-<span id="cb91-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb91-2" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb90"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb90-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb90-1" tabindex="-1"></a><span class="co"># does not match</span></span>
+<span id="cb90-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb90-2" tabindex="-1"></a>varpoord_arpr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.2952722</code></pre>
-<div class="sourceCode" id="cb93"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb93-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb93-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb92"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb92-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb92-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>##           eqincome
 ## eqincome 0.2754305</code></pre>
 <p>Still, there is a difference in the estimates. This is discussed in detail in <a href="https://github.com/ajdamico/convey/issues/372">this issue</a>.
 In order to still provide additional examples for our code, we proceed with a Monte Carlo experiment.</p>
 <p>Using the <code>eusilcP</code> data from the <code>simPop</code> package <span class="citation">(<label for="tufte-mn-29" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-29" class="margin-toggle">Templ et al. 2017<span class="marginnote">Templ, Matthias, Bernhard Meindl, Alexander Kowarik, and Olivier Dupriez. 2017. <span>“Simulation of Synthetic Complex Data: The <span>R</span> Package <span class="nocase">simPop</span>.”</span> <em>Journal of Statistical Software</em> 79 (10): 1–38. <a href="https://doi.org/10.18637/jss.v079.i10">https://doi.org/10.18637/jss.v079.i10</a>.</span>)</span>, we can compute the actual value of the at risk of poverty rate for that population:</p>
-<div class="sourceCode" id="cb95"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb95-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
-<span id="cb95-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-2" tabindex="-1"></a><span class="fu">library</span>(sampling)</span>
-<span id="cb95-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-3" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb95-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-4" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb95-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-5" tabindex="-1"></a><span class="fu">library</span>(parallel)</span>
-<span id="cb95-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-6" tabindex="-1"></a></span>
-<span id="cb95-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-7" tabindex="-1"></a><span class="co"># load pseudo population data</span></span>
-<span id="cb95-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-8" tabindex="-1"></a><span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
-<span id="cb95-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-9" tabindex="-1"></a></span>
-<span id="cb95-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-10" tabindex="-1"></a><span class="co"># compute population median</span></span>
-<span id="cb95-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-11" tabindex="-1"></a>q50.pop <span class="ot">&lt;-</span></span>
-<span id="cb95-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-12" tabindex="-1"></a>  convey<span class="sc">:::</span><span class="fu">computeQuantiles</span>(eusilcP<span class="sc">$</span>eqIncome , <span class="fu">rep</span>(<span class="dv">1</span> , <span class="fu">length</span>(eusilcP<span class="sc">$</span>eqIncome)) , .<span class="dv">50</span>)</span>
-<span id="cb95-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-13" tabindex="-1"></a></span>
-<span id="cb95-14"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-14" tabindex="-1"></a><span class="co"># compute population poverty threshold</span></span>
-<span id="cb95-15"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-15" tabindex="-1"></a><span class="co"># as 60% of the median</span></span>
-<span id="cb95-16"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-16" tabindex="-1"></a>thresh.pop <span class="ot">&lt;-</span> .<span class="dv">60</span> <span class="sc">*</span> q50.pop</span>
-<span id="cb95-17"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-17" tabindex="-1"></a></span>
-<span id="cb95-18"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-18" tabindex="-1"></a><span class="co"># compute population at risk of poverty rate</span></span>
-<span id="cb95-19"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-19" tabindex="-1"></a>(theta.pop <span class="ot">&lt;-</span></span>
-<span id="cb95-20"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb95-20" tabindex="-1"></a>    <span class="fu">mean</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&lt;=</span> thresh.pop , <span class="at">na.rm =</span> <span class="cn">TRUE</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb94"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb94-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
+<span id="cb94-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-2" tabindex="-1"></a><span class="fu">library</span>(sampling)</span>
+<span id="cb94-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-3" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb94-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-4" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb94-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-5" tabindex="-1"></a><span class="fu">library</span>(parallel)</span>
+<span id="cb94-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-6" tabindex="-1"></a></span>
+<span id="cb94-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-7" tabindex="-1"></a><span class="co"># load pseudo population data</span></span>
+<span id="cb94-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-8" tabindex="-1"></a><span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
+<span id="cb94-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-9" tabindex="-1"></a></span>
+<span id="cb94-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-10" tabindex="-1"></a><span class="co"># compute population median</span></span>
+<span id="cb94-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-11" tabindex="-1"></a>q50.pop <span class="ot">&lt;-</span></span>
+<span id="cb94-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-12" tabindex="-1"></a>  convey<span class="sc">:::</span><span class="fu">computeQuantiles</span>(eusilcP<span class="sc">$</span>eqIncome , <span class="fu">rep</span>(<span class="dv">1</span> , <span class="fu">length</span>(eusilcP<span class="sc">$</span>eqIncome)) , .<span class="dv">50</span>)</span>
+<span id="cb94-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-13" tabindex="-1"></a></span>
+<span id="cb94-14"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-14" tabindex="-1"></a><span class="co"># compute population poverty threshold</span></span>
+<span id="cb94-15"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-15" tabindex="-1"></a><span class="co"># as 60% of the median</span></span>
+<span id="cb94-16"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-16" tabindex="-1"></a>thresh.pop <span class="ot">&lt;-</span> .<span class="dv">60</span> <span class="sc">*</span> q50.pop</span>
+<span id="cb94-17"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-17" tabindex="-1"></a></span>
+<span id="cb94-18"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-18" tabindex="-1"></a><span class="co"># compute population at risk of poverty rate</span></span>
+<span id="cb94-19"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-19" tabindex="-1"></a>(theta.pop <span class="ot">&lt;-</span></span>
+<span id="cb94-20"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb94-20" tabindex="-1"></a>    <span class="fu">mean</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&lt;=</span> thresh.pop , <span class="at">na.rm =</span> <span class="cn">TRUE</span>))</span></code></pre></div>
 <pre><code>## [1] 0.1469295</code></pre>
 <p>Now, to study the distribution of the estimator under a particular sampling design, we select 5000 samples under one-stage cluster sampling of 100 households using the <code>cluster</code> function from the <code>sampling</code> package <span class="citation">(<label for="tufte-mn-30" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-30" class="margin-toggle">Tillé and Matei 2021<span class="marginnote">Tillé, Yves, and Alina Matei. 2021. <em>Sampling: Survey Sampling</em>. <a href="https://CRAN.R-project.org/package=sampling">https://CRAN.R-project.org/package=sampling</a>.</span>)</span>, and use the <code>svyarpr</code> function to estimate the ARPR for each of those samples:</p>
-<div class="sourceCode" id="cb97"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb97-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-1" tabindex="-1"></a><span class="co"># define the number of monte carlo replicates</span></span>
-<span id="cb97-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-2" tabindex="-1"></a>mc.rep <span class="ot">&lt;-</span> 5000L</span>
-<span id="cb97-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-3" tabindex="-1"></a></span>
-<span id="cb97-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-4" tabindex="-1"></a><span class="co"># simulation function</span></span>
-<span id="cb97-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-5" tabindex="-1"></a>arpr_sim_fun <span class="ot">&lt;-</span> <span class="cf">function</span>(this.iter) {</span>
-<span id="cb97-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-6" tabindex="-1"></a>  </span>
-<span id="cb97-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-7" tabindex="-1"></a>  <span class="fu">set.seed</span>(this.iter)</span>
-<span id="cb97-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-8" tabindex="-1"></a>  </span>
-<span id="cb97-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-9" tabindex="-1"></a>  </span>
-<span id="cb97-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-10" tabindex="-1"></a>  <span class="fu">library</span>(survey)</span>
-<span id="cb97-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-11" tabindex="-1"></a>  <span class="fu">library</span>(convey)</span>
-<span id="cb97-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-12" tabindex="-1"></a>  <span class="fu">library</span>(sampling)</span>
-<span id="cb97-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-13" tabindex="-1"></a>  </span>
-<span id="cb97-14"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-14" tabindex="-1"></a>  <span class="co"># load pseudo population data</span></span>
-<span id="cb97-15"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-15" tabindex="-1"></a>  <span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
-<span id="cb97-16"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-16" tabindex="-1"></a>  </span>
-<span id="cb97-17"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-17" tabindex="-1"></a>  <span class="co"># compute size-like variable for PPS sampling design</span></span>
-<span id="cb97-18"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-18" tabindex="-1"></a>  eusilcP<span class="sc">$</span>aux <span class="ot">&lt;-</span></span>
-<span id="cb97-19"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-19" tabindex="-1"></a>    <span class="fu">log</span>(<span class="fu">ifelse</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;=</span> <span class="dv">1000</span> , eusilcP<span class="sc">$</span>eqIncome , <span class="dv">1000</span>))</span>
-<span id="cb97-20"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-20" tabindex="-1"></a>  </span>
-<span id="cb97-21"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-21" tabindex="-1"></a>  </span>
-<span id="cb97-22"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-22" tabindex="-1"></a>  <span class="co"># select sample</span></span>
-<span id="cb97-23"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-23" tabindex="-1"></a>  tt <span class="ot">&lt;-</span></span>
-<span id="cb97-24"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-24" tabindex="-1"></a>    sampling<span class="sc">::</span><span class="fu">cluster</span>(</span>
-<span id="cb97-25"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-25" tabindex="-1"></a>      <span class="at">data =</span> eusilcP[<span class="fu">sample.int</span>(<span class="fu">nrow</span>(eusilcP) , <span class="fu">nrow</span>(eusilcP) , <span class="at">replace =</span> <span class="cn">FALSE</span>) , ] ,</span>
-<span id="cb97-26"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-26" tabindex="-1"></a>      <span class="at">clustername =</span> <span class="st">&quot;hid&quot;</span> ,</span>
-<span id="cb97-27"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-27" tabindex="-1"></a>      <span class="at">size =</span> 1000L ,</span>
-<span id="cb97-28"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-28" tabindex="-1"></a>      <span class="at">method =</span> <span class="st">&quot;systematic&quot;</span> ,</span>
-<span id="cb97-29"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-29" tabindex="-1"></a>      <span class="at">pik =</span> eusilcP<span class="sc">$</span>aux</span>
-<span id="cb97-30"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-30" tabindex="-1"></a>    )</span>
-<span id="cb97-31"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-31" tabindex="-1"></a>  </span>
-<span id="cb97-32"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-32" tabindex="-1"></a>  <span class="co"># collect data</span></span>
-<span id="cb97-33"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-33" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">getdata</span>(eusilcP , tt)</span>
-<span id="cb97-34"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-34" tabindex="-1"></a>  </span>
-<span id="cb97-35"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-35" tabindex="-1"></a>  <span class="co"># create survey design object</span></span>
-<span id="cb97-36"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-36" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span></span>
-<span id="cb97-37"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-37" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
-<span id="cb97-38"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-38" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> hid ,</span>
-<span id="cb97-39"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-39" tabindex="-1"></a>      <span class="at">probs =</span> <span class="sc">~</span> Prob ,</span>
-<span id="cb97-40"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-40" tabindex="-1"></a>      <span class="at">data =</span> this.sample ,</span>
-<span id="cb97-41"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-41" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
-<span id="cb97-42"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-42" tabindex="-1"></a>    )</span>
-<span id="cb97-43"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-43" tabindex="-1"></a>  </span>
-<span id="cb97-44"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-44" tabindex="-1"></a>  <span class="co"># prepare for convey functions</span></span>
-<span id="cb97-45"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-45" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(this.desobj)</span>
-<span id="cb97-46"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-46" tabindex="-1"></a>  </span>
-<span id="cb97-47"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-47" tabindex="-1"></a>  <span class="co"># compute estimates</span></span>
-<span id="cb97-48"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-48" tabindex="-1"></a>  <span class="fu">svyarpr</span>( <span class="sc">~</span> eqIncome , this.desobj)</span>
-<span id="cb97-49"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-49" tabindex="-1"></a>  </span>
-<span id="cb97-50"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-50" tabindex="-1"></a>}</span>
-<span id="cb97-51"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-51" tabindex="-1"></a></span>
-<span id="cb97-52"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-52" tabindex="-1"></a><span class="co"># run replications</span></span>
-<span id="cb97-53"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-53" tabindex="-1"></a>cl <span class="ot">&lt;-</span> <span class="fu">makeCluster</span>(<span class="fu">detectCores</span>() <span class="sc">-</span> <span class="dv">1</span>)</span>
-<span id="cb97-54"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-54" tabindex="-1"></a></span>
-<span id="cb97-55"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-55" tabindex="-1"></a>arpr.estimate.list <span class="ot">&lt;-</span></span>
-<span id="cb97-56"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-56" tabindex="-1"></a>  <span class="fu">clusterApply</span>(cl, <span class="fu">seq_len</span>(mc.rep) , arpr_sim_fun)</span>
-<span id="cb97-57"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-57" tabindex="-1"></a></span>
-<span id="cb97-58"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-58" tabindex="-1"></a><span class="fu">stopCluster</span>(cl)</span></code></pre></div>
+<div class="sourceCode" id="cb96"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb96-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-1" tabindex="-1"></a><span class="co"># define the number of monte carlo replicates</span></span>
+<span id="cb96-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-2" tabindex="-1"></a>mc.rep <span class="ot">&lt;-</span> 5000L</span>
+<span id="cb96-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-3" tabindex="-1"></a></span>
+<span id="cb96-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-4" tabindex="-1"></a><span class="co"># simulation function</span></span>
+<span id="cb96-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-5" tabindex="-1"></a>arpr_sim_fun <span class="ot">&lt;-</span> <span class="cf">function</span>(this.iter) {</span>
+<span id="cb96-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-6" tabindex="-1"></a>  </span>
+<span id="cb96-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-7" tabindex="-1"></a>  <span class="fu">set.seed</span>(this.iter)</span>
+<span id="cb96-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-8" tabindex="-1"></a>  </span>
+<span id="cb96-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-9" tabindex="-1"></a>  </span>
+<span id="cb96-10"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-10" tabindex="-1"></a>  <span class="fu">library</span>(survey)</span>
+<span id="cb96-11"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-11" tabindex="-1"></a>  <span class="fu">library</span>(convey)</span>
+<span id="cb96-12"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-12" tabindex="-1"></a>  <span class="fu">library</span>(sampling)</span>
+<span id="cb96-13"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-13" tabindex="-1"></a>  </span>
+<span id="cb96-14"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-14" tabindex="-1"></a>  <span class="co"># load pseudo population data</span></span>
+<span id="cb96-15"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-15" tabindex="-1"></a>  <span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
+<span id="cb96-16"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-16" tabindex="-1"></a>  </span>
+<span id="cb96-17"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-17" tabindex="-1"></a>  <span class="co"># compute size-like variable for PPS sampling design</span></span>
+<span id="cb96-18"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-18" tabindex="-1"></a>  eusilcP<span class="sc">$</span>aux <span class="ot">&lt;-</span></span>
+<span id="cb96-19"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-19" tabindex="-1"></a>    <span class="fu">log</span>(<span class="fu">ifelse</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;=</span> <span class="dv">1000</span> , eusilcP<span class="sc">$</span>eqIncome , <span class="dv">1000</span>))</span>
+<span id="cb96-20"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-20" tabindex="-1"></a>  </span>
+<span id="cb96-21"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-21" tabindex="-1"></a>  </span>
+<span id="cb96-22"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-22" tabindex="-1"></a>  <span class="co"># select sample</span></span>
+<span id="cb96-23"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-23" tabindex="-1"></a>  tt <span class="ot">&lt;-</span></span>
+<span id="cb96-24"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-24" tabindex="-1"></a>    sampling<span class="sc">::</span><span class="fu">cluster</span>(</span>
+<span id="cb96-25"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-25" tabindex="-1"></a>      <span class="at">data =</span> eusilcP[<span class="fu">sample.int</span>(<span class="fu">nrow</span>(eusilcP) , <span class="fu">nrow</span>(eusilcP) , <span class="at">replace =</span> <span class="cn">FALSE</span>) , ] ,</span>
+<span id="cb96-26"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-26" tabindex="-1"></a>      <span class="at">clustername =</span> <span class="st">&quot;hid&quot;</span> ,</span>
+<span id="cb96-27"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-27" tabindex="-1"></a>      <span class="at">size =</span> 1000L ,</span>
+<span id="cb96-28"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-28" tabindex="-1"></a>      <span class="at">method =</span> <span class="st">&quot;systematic&quot;</span> ,</span>
+<span id="cb96-29"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-29" tabindex="-1"></a>      <span class="at">pik =</span> eusilcP<span class="sc">$</span>aux</span>
+<span id="cb96-30"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-30" tabindex="-1"></a>    )</span>
+<span id="cb96-31"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-31" tabindex="-1"></a>  </span>
+<span id="cb96-32"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-32" tabindex="-1"></a>  <span class="co"># collect data</span></span>
+<span id="cb96-33"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-33" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">getdata</span>(eusilcP , tt)</span>
+<span id="cb96-34"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-34" tabindex="-1"></a>  </span>
+<span id="cb96-35"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-35" tabindex="-1"></a>  <span class="co"># create survey design object</span></span>
+<span id="cb96-36"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-36" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span></span>
+<span id="cb96-37"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-37" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
+<span id="cb96-38"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-38" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> hid ,</span>
+<span id="cb96-39"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-39" tabindex="-1"></a>      <span class="at">probs =</span> <span class="sc">~</span> Prob ,</span>
+<span id="cb96-40"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-40" tabindex="-1"></a>      <span class="at">data =</span> this.sample ,</span>
+<span id="cb96-41"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-41" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
+<span id="cb96-42"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-42" tabindex="-1"></a>    )</span>
+<span id="cb96-43"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-43" tabindex="-1"></a>  </span>
+<span id="cb96-44"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-44" tabindex="-1"></a>  <span class="co"># prepare for convey functions</span></span>
+<span id="cb96-45"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-45" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(this.desobj)</span>
+<span id="cb96-46"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-46" tabindex="-1"></a>  </span>
+<span id="cb96-47"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-47" tabindex="-1"></a>  <span class="co"># compute estimates</span></span>
+<span id="cb96-48"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-48" tabindex="-1"></a>  <span class="fu">svyarpr</span>( <span class="sc">~</span> eqIncome , this.desobj)</span>
+<span id="cb96-49"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-49" tabindex="-1"></a>  </span>
+<span id="cb96-50"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-50" tabindex="-1"></a>}</span>
+<span id="cb96-51"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-51" tabindex="-1"></a></span>
+<span id="cb96-52"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-52" tabindex="-1"></a><span class="co"># run replications</span></span>
+<span id="cb96-53"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-53" tabindex="-1"></a>cl <span class="ot">&lt;-</span> <span class="fu">makeCluster</span>(<span class="fu">detectCores</span>() <span class="sc">-</span> <span class="dv">1</span>)</span>
+<span id="cb96-54"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-54" tabindex="-1"></a></span>
+<span id="cb96-55"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-55" tabindex="-1"></a>arpr.estimate.list <span class="ot">&lt;-</span></span>
+<span id="cb96-56"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-56" tabindex="-1"></a>  <span class="fu">clusterApply</span>(cl, <span class="fu">seq_len</span>(mc.rep) , arpr_sim_fun)</span>
+<span id="cb96-57"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-57" tabindex="-1"></a></span>
+<span id="cb96-58"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb96-58" tabindex="-1"></a><span class="fu">stopCluster</span>(cl)</span></code></pre></div>
 <p>Then, we evaluate the Percentage Relative Bias (PRB) of the ARPR estimator. Under this scenario, the PRB of the ARPR estimator is -0.19830%.</p>
-<div class="sourceCode" id="cb98"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb98-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb98-1" tabindex="-1"></a><span class="co"># estimate the expected value of the ARPR estimator</span></span>
-<span id="cb98-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb98-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
-<span id="cb98-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb98-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(arpr.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb97"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb97-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-1" tabindex="-1"></a><span class="co"># estimate the expected value of the ARPR estimator</span></span>
+<span id="cb97-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
+<span id="cb97-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb97-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(arpr.estimate.list , coef)))</span></code></pre></div>
 <pre><code>## [1] 0.1466381</code></pre>
-<div class="sourceCode" id="cb100"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb100-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb100-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
-<span id="cb100-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb100-2" tabindex="-1"></a>(percentage_relative_bias_arpr <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb99"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb99-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb99-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
+<span id="cb99-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb99-2" tabindex="-1"></a>(percentage_relative_bias_arpr <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
 <pre><code>## [1] -0.1982981</code></pre>
-<div class="sourceCode" id="cb102"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb102-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb102-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(percentage_relative_bias_arpr , <span class="dv">4</span>) <span class="sc">==</span> <span class="sc">-</span><span class="fl">0.19830</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb101"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb101-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb101-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(percentage_relative_bias_arpr , <span class="dv">4</span>) <span class="sc">==</span> <span class="sc">-</span><span class="fl">0.19830</span>)</span></code></pre></div>
 <p>For the variance estimator, we have:</p>
-<div class="sourceCode" id="cb103"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb103-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb103-1" tabindex="-1"></a><span class="co"># estimate the variance of the ARPR estimator</span></span>
-<span id="cb103-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb103-2" tabindex="-1"></a><span class="co"># using the empirical variance of the estimates</span></span>
-<span id="cb103-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb103-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span> <span class="fu">var</span>(<span class="fu">sapply</span>(arpr.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb102"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb102-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb102-1" tabindex="-1"></a><span class="co"># estimate the variance of the ARPR estimator</span></span>
+<span id="cb102-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb102-2" tabindex="-1"></a><span class="co"># using the empirical variance of the estimates</span></span>
+<span id="cb102-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb102-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span> <span class="fu">var</span>(<span class="fu">sapply</span>(arpr.estimate.list , coef)))</span></code></pre></div>
 <pre><code>## [1] 0.0001048728</code></pre>
-<div class="sourceCode" id="cb105"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb105-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb105-1" tabindex="-1"></a><span class="co"># estimate the expected value of the ARPR variance estimator</span></span>
-<span id="cb105-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb105-2" tabindex="-1"></a><span class="co"># using the (estimated) expected value of the variance estimates</span></span>
-<span id="cb105-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb105-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(arpr.estimate.list , vcov)))</span></code></pre></div>
+<div class="sourceCode" id="cb104"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb104-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb104-1" tabindex="-1"></a><span class="co"># estimate the expected value of the ARPR variance estimator</span></span>
+<span id="cb104-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb104-2" tabindex="-1"></a><span class="co"># using the (estimated) expected value of the variance estimates</span></span>
+<span id="cb104-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb104-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(arpr.estimate.list , vcov)))</span></code></pre></div>
 <pre><code>## [1] 0.0001081994</code></pre>
-<div class="sourceCode" id="cb107"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb107-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb107-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimator</span></span>
-<span id="cb107-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb107-2" tabindex="-1"></a>( percentage_relative_bias_variance <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span>  (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>) )</span></code></pre></div>
+<div class="sourceCode" id="cb106"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb106-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb106-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimator</span></span>
+<span id="cb106-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb106-2" tabindex="-1"></a>( percentage_relative_bias_variance <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span>  (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>) )</span></code></pre></div>
 <pre><code>## [1] 3.172023</code></pre>
-<div class="sourceCode" id="cb109"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb109-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb109-1" tabindex="-1"></a><span class="fu">stopifnot</span>( <span class="fu">round</span>( percentage_relative_bias_variance , <span class="dv">4</span> ) <span class="sc">==</span> <span class="fl">3.1720</span> ) </span></code></pre></div>
+<div class="sourceCode" id="cb108"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb108-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb108-1" tabindex="-1"></a><span class="fu">stopifnot</span>( <span class="fu">round</span>( percentage_relative_bias_variance , <span class="dv">4</span> ) <span class="sc">==</span> <span class="fl">3.1720</span> ) </span></code></pre></div>
 <p>Under this scenario, the PRB of the ARPR variance estimator is 3.1720%.</p>
 <p>Our simulation shows that the Bias Ratio of this estimator is approximately 2%:</p>
-<div class="sourceCode" id="cb110"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb110-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb110-1" tabindex="-1"></a><span class="co"># compute bias ratio</span></span>
-<span id="cb110-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb110-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> <span class="fu">abs</span>( theta.exp <span class="sc">-</span> theta.pop ) <span class="sc">/</span> <span class="fu">sqrt</span>( vartheta.popest )</span></code></pre></div>
+<div class="sourceCode" id="cb109"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb109-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb109-1" tabindex="-1"></a><span class="co"># compute bias ratio</span></span>
+<span id="cb109-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb109-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> <span class="fu">abs</span>( theta.exp <span class="sc">-</span> theta.pop ) <span class="sc">/</span> <span class="fu">sqrt</span>( vartheta.popest )</span></code></pre></div>
 <pre><code>## [1] 2.84509</code></pre>
 <p>if the normal approximation holds, a small bias ratio still allows for approximately valid estimates of the confidence intervals.</p>
 <p>Next, we evaluate the Percentage Coverage Rate (PCR). In theory, under repeated sampling, the estimated 95% CIs should cover the population parameter approximately 95% of the time. We can evaluate that using:</p>
-<div class="sourceCode" id="cb112"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb112-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb112-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the ARPR</span></span>
-<span id="cb112-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb112-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
-<span id="cb112-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb112-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
-<span id="cb112-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb112-4" tabindex="-1"></a>  <span class="fu">sapply</span>(arpr.estimate.list, <span class="cf">function</span>(this.stat)</span>
-<span id="cb112-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb112-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
-<span id="cb112-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb112-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop)</span>
-<span id="cb112-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb112-7" tabindex="-1"></a></span>
-<span id="cb112-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb112-8" tabindex="-1"></a><span class="co"># evaluate empirical coverage</span></span>
-<span id="cb112-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb112-9" tabindex="-1"></a>(empirical_coverage <span class="ot">&lt;-</span> <span class="fu">mean</span>(est.coverage))</span></code></pre></div>
+<div class="sourceCode" id="cb111"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb111-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb111-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the ARPR</span></span>
+<span id="cb111-2"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb111-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
+<span id="cb111-3"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb111-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
+<span id="cb111-4"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb111-4" tabindex="-1"></a>  <span class="fu">sapply</span>(arpr.estimate.list, <span class="cf">function</span>(this.stat)</span>
+<span id="cb111-5"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb111-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
+<span id="cb111-6"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb111-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop)</span>
+<span id="cb111-7"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb111-7" tabindex="-1"></a></span>
+<span id="cb111-8"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb111-8" tabindex="-1"></a><span class="co"># evaluate empirical coverage</span></span>
+<span id="cb111-9"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb111-9" tabindex="-1"></a>(empirical_coverage <span class="ot">&lt;-</span> <span class="fu">mean</span>(est.coverage))</span></code></pre></div>
 <pre><code>## [1] 0.9516</code></pre>
-<div class="sourceCode" id="cb114"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb114-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb114-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(empirical_coverage , <span class="dv">2</span>) <span class="sc">==</span> <span class="fl">0.95</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb113"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb113-1"><a href="3.2-at-risk-of-poverty-ratio-svyarpr.html#cb113-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(empirical_coverage , <span class="dv">2</span>) <span class="sc">==</span> <span class="fl">0.95</span>)</span></code></pre></div>
 <p>Our coverages are not too far from the nominal coverage level of 95%.</p>
 <p>For additional usage examples of <code>svyarpr</code>, type <code>?convey::svyarpr</code> in the R console.</p>
 </div>
diff --git a/docs/3.3-relative-median-income-ratio-svyrmir.html b/docs/3.3-relative-median-income-ratio-svyrmir.html
index d3a5c80..878f3d9 100644
--- a/docs/3.3-relative-median-income-ratio-svyrmir.html
+++ b/docs/3.3-relative-median-income-ratio-svyrmir.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,15 +253,15 @@
 <div class="col-sm-12">
 <div id="relative-median-income-ratio-svyrmir" class="section level2" number="3.3">
 <h2><span class="header-section-number">3.3</span> Relative Median Income Ratio (svyrmir)</h2>
-<div class="sourceCode" id="cb115"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb115-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-1" tabindex="-1"></a>✔️ mainly useful <span class="cf">for</span> studies of the income of the elderly following EU definitions</span>
-<span id="cb115-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-2" tabindex="-1"></a>✔️ a ratio of medians</span>
-<span id="cb115-3"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-3" tabindex="-1"></a>✔️ less sensitive to outliers</span>
-<span id="cb115-4"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-4" tabindex="-1"></a>❌ solely a measure of medians and does not fully account <span class="cf">for</span> the income distribution</span>
-<span id="cb115-5"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-5" tabindex="-1"></a>❌ not very common outside of the EU</span>
-<span id="cb115-6"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-6" tabindex="-1"></a>❌ hard to interpret</span>
-<span id="cb115-7"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-7" tabindex="-1"></a>❌ <span class="fu">not</span> (necessarily) a dependency measure</span>
-<span id="cb115-8"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-8" tabindex="-1"></a>❌ not an inequality <span class="fu">measure</span> (fails the Pigou<span class="sc">-</span>Dalton principle)</span>
-<span id="cb115-9"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-9" tabindex="-1"></a>❌ <span class="fu">not</span> (exactly) a poverty <span class="fu">measure</span> (fails the poverty<span class="sc">-</span>focus axiom)</span></code></pre></div>
+<div class="sourceCode" id="cb114"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb114-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb114-1" tabindex="-1"></a>✔️ mainly useful <span class="cf">for</span> studies of the income of the elderly following EU definitions</span>
+<span id="cb114-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb114-2" tabindex="-1"></a>✔️ a ratio of medians</span>
+<span id="cb114-3"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb114-3" tabindex="-1"></a>✔️ less sensitive to outliers</span>
+<span id="cb114-4"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb114-4" tabindex="-1"></a>❌ solely a measure of medians and does not fully account <span class="cf">for</span> the income distribution</span>
+<span id="cb114-5"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb114-5" tabindex="-1"></a>❌ not very common outside of the EU</span>
+<span id="cb114-6"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb114-6" tabindex="-1"></a>❌ hard to interpret</span>
+<span id="cb114-7"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb114-7" tabindex="-1"></a>❌ <span class="fu">not</span> (necessarily) a dependency measure</span>
+<span id="cb114-8"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb114-8" tabindex="-1"></a>❌ not an inequality <span class="fu">measure</span> (fails the Pigou<span class="sc">-</span>Dalton principle)</span>
+<span id="cb114-9"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb114-9" tabindex="-1"></a>❌ <span class="fu">not</span> (exactly) a poverty <span class="fu">measure</span> (fails the poverty<span class="sc">-</span>focus axiom)</span></code></pre></div>
 <p>The relative median income ratio (RMIR) is the ratio of the median income of people aged above a value (65) to the median of people aged below the same value. In mathematical terms,</p>
 <p><span class="math display">\[
 rmir = \frac{median\{y_i; age_i &gt;65 \}}{median\{y_i; age_i \leq 65 \}}.
@@ -272,149 +272,149 @@ <h2><span class="header-section-number">3.3</span> Relative Median Income Ratio
 <h3><span class="header-section-number">3.3.1</span> Replication Example</h3>
 <p>The R <code>vardpoor</code> package <span class="citation">(<label for="tufte-mn-33" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-33" class="margin-toggle">Breidaks, Liberts, and Ivanova 2016<span class="marginnote">Breidaks, Juris, Martins Liberts, and Santa Ivanova. 2016. <span>“Vardpoor: Estimation of Indicators on Social Exclusion and Poverty and Its Linearization, Variance Estimation.”</span> Riga, Latvia: CSB.</span>)</span>, created by researchers at the Central Statistical Bureau of Latvia, includes a RMIR coefficient calculation using the ultimate cluster method. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb116"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb116-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb116-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb116-3"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-3" tabindex="-1"></a></span>
-<span id="cb116-4"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb116-5"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb116-6"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-6" tabindex="-1"></a></span>
-<span id="cb116-7"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb116-8"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
-<span id="cb116-9"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-9" tabindex="-1"></a></span>
-<span id="cb116-10"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-10" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb116-11"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
-<span id="cb116-12"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-12" tabindex="-1"></a></span>
-<span id="cb116-13"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
-<span id="cb116-14"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
-<span id="cb116-15"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-15" tabindex="-1"></a></span>
-<span id="cb116-16"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
-<span id="cb116-17"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
-<span id="cb116-18"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-18" tabindex="-1"></a></span>
-<span id="cb116-19"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
-<span id="cb116-20"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
-<span id="cb116-21"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-21" tabindex="-1"></a></span>
-<span id="cb116-22"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-22" tabindex="-1"></a><span class="co"># calculate the rmir coefficient</span></span>
-<span id="cb116-23"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
-<span id="cb116-24"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-24" tabindex="-1"></a>varpoord_rmir_calculation <span class="ot">&lt;-</span></span>
-<span id="cb116-25"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
-<span id="cb116-26"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
-<span id="cb116-27"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
-<span id="cb116-28"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-28" tabindex="-1"></a>    </span>
-<span id="cb116-29"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
-<span id="cb116-30"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
-<span id="cb116-31"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-31" tabindex="-1"></a>    </span>
-<span id="cb116-32"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb116-33"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb116-34"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-34" tabindex="-1"></a>    </span>
-<span id="cb116-35"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb116-36"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb116-37"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-37" tabindex="-1"></a>    </span>
-<span id="cb116-38"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
-<span id="cb116-39"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
-<span id="cb116-40"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-40" tabindex="-1"></a>    </span>
-<span id="cb116-41"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
-<span id="cb116-42"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-42" tabindex="-1"></a>    </span>
-<span id="cb116-43"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
-<span id="cb116-44"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
-<span id="cb116-45"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-45" tabindex="-1"></a>    </span>
-<span id="cb116-46"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
-<span id="cb116-47"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
-<span id="cb116-48"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-48" tabindex="-1"></a>    </span>
-<span id="cb116-49"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-49" tabindex="-1"></a>    <span class="co"># age variable</span></span>
-<span id="cb116-50"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-50" tabindex="-1"></a>    <span class="at">age =</span> <span class="st">&quot;age&quot;</span>,</span>
-<span id="cb116-51"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-51" tabindex="-1"></a>    </span>
-<span id="cb116-52"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-52" tabindex="-1"></a>    <span class="co"># rmir coefficient function</span></span>
-<span id="cb116-53"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-53" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linrmir&quot;</span>,</span>
-<span id="cb116-54"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-54" tabindex="-1"></a>    </span>
-<span id="cb116-55"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-55" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
-<span id="cb116-56"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-56" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
-<span id="cb116-57"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-57" tabindex="-1"></a>    </span>
-<span id="cb116-58"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-58" tabindex="-1"></a>  )</span>
-<span id="cb116-59"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-59" tabindex="-1"></a></span>
-<span id="cb116-60"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-60" tabindex="-1"></a></span>
-<span id="cb116-61"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-61" tabindex="-1"></a></span>
-<span id="cb116-62"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-62" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb116-63"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-63" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
-<span id="cb116-64"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-64" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
-<span id="cb116-65"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-65" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb116-66"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-66" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb116-67"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-67" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb116-68"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-68" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb116-69"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-69" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
-<span id="cb116-70"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-70" tabindex="-1"></a>  )</span>
-<span id="cb116-71"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-71" tabindex="-1"></a></span>
-<span id="cb116-72"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-72" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
-<span id="cb116-73"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-73" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
-<span id="cb116-74"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-74" tabindex="-1"></a></span>
-<span id="cb116-75"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-75" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
-<span id="cb116-76"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb116-76" tabindex="-1"></a>varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
+<div class="sourceCode" id="cb115"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb115-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb115-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb115-3"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-3" tabindex="-1"></a></span>
+<span id="cb115-4"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb115-5"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb115-6"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-6" tabindex="-1"></a></span>
+<span id="cb115-7"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb115-8"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
+<span id="cb115-9"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-9" tabindex="-1"></a></span>
+<span id="cb115-10"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-10" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb115-11"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
+<span id="cb115-12"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-12" tabindex="-1"></a></span>
+<span id="cb115-13"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
+<span id="cb115-14"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
+<span id="cb115-15"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-15" tabindex="-1"></a></span>
+<span id="cb115-16"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
+<span id="cb115-17"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
+<span id="cb115-18"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-18" tabindex="-1"></a></span>
+<span id="cb115-19"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
+<span id="cb115-20"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
+<span id="cb115-21"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-21" tabindex="-1"></a></span>
+<span id="cb115-22"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-22" tabindex="-1"></a><span class="co"># calculate the rmir coefficient</span></span>
+<span id="cb115-23"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
+<span id="cb115-24"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-24" tabindex="-1"></a>varpoord_rmir_calculation <span class="ot">&lt;-</span></span>
+<span id="cb115-25"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
+<span id="cb115-26"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
+<span id="cb115-27"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
+<span id="cb115-28"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-28" tabindex="-1"></a>    </span>
+<span id="cb115-29"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
+<span id="cb115-30"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
+<span id="cb115-31"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-31" tabindex="-1"></a>    </span>
+<span id="cb115-32"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb115-33"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb115-34"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-34" tabindex="-1"></a>    </span>
+<span id="cb115-35"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb115-36"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb115-37"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-37" tabindex="-1"></a>    </span>
+<span id="cb115-38"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
+<span id="cb115-39"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
+<span id="cb115-40"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-40" tabindex="-1"></a>    </span>
+<span id="cb115-41"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
+<span id="cb115-42"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-42" tabindex="-1"></a>    </span>
+<span id="cb115-43"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
+<span id="cb115-44"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
+<span id="cb115-45"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-45" tabindex="-1"></a>    </span>
+<span id="cb115-46"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
+<span id="cb115-47"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
+<span id="cb115-48"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-48" tabindex="-1"></a>    </span>
+<span id="cb115-49"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-49" tabindex="-1"></a>    <span class="co"># age variable</span></span>
+<span id="cb115-50"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-50" tabindex="-1"></a>    <span class="at">age =</span> <span class="st">&quot;age&quot;</span>,</span>
+<span id="cb115-51"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-51" tabindex="-1"></a>    </span>
+<span id="cb115-52"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-52" tabindex="-1"></a>    <span class="co"># rmir coefficient function</span></span>
+<span id="cb115-53"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-53" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linrmir&quot;</span>,</span>
+<span id="cb115-54"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-54" tabindex="-1"></a>    </span>
+<span id="cb115-55"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-55" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
+<span id="cb115-56"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-56" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
+<span id="cb115-57"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-57" tabindex="-1"></a>    </span>
+<span id="cb115-58"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-58" tabindex="-1"></a>  )</span>
+<span id="cb115-59"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-59" tabindex="-1"></a></span>
+<span id="cb115-60"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-60" tabindex="-1"></a></span>
+<span id="cb115-61"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-61" tabindex="-1"></a></span>
+<span id="cb115-62"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-62" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb115-63"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-63" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
+<span id="cb115-64"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-64" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
+<span id="cb115-65"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-65" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb115-66"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-66" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb115-67"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-67" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb115-68"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-68" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb115-69"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-69" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
+<span id="cb115-70"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-70" tabindex="-1"></a>  )</span>
+<span id="cb115-71"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-71" tabindex="-1"></a></span>
+<span id="cb115-72"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-72" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
+<span id="cb115-73"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-73" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
+<span id="cb115-74"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-74" tabindex="-1"></a></span>
+<span id="cb115-75"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-75" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
+<span id="cb115-76"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb115-76" tabindex="-1"></a>varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
 <pre><code>## [1] 0.9330361</code></pre>
-<div class="sourceCode" id="cb118"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb118-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb118-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyrmir</span>( <span class="sc">~</span> eqincome , des_eusilc, <span class="at">age =</span> <span class="sc">~</span> age))</span></code></pre></div>
+<div class="sourceCode" id="cb117"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb117-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb117-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyrmir</span>( <span class="sc">~</span> eqincome , des_eusilc, <span class="at">age =</span> <span class="sc">~</span> age))</span></code></pre></div>
 <pre><code>##  eqincome 
 ## 0.9330361</code></pre>
-<div class="sourceCode" id="cb120"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb120-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb120-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
-<span id="cb120-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb120-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
-<span id="cb120-3"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb120-3" tabindex="-1"></a>lin_rmir_varpoord <span class="ot">&lt;-</span> varpoord_rmir_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_rmir</span>
-<span id="cb120-4"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb120-4" tabindex="-1"></a><span class="co"># convey</span></span>
-<span id="cb120-5"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb120-5" tabindex="-1"></a>lin_rmir_convey <span class="ot">&lt;-</span></span>
-<span id="cb120-6"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb120-6" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svyrmir</span>( <span class="sc">~</span> eqincome , des_eusilc, <span class="at">age =</span> <span class="sc">~</span> age), <span class="st">&quot;lin&quot;</span>)</span>
-<span id="cb120-7"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb120-7" tabindex="-1"></a></span>
-<span id="cb120-8"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb120-8" tabindex="-1"></a><span class="co"># check equality</span></span>
-<span id="cb120-9"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb120-9" tabindex="-1"></a><span class="fu">all.equal</span>(lin_rmir_varpoord, lin_rmir_convey[, <span class="dv">1</span>])</span></code></pre></div>
+<div class="sourceCode" id="cb119"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb119-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb119-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
+<span id="cb119-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb119-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
+<span id="cb119-3"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb119-3" tabindex="-1"></a>lin_rmir_varpoord <span class="ot">&lt;-</span> varpoord_rmir_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_rmir</span>
+<span id="cb119-4"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb119-4" tabindex="-1"></a><span class="co"># convey</span></span>
+<span id="cb119-5"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb119-5" tabindex="-1"></a>lin_rmir_convey <span class="ot">&lt;-</span></span>
+<span id="cb119-6"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb119-6" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svyrmir</span>( <span class="sc">~</span> eqincome , des_eusilc, <span class="at">age =</span> <span class="sc">~</span> age), <span class="st">&quot;lin&quot;</span>)</span>
+<span id="cb119-7"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb119-7" tabindex="-1"></a></span>
+<span id="cb119-8"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb119-8" tabindex="-1"></a><span class="co"># check equality</span></span>
+<span id="cb119-9"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb119-9" tabindex="-1"></a><span class="fu">all.equal</span>(lin_rmir_varpoord, lin_rmir_convey[, <span class="dv">1</span>])</span></code></pre></div>
 <pre><code>## [1] TRUE</code></pre>
-<div class="sourceCode" id="cb122"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb122-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb122-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
-<span id="cb122-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb122-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyrmir</span>( <span class="sc">~</span> eqincome , des_eusilc, <span class="at">age =</span> <span class="sc">~</span> age) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb121"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb121-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb121-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
+<span id="cb121-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb121-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyrmir</span>( <span class="sc">~</span> eqincome , des_eusilc, <span class="at">age =</span> <span class="sc">~</span> age) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
 <pre><code>##             eqincome
 ## eqincome 0.000127444</code></pre>
-<div class="sourceCode" id="cb124"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb124-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb124-1" tabindex="-1"></a>varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb123"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb123-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb123-1" tabindex="-1"></a>varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.0001272137</code></pre>
-<div class="sourceCode" id="cb126"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb126-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb126-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
-<span id="cb126-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb126-2" tabindex="-1"></a>varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb125"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb125-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb125-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
+<span id="cb125-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb125-2" tabindex="-1"></a>varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.0112789</code></pre>
-<div class="sourceCode" id="cb128"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb128-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb128-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyrmir</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">age =</span> <span class="sc">~</span> age)) </span></code></pre></div>
+<div class="sourceCode" id="cb127"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb127-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb127-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyrmir</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">age =</span> <span class="sc">~</span> age)) </span></code></pre></div>
 <pre><code>##            eqincome
 ## eqincome 0.01128911</code></pre>
 <p>The variance estimate is computed by using the approximation defined in <a href="2-var.html#var">2</a>, while the linearized variable <span class="math inline">\(z\)</span> is defined by <a href="2.1-lin.html#lin">2.1</a>. The functions <code>convey::svyrmir</code> and <code>vardpoor::linrmir</code> produce the same linearized variable <span class="math inline">\(z\)</span>.</p>
 <p>However, the measures of uncertainty do not line up, because <code>library(vardpoor)</code> defaults to an ultimate cluster method that can be replicated with an alternative setup of the <code>survey.design</code> object.</p>
-<div class="sourceCode" id="cb130"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb130-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
-<span id="cb130-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
-<span id="cb130-3"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
-<span id="cb130-4"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-4" tabindex="-1"></a></span>
-<span id="cb130-5"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
-<span id="cb130-6"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
-<span id="cb130-7"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-7" tabindex="-1"></a></span>
-<span id="cb130-8"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
-<span id="cb130-9"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
-<span id="cb130-10"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-10" tabindex="-1"></a></span>
-<span id="cb130-11"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb130-12"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
-<span id="cb130-13"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb130-14"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb130-15"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb130-16"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb130-17"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb130-18"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
-<span id="cb130-19"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
-<span id="cb130-20"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-20" tabindex="-1"></a>  )</span>
-<span id="cb130-21"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-21" tabindex="-1"></a></span>
-<span id="cb130-22"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
-<span id="cb130-23"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb130-24"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
-<span id="cb130-25"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-25" tabindex="-1"></a></span>
-<span id="cb130-26"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-26" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb130-27"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-27" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
-<span id="cb130-28"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-28" tabindex="-1"></a>  <span class="fu">attr</span>(</span>
-<span id="cb130-29"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-29" tabindex="-1"></a>    <span class="fu">svyrmir</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster , <span class="at">age =</span> <span class="sc">~</span> age) ,</span>
-<span id="cb130-30"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-30" tabindex="-1"></a>    <span class="st">&#39;var&#39;</span></span>
-<span id="cb130-31"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-31" tabindex="-1"></a>  )[<span class="dv">1</span>],</span>
-<span id="cb130-32"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-32" tabindex="-1"></a>  varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span>
-<span id="cb130-33"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-33" tabindex="-1"></a>))</span>
-<span id="cb130-34"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-34" tabindex="-1"></a></span>
-<span id="cb130-35"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-35" tabindex="-1"></a></span>
-<span id="cb130-36"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-36" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb130-37"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-37" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(<span class="fu">SE</span>(</span>
-<span id="cb130-38"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-38" tabindex="-1"></a>  <span class="fu">svyrmir</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster, <span class="at">age =</span> <span class="sc">~</span> age)</span>
-<span id="cb130-39"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb130-39" tabindex="-1"></a>)[<span class="dv">1</span>], varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se))</span></code></pre></div>
+<div class="sourceCode" id="cb129"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb129-1"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
+<span id="cb129-2"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
+<span id="cb129-3"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
+<span id="cb129-4"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-4" tabindex="-1"></a></span>
+<span id="cb129-5"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
+<span id="cb129-6"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
+<span id="cb129-7"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-7" tabindex="-1"></a></span>
+<span id="cb129-8"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
+<span id="cb129-9"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
+<span id="cb129-10"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-10" tabindex="-1"></a></span>
+<span id="cb129-11"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb129-12"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
+<span id="cb129-13"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb129-14"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb129-15"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb129-16"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb129-17"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb129-18"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
+<span id="cb129-19"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
+<span id="cb129-20"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-20" tabindex="-1"></a>  )</span>
+<span id="cb129-21"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-21" tabindex="-1"></a></span>
+<span id="cb129-22"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
+<span id="cb129-23"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb129-24"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
+<span id="cb129-25"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-25" tabindex="-1"></a></span>
+<span id="cb129-26"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-26" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb129-27"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-27" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
+<span id="cb129-28"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-28" tabindex="-1"></a>  <span class="fu">attr</span>(</span>
+<span id="cb129-29"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-29" tabindex="-1"></a>    <span class="fu">svyrmir</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster , <span class="at">age =</span> <span class="sc">~</span> age) ,</span>
+<span id="cb129-30"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-30" tabindex="-1"></a>    <span class="st">&#39;var&#39;</span></span>
+<span id="cb129-31"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-31" tabindex="-1"></a>  )[<span class="dv">1</span>],</span>
+<span id="cb129-32"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-32" tabindex="-1"></a>  varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span>
+<span id="cb129-33"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-33" tabindex="-1"></a>))</span>
+<span id="cb129-34"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-34" tabindex="-1"></a></span>
+<span id="cb129-35"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-35" tabindex="-1"></a></span>
+<span id="cb129-36"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-36" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb129-37"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-37" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(<span class="fu">SE</span>(</span>
+<span id="cb129-38"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-38" tabindex="-1"></a>  <span class="fu">svyrmir</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster, <span class="at">age =</span> <span class="sc">~</span> age)</span>
+<span id="cb129-39"><a href="3.3-relative-median-income-ratio-svyrmir.html#cb129-39" tabindex="-1"></a>)[<span class="dv">1</span>], varpoord_rmir_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se))</span></code></pre></div>
 <p>For additional usage examples of <code>svyrmir</code>, type <code>?convey::svyrmir</code> in the R console.</p>
 </div>
 </div>
diff --git a/docs/3.4-relative-median-poverty-gap-svyrmpg.html b/docs/3.4-relative-median-poverty-gap-svyrmpg.html
index 5b4528f..ab232b5 100644
--- a/docs/3.4-relative-median-poverty-gap-svyrmpg.html
+++ b/docs/3.4-relative-median-poverty-gap-svyrmpg.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
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@@ -253,11 +253,11 @@
 <div class="col-sm-12">
 <div id="relative-median-poverty-gap-svyrmpg" class="section level2" number="3.4">
 <h2><span class="header-section-number">3.4</span> Relative Median Poverty Gap (svyrmpg)</h2>
-<div class="sourceCode" id="cb131"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb131-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-1" tabindex="-1"></a>✔️ how poor are those below the ARPT?</span>
-<span id="cb131-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-2" tabindex="-1"></a>✔️ median poverty gap expressed as a percentage of the threshold</span>
-<span id="cb131-3"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-3" tabindex="-1"></a>✔️ useful <span class="cf">for</span> understanding the depth of poverty</span>
-<span id="cb131-4"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-4" tabindex="-1"></a>❌ not common outside of the EU</span>
-<span id="cb131-5"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-5" tabindex="-1"></a>❌ not immediately interpretable <span class="cf">in</span> terms of income</span></code></pre></div>
+<div class="sourceCode" id="cb130"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb130-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb130-1" tabindex="-1"></a>✔️ how poor are those below the ARPT?</span>
+<span id="cb130-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb130-2" tabindex="-1"></a>✔️ median poverty gap expressed as a percentage of the threshold</span>
+<span id="cb130-3"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb130-3" tabindex="-1"></a>✔️ useful <span class="cf">for</span> understanding the depth of poverty</span>
+<span id="cb130-4"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb130-4" tabindex="-1"></a>❌ not common outside of the EU</span>
+<span id="cb130-5"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb130-5" tabindex="-1"></a>❌ not immediately interpretable <span class="cf">in</span> terms of income</span></code></pre></div>
 <p>The relative median poverty gap (RMPG) is the relative difference between the median income of people having income below the ARPT and the ARPT itself:</p>
 <p><span class="math display">\[
 rmpg = \frac{median\{y_i, y_i&lt;arpt\}-arpt}{arpt}
@@ -268,144 +268,144 @@ <h2><span class="header-section-number">3.4</span> Relative Median Poverty Gap (
 <h3><span class="header-section-number">3.4.1</span> Replication Example</h3>
 <p>The R <code>vardpoor</code> package <span class="citation">(<label for="tufte-mn-36" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-36" class="margin-toggle">Breidaks, Liberts, and Ivanova 2016<span class="marginnote">Breidaks, Juris, Martins Liberts, and Santa Ivanova. 2016. <span>“Vardpoor: Estimation of Indicators on Social Exclusion and Poverty and Its Linearization, Variance Estimation.”</span> Riga, Latvia: CSB.</span>)</span>, created by researchers at the Central Statistical Bureau of Latvia, includes a RMPG coefficient calculation using the ultimate cluster method. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb132"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb132-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb132-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb132-3"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-3" tabindex="-1"></a></span>
-<span id="cb132-4"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb132-5"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb132-6"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-6" tabindex="-1"></a></span>
-<span id="cb132-7"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb132-8"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
-<span id="cb132-9"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-9" tabindex="-1"></a></span>
-<span id="cb132-10"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-10" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb132-11"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
-<span id="cb132-12"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-12" tabindex="-1"></a></span>
-<span id="cb132-13"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
-<span id="cb132-14"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
-<span id="cb132-15"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-15" tabindex="-1"></a></span>
-<span id="cb132-16"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
-<span id="cb132-17"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
-<span id="cb132-18"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-18" tabindex="-1"></a></span>
-<span id="cb132-19"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
-<span id="cb132-20"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
-<span id="cb132-21"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-21" tabindex="-1"></a></span>
-<span id="cb132-22"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-22" tabindex="-1"></a><span class="co"># calculate the rmpg coefficient</span></span>
-<span id="cb132-23"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
-<span id="cb132-24"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-24" tabindex="-1"></a>varpoord_rmpg_calculation <span class="ot">&lt;-</span></span>
-<span id="cb132-25"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
-<span id="cb132-26"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
-<span id="cb132-27"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
-<span id="cb132-28"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-28" tabindex="-1"></a>    </span>
-<span id="cb132-29"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
-<span id="cb132-30"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
-<span id="cb132-31"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-31" tabindex="-1"></a>    </span>
-<span id="cb132-32"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb132-33"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb132-34"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-34" tabindex="-1"></a>    </span>
-<span id="cb132-35"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb132-36"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb132-37"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-37" tabindex="-1"></a>    </span>
-<span id="cb132-38"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
-<span id="cb132-39"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
-<span id="cb132-40"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-40" tabindex="-1"></a>    </span>
-<span id="cb132-41"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
-<span id="cb132-42"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-42" tabindex="-1"></a>    </span>
-<span id="cb132-43"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
-<span id="cb132-44"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
-<span id="cb132-45"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-45" tabindex="-1"></a>    </span>
-<span id="cb132-46"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
-<span id="cb132-47"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
-<span id="cb132-48"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-48" tabindex="-1"></a>    </span>
-<span id="cb132-49"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-49" tabindex="-1"></a>    <span class="co"># rmpg coefficient function</span></span>
-<span id="cb132-50"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linrmpg&quot;</span>,</span>
-<span id="cb132-51"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-51" tabindex="-1"></a>    </span>
-<span id="cb132-52"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
-<span id="cb132-53"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
-<span id="cb132-54"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-54" tabindex="-1"></a>    </span>
-<span id="cb132-55"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-55" tabindex="-1"></a>  )</span>
-<span id="cb132-56"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-56" tabindex="-1"></a></span>
-<span id="cb132-57"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-57" tabindex="-1"></a></span>
-<span id="cb132-58"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-58" tabindex="-1"></a></span>
-<span id="cb132-59"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-59" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb132-60"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-60" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
-<span id="cb132-61"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-61" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
-<span id="cb132-62"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-62" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb132-63"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-63" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb132-64"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-64" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb132-65"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-65" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb132-66"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-66" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
-<span id="cb132-67"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-67" tabindex="-1"></a>  )</span>
-<span id="cb132-68"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-68" tabindex="-1"></a></span>
-<span id="cb132-69"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-69" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
-<span id="cb132-70"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-70" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
-<span id="cb132-71"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-71" tabindex="-1"></a></span>
-<span id="cb132-72"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-72" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
-<span id="cb132-73"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb132-73" tabindex="-1"></a>varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
+<div class="sourceCode" id="cb131"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb131-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb131-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb131-3"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-3" tabindex="-1"></a></span>
+<span id="cb131-4"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb131-5"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb131-6"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-6" tabindex="-1"></a></span>
+<span id="cb131-7"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb131-8"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
+<span id="cb131-9"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-9" tabindex="-1"></a></span>
+<span id="cb131-10"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-10" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb131-11"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
+<span id="cb131-12"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-12" tabindex="-1"></a></span>
+<span id="cb131-13"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
+<span id="cb131-14"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
+<span id="cb131-15"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-15" tabindex="-1"></a></span>
+<span id="cb131-16"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
+<span id="cb131-17"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
+<span id="cb131-18"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-18" tabindex="-1"></a></span>
+<span id="cb131-19"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
+<span id="cb131-20"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
+<span id="cb131-21"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-21" tabindex="-1"></a></span>
+<span id="cb131-22"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-22" tabindex="-1"></a><span class="co"># calculate the rmpg coefficient</span></span>
+<span id="cb131-23"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
+<span id="cb131-24"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-24" tabindex="-1"></a>varpoord_rmpg_calculation <span class="ot">&lt;-</span></span>
+<span id="cb131-25"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
+<span id="cb131-26"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
+<span id="cb131-27"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
+<span id="cb131-28"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-28" tabindex="-1"></a>    </span>
+<span id="cb131-29"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
+<span id="cb131-30"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
+<span id="cb131-31"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-31" tabindex="-1"></a>    </span>
+<span id="cb131-32"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb131-33"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb131-34"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-34" tabindex="-1"></a>    </span>
+<span id="cb131-35"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb131-36"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb131-37"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-37" tabindex="-1"></a>    </span>
+<span id="cb131-38"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
+<span id="cb131-39"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
+<span id="cb131-40"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-40" tabindex="-1"></a>    </span>
+<span id="cb131-41"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
+<span id="cb131-42"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-42" tabindex="-1"></a>    </span>
+<span id="cb131-43"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
+<span id="cb131-44"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
+<span id="cb131-45"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-45" tabindex="-1"></a>    </span>
+<span id="cb131-46"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
+<span id="cb131-47"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
+<span id="cb131-48"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-48" tabindex="-1"></a>    </span>
+<span id="cb131-49"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-49" tabindex="-1"></a>    <span class="co"># rmpg coefficient function</span></span>
+<span id="cb131-50"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linrmpg&quot;</span>,</span>
+<span id="cb131-51"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-51" tabindex="-1"></a>    </span>
+<span id="cb131-52"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
+<span id="cb131-53"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
+<span id="cb131-54"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-54" tabindex="-1"></a>    </span>
+<span id="cb131-55"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-55" tabindex="-1"></a>  )</span>
+<span id="cb131-56"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-56" tabindex="-1"></a></span>
+<span id="cb131-57"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-57" tabindex="-1"></a></span>
+<span id="cb131-58"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-58" tabindex="-1"></a></span>
+<span id="cb131-59"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-59" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb131-60"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-60" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
+<span id="cb131-61"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-61" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
+<span id="cb131-62"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-62" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb131-63"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-63" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb131-64"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-64" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb131-65"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-65" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb131-66"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-66" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
+<span id="cb131-67"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-67" tabindex="-1"></a>  )</span>
+<span id="cb131-68"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-68" tabindex="-1"></a></span>
+<span id="cb131-69"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-69" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
+<span id="cb131-70"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-70" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
+<span id="cb131-71"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-71" tabindex="-1"></a></span>
+<span id="cb131-72"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-72" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
+<span id="cb131-73"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb131-73" tabindex="-1"></a>varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
 <pre><code>## [1] 18.9286</code></pre>
-<div class="sourceCode" id="cb134"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb134-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb134-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb133"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb133-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb133-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>## eqincome 
 ##  18.9286</code></pre>
-<div class="sourceCode" id="cb136"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb136-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb136-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
-<span id="cb136-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb136-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
-<span id="cb136-3"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb136-3" tabindex="-1"></a>lin_rmpg_varpoord <span class="ot">&lt;-</span> varpoord_rmpg_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_rmpg</span>
-<span id="cb136-4"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb136-4" tabindex="-1"></a><span class="co"># convey</span></span>
-<span id="cb136-5"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb136-5" tabindex="-1"></a>lin_rmpg_convey <span class="ot">&lt;-</span> <span class="fu">attr</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc), <span class="st">&quot;lin&quot;</span>)</span>
-<span id="cb136-6"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb136-6" tabindex="-1"></a></span>
-<span id="cb136-7"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb136-7" tabindex="-1"></a><span class="co"># check equality</span></span>
-<span id="cb136-8"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb136-8" tabindex="-1"></a><span class="fu">all.equal</span>(lin_rmpg_varpoord, <span class="dv">100</span> <span class="sc">*</span> lin_rmpg_convey[, <span class="dv">1</span>])</span></code></pre></div>
+<div class="sourceCode" id="cb135"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb135-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb135-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
+<span id="cb135-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb135-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
+<span id="cb135-3"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb135-3" tabindex="-1"></a>lin_rmpg_varpoord <span class="ot">&lt;-</span> varpoord_rmpg_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_rmpg</span>
+<span id="cb135-4"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb135-4" tabindex="-1"></a><span class="co"># convey</span></span>
+<span id="cb135-5"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb135-5" tabindex="-1"></a>lin_rmpg_convey <span class="ot">&lt;-</span> <span class="fu">attr</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc), <span class="st">&quot;lin&quot;</span>)</span>
+<span id="cb135-6"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb135-6" tabindex="-1"></a></span>
+<span id="cb135-7"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb135-7" tabindex="-1"></a><span class="co"># check equality</span></span>
+<span id="cb135-8"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb135-8" tabindex="-1"></a><span class="fu">all.equal</span>(lin_rmpg_varpoord, <span class="dv">100</span> <span class="sc">*</span> lin_rmpg_convey[, <span class="dv">1</span>])</span></code></pre></div>
 <pre><code>## [1] TRUE</code></pre>
-<div class="sourceCode" id="cb138"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb138-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb138-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
-<span id="cb138-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb138-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
+<div class="sourceCode" id="cb137"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb137-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb137-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
+<span id="cb137-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb137-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
 <pre><code>##          eqincome
 ## eqincome 0.332234</code></pre>
-<div class="sourceCode" id="cb140"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb140-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb140-1" tabindex="-1"></a>varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb139"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb139-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb139-1" tabindex="-1"></a>varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.3316454</code></pre>
-<div class="sourceCode" id="cb142"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb142-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb142-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
-<span id="cb142-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb142-2" tabindex="-1"></a>varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb141"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb141-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb141-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
+<span id="cb141-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb141-2" tabindex="-1"></a>varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.5758866</code></pre>
-<div class="sourceCode" id="cb144"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb144-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb144-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb143"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb143-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb143-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>##           eqincome
 ## eqincome 0.5763974</code></pre>
 <p>The variance estimate is computed by using the approximation defined in <a href="2-var.html#var">2</a>, while the linearized variable <span class="math inline">\(z\)</span> is defined by <a href="2.1-lin.html#lin">2.1</a>. The functions <code>convey::svyrmpg</code> and <code>vardpoor::linrmpg</code> produce the same linearized variable <span class="math inline">\(z\)</span>.</p>
 <p>However, the measures of uncertainty do not line up, because <code>library(vardpoor)</code> defaults to an ultimate cluster method that can be replicated with an alternative setup of the <code>survey.design</code> object.</p>
-<div class="sourceCode" id="cb146"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb146-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
-<span id="cb146-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
-<span id="cb146-3"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
-<span id="cb146-4"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-4" tabindex="-1"></a></span>
-<span id="cb146-5"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
-<span id="cb146-6"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
-<span id="cb146-7"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-7" tabindex="-1"></a></span>
-<span id="cb146-8"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
-<span id="cb146-9"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
-<span id="cb146-10"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-10" tabindex="-1"></a></span>
-<span id="cb146-11"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb146-12"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
-<span id="cb146-13"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb146-14"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb146-15"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb146-16"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb146-17"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb146-18"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
-<span id="cb146-19"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
-<span id="cb146-20"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-20" tabindex="-1"></a>  )</span>
-<span id="cb146-21"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-21" tabindex="-1"></a></span>
-<span id="cb146-22"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
-<span id="cb146-23"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb146-24"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
-<span id="cb146-25"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-25" tabindex="-1"></a></span>
-<span id="cb146-26"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-26" tabindex="-1"></a></span>
-<span id="cb146-27"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-27" tabindex="-1"></a></span>
-<span id="cb146-28"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-28" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb146-29"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-29" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
-<span id="cb146-30"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-30" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>)[<span class="dv">1</span>] <span class="sc">*</span> <span class="dv">10000</span> ,</span>
-<span id="cb146-31"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-31" tabindex="-1"></a>  varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span>
-<span id="cb146-32"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-32" tabindex="-1"></a>))</span>
-<span id="cb146-33"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-33" tabindex="-1"></a></span>
-<span id="cb146-34"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-34" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb146-35"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-35" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(<span class="fu">SE</span>(</span>
-<span id="cb146-36"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-36" tabindex="-1"></a>  <span class="fu">svyrmpg</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster)</span>
-<span id="cb146-37"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-37" tabindex="-1"></a>)[<span class="dv">1</span>] <span class="sc">*</span> <span class="dv">100</span> ,</span>
-<span id="cb146-38"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb146-38" tabindex="-1"></a>varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se))</span></code></pre></div>
+<div class="sourceCode" id="cb145"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb145-1"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
+<span id="cb145-2"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
+<span id="cb145-3"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
+<span id="cb145-4"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-4" tabindex="-1"></a></span>
+<span id="cb145-5"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
+<span id="cb145-6"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
+<span id="cb145-7"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-7" tabindex="-1"></a></span>
+<span id="cb145-8"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
+<span id="cb145-9"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
+<span id="cb145-10"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-10" tabindex="-1"></a></span>
+<span id="cb145-11"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb145-12"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
+<span id="cb145-13"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb145-14"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb145-15"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb145-16"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb145-17"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb145-18"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
+<span id="cb145-19"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
+<span id="cb145-20"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-20" tabindex="-1"></a>  )</span>
+<span id="cb145-21"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-21" tabindex="-1"></a></span>
+<span id="cb145-22"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
+<span id="cb145-23"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb145-24"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
+<span id="cb145-25"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-25" tabindex="-1"></a></span>
+<span id="cb145-26"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-26" tabindex="-1"></a></span>
+<span id="cb145-27"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-27" tabindex="-1"></a></span>
+<span id="cb145-28"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-28" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb145-29"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-29" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
+<span id="cb145-30"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-30" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svyrmpg</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>)[<span class="dv">1</span>] <span class="sc">*</span> <span class="dv">10000</span> ,</span>
+<span id="cb145-31"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-31" tabindex="-1"></a>  varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span>
+<span id="cb145-32"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-32" tabindex="-1"></a>))</span>
+<span id="cb145-33"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-33" tabindex="-1"></a></span>
+<span id="cb145-34"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-34" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb145-35"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-35" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(<span class="fu">SE</span>(</span>
+<span id="cb145-36"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-36" tabindex="-1"></a>  <span class="fu">svyrmpg</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster)</span>
+<span id="cb145-37"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-37" tabindex="-1"></a>)[<span class="dv">1</span>] <span class="sc">*</span> <span class="dv">100</span> ,</span>
+<span id="cb145-38"><a href="3.4-relative-median-poverty-gap-svyrmpg.html#cb145-38" tabindex="-1"></a>varpoord_rmpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se))</span></code></pre></div>
 <p>For additional usage examples of <code>svyrmpg</code>, type <code>?convey::svyrmpg</code> in the R console.</p>
 </div>
 </div>
diff --git a/docs/3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html b/docs/3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html
index 415eebd..51d738c 100644
--- a/docs/3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html
+++ b/docs/3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,11 +253,11 @@
 <div class="col-sm-12">
 <div id="median-income-below-the-at-risk-of-poverty-threshold-svypoormed" class="section level2" number="3.5">
 <h2><span class="header-section-number">3.5</span> Median Income Below the At Risk of Poverty Threshold (svypoormed)</h2>
-<div class="sourceCode" id="cb147"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb147-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-1" tabindex="-1"></a>✔️ median income among those below the threshold</span>
-<span id="cb147-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-2" tabindex="-1"></a>✔️ useful <span class="cf">for</span> understanding the depth of poverty</span>
-<span id="cb147-3"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-3" tabindex="-1"></a>✔️ related to the RMPG</span>
-<span id="cb147-4"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-4" tabindex="-1"></a>❌ not very common outside the EU</span>
-<span id="cb147-5"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-5" tabindex="-1"></a>❌ not immediately interpretable <span class="cf">in</span> terms of the poverty gap</span></code></pre></div>
+<div class="sourceCode" id="cb146"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb146-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb146-1" tabindex="-1"></a>✔️ median income among those below the threshold</span>
+<span id="cb146-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb146-2" tabindex="-1"></a>✔️ useful <span class="cf">for</span> understanding the depth of poverty</span>
+<span id="cb146-3"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb146-3" tabindex="-1"></a>✔️ related to the RMPG</span>
+<span id="cb146-4"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb146-4" tabindex="-1"></a>❌ not very common outside the EU</span>
+<span id="cb146-5"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb146-5" tabindex="-1"></a>❌ not immediately interpretable <span class="cf">in</span> terms of the poverty gap</span></code></pre></div>
 <p>Median income below the at-risk-of-poverty-threshold (POORMED) is median of incomes of people having the income below the ARPT:</p>
 <p><span class="math display">\[
 poormed = median\{y_i; y_i&lt; arpt\}
@@ -268,145 +268,145 @@ <h2><span class="header-section-number">3.5</span> Median Income Below the At Ri
 <h3><span class="header-section-number">3.5.1</span> Replication Example</h3>
 <p>The R <code>vardpoor</code> package <span class="citation">(<label for="tufte-mn-39" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-39" class="margin-toggle">Breidaks, Liberts, and Ivanova 2016<span class="marginnote">Breidaks, Juris, Martins Liberts, and Santa Ivanova. 2016. <span>“Vardpoor: Estimation of Indicators on Social Exclusion and Poverty and Its Linearization, Variance Estimation.”</span> Riga, Latvia: CSB.</span>)</span>, created by researchers at the Central Statistical Bureau of Latvia, includes a POORMED coefficient calculation using the ultimate cluster method. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb148"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb148-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb148-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb148-3"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-3" tabindex="-1"></a></span>
-<span id="cb148-4"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb148-5"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb148-6"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-6" tabindex="-1"></a></span>
-<span id="cb148-7"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb148-8"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
-<span id="cb148-9"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-9" tabindex="-1"></a></span>
-<span id="cb148-10"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-10" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb148-11"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
-<span id="cb148-12"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-12" tabindex="-1"></a></span>
-<span id="cb148-13"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
-<span id="cb148-14"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
-<span id="cb148-15"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-15" tabindex="-1"></a></span>
-<span id="cb148-16"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
-<span id="cb148-17"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
-<span id="cb148-18"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-18" tabindex="-1"></a></span>
-<span id="cb148-19"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
-<span id="cb148-20"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
-<span id="cb148-21"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-21" tabindex="-1"></a></span>
-<span id="cb148-22"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-22" tabindex="-1"></a><span class="co"># calculate the poormed coefficient</span></span>
-<span id="cb148-23"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
-<span id="cb148-24"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-24" tabindex="-1"></a>varpoord_poormed_calculation <span class="ot">&lt;-</span></span>
-<span id="cb148-25"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
-<span id="cb148-26"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
-<span id="cb148-27"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
-<span id="cb148-28"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-28" tabindex="-1"></a>    </span>
-<span id="cb148-29"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
-<span id="cb148-30"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
-<span id="cb148-31"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-31" tabindex="-1"></a>    </span>
-<span id="cb148-32"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb148-33"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb148-34"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-34" tabindex="-1"></a>    </span>
-<span id="cb148-35"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb148-36"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb148-37"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-37" tabindex="-1"></a>    </span>
-<span id="cb148-38"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
-<span id="cb148-39"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
-<span id="cb148-40"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-40" tabindex="-1"></a>    </span>
-<span id="cb148-41"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
-<span id="cb148-42"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-42" tabindex="-1"></a>    </span>
-<span id="cb148-43"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
-<span id="cb148-44"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
-<span id="cb148-45"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-45" tabindex="-1"></a>    </span>
-<span id="cb148-46"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
-<span id="cb148-47"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
-<span id="cb148-48"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-48" tabindex="-1"></a>    </span>
-<span id="cb148-49"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-49" tabindex="-1"></a>    <span class="co"># poormed coefficient function</span></span>
-<span id="cb148-50"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linpoormed&quot;</span>,</span>
-<span id="cb148-51"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-51" tabindex="-1"></a>    </span>
-<span id="cb148-52"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
-<span id="cb148-53"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
-<span id="cb148-54"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-54" tabindex="-1"></a>    </span>
-<span id="cb148-55"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-55" tabindex="-1"></a>  )</span>
-<span id="cb148-56"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-56" tabindex="-1"></a></span>
-<span id="cb148-57"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-57" tabindex="-1"></a></span>
-<span id="cb148-58"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-58" tabindex="-1"></a></span>
-<span id="cb148-59"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-59" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb148-60"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-60" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
-<span id="cb148-61"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-61" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
-<span id="cb148-62"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-62" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb148-63"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-63" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb148-64"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-64" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb148-65"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-65" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb148-66"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-66" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
-<span id="cb148-67"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-67" tabindex="-1"></a>  )</span>
-<span id="cb148-68"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-68" tabindex="-1"></a></span>
-<span id="cb148-69"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-69" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
-<span id="cb148-70"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-70" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
-<span id="cb148-71"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-71" tabindex="-1"></a></span>
-<span id="cb148-72"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-72" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
-<span id="cb148-73"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb148-73" tabindex="-1"></a>varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
+<div class="sourceCode" id="cb147"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb147-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb147-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb147-3"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-3" tabindex="-1"></a></span>
+<span id="cb147-4"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb147-5"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb147-6"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-6" tabindex="-1"></a></span>
+<span id="cb147-7"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb147-8"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
+<span id="cb147-9"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-9" tabindex="-1"></a></span>
+<span id="cb147-10"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-10" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb147-11"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
+<span id="cb147-12"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-12" tabindex="-1"></a></span>
+<span id="cb147-13"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
+<span id="cb147-14"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
+<span id="cb147-15"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-15" tabindex="-1"></a></span>
+<span id="cb147-16"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
+<span id="cb147-17"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
+<span id="cb147-18"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-18" tabindex="-1"></a></span>
+<span id="cb147-19"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
+<span id="cb147-20"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
+<span id="cb147-21"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-21" tabindex="-1"></a></span>
+<span id="cb147-22"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-22" tabindex="-1"></a><span class="co"># calculate the poormed coefficient</span></span>
+<span id="cb147-23"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
+<span id="cb147-24"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-24" tabindex="-1"></a>varpoord_poormed_calculation <span class="ot">&lt;-</span></span>
+<span id="cb147-25"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
+<span id="cb147-26"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
+<span id="cb147-27"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
+<span id="cb147-28"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-28" tabindex="-1"></a>    </span>
+<span id="cb147-29"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
+<span id="cb147-30"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
+<span id="cb147-31"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-31" tabindex="-1"></a>    </span>
+<span id="cb147-32"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb147-33"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb147-34"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-34" tabindex="-1"></a>    </span>
+<span id="cb147-35"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb147-36"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb147-37"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-37" tabindex="-1"></a>    </span>
+<span id="cb147-38"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
+<span id="cb147-39"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
+<span id="cb147-40"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-40" tabindex="-1"></a>    </span>
+<span id="cb147-41"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
+<span id="cb147-42"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-42" tabindex="-1"></a>    </span>
+<span id="cb147-43"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
+<span id="cb147-44"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
+<span id="cb147-45"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-45" tabindex="-1"></a>    </span>
+<span id="cb147-46"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
+<span id="cb147-47"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
+<span id="cb147-48"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-48" tabindex="-1"></a>    </span>
+<span id="cb147-49"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-49" tabindex="-1"></a>    <span class="co"># poormed coefficient function</span></span>
+<span id="cb147-50"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linpoormed&quot;</span>,</span>
+<span id="cb147-51"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-51" tabindex="-1"></a>    </span>
+<span id="cb147-52"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
+<span id="cb147-53"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
+<span id="cb147-54"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-54" tabindex="-1"></a>    </span>
+<span id="cb147-55"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-55" tabindex="-1"></a>  )</span>
+<span id="cb147-56"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-56" tabindex="-1"></a></span>
+<span id="cb147-57"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-57" tabindex="-1"></a></span>
+<span id="cb147-58"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-58" tabindex="-1"></a></span>
+<span id="cb147-59"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-59" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb147-60"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-60" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
+<span id="cb147-61"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-61" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
+<span id="cb147-62"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-62" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb147-63"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-63" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb147-64"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-64" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb147-65"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-65" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb147-66"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-66" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
+<span id="cb147-67"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-67" tabindex="-1"></a>  )</span>
+<span id="cb147-68"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-68" tabindex="-1"></a></span>
+<span id="cb147-69"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-69" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
+<span id="cb147-70"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-70" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
+<span id="cb147-71"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-71" tabindex="-1"></a></span>
+<span id="cb147-72"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-72" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
+<span id="cb147-73"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb147-73" tabindex="-1"></a>varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
 <pre><code>## [1] 8803.735</code></pre>
-<div class="sourceCode" id="cb150"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb150-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb150-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svypoormed</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
+<div class="sourceCode" id="cb149"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb149-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb149-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svypoormed</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
 <pre><code>## eqincome 
 ## 8803.735</code></pre>
-<div class="sourceCode" id="cb152"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb152-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
-<span id="cb152-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
-<span id="cb152-3"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-3" tabindex="-1"></a>lin_poormed_varpoord <span class="ot">&lt;-</span></span>
-<span id="cb152-4"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-4" tabindex="-1"></a>  varpoord_poormed_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_poormed</span>
-<span id="cb152-5"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-5" tabindex="-1"></a><span class="co"># convey</span></span>
-<span id="cb152-6"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-6" tabindex="-1"></a>lin_poormed_convey <span class="ot">&lt;-</span></span>
-<span id="cb152-7"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-7" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svypoormed</span>( <span class="sc">~</span> eqincome , des_eusilc), <span class="st">&quot;lin&quot;</span>)</span>
-<span id="cb152-8"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-8" tabindex="-1"></a></span>
-<span id="cb152-9"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-9" tabindex="-1"></a><span class="co"># check equality</span></span>
-<span id="cb152-10"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb152-10" tabindex="-1"></a><span class="fu">all.equal</span>(lin_poormed_varpoord, lin_poormed_convey)</span></code></pre></div>
+<div class="sourceCode" id="cb151"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb151-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
+<span id="cb151-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
+<span id="cb151-3"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-3" tabindex="-1"></a>lin_poormed_varpoord <span class="ot">&lt;-</span></span>
+<span id="cb151-4"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-4" tabindex="-1"></a>  varpoord_poormed_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_poormed</span>
+<span id="cb151-5"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-5" tabindex="-1"></a><span class="co"># convey</span></span>
+<span id="cb151-6"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-6" tabindex="-1"></a>lin_poormed_convey <span class="ot">&lt;-</span></span>
+<span id="cb151-7"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-7" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svypoormed</span>( <span class="sc">~</span> eqincome , des_eusilc), <span class="st">&quot;lin&quot;</span>)</span>
+<span id="cb151-8"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-8" tabindex="-1"></a></span>
+<span id="cb151-9"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-9" tabindex="-1"></a><span class="co"># check equality</span></span>
+<span id="cb151-10"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb151-10" tabindex="-1"></a><span class="fu">all.equal</span>(lin_poormed_varpoord, lin_poormed_convey)</span></code></pre></div>
 <pre><code>## [1] &quot;names for current but not for target&quot;</code></pre>
-<div class="sourceCode" id="cb154"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb154-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb154-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
-<span id="cb154-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb154-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svypoormed</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb153"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb153-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb153-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
+<span id="cb153-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb153-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svypoormed</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
 <pre><code>##          eqincome
 ## eqincome  5311.47</code></pre>
-<div class="sourceCode" id="cb156"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb156-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb156-1" tabindex="-1"></a>varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb155"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb155-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb155-1" tabindex="-1"></a>varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 5302.086</code></pre>
-<div class="sourceCode" id="cb158"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb158-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb158-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
-<span id="cb158-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb158-2" tabindex="-1"></a>varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb157"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb157-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb157-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
+<span id="cb157-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb157-2" tabindex="-1"></a>varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 72.81542</code></pre>
-<div class="sourceCode" id="cb160"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb160-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb160-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svypoormed</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
+<div class="sourceCode" id="cb159"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb159-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb159-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svypoormed</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
 <pre><code>##          eqincome
 ## eqincome 72.87983</code></pre>
 <p>The variance estimate is computed by using the approximation defined in <a href="2-var.html#var">2</a>, while the linearized variable <span class="math inline">\(z\)</span> is defined by <a href="2.1-lin.html#lin">2.1</a>. The functions <code>convey::svypoormed</code> and <code>vardpoor::linpoormed</code> produce the same linearized variable <span class="math inline">\(z\)</span>.</p>
 <p>However, the measures of uncertainty do not line up, because <code>library(vardpoor)</code> defaults to an ultimate cluster method that can be replicated with an alternative setup of the <code>survey.design</code> object.</p>
-<div class="sourceCode" id="cb162"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb162-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
-<span id="cb162-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
-<span id="cb162-3"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
-<span id="cb162-4"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-4" tabindex="-1"></a></span>
-<span id="cb162-5"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
-<span id="cb162-6"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
-<span id="cb162-7"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-7" tabindex="-1"></a></span>
-<span id="cb162-8"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
-<span id="cb162-9"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
-<span id="cb162-10"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-10" tabindex="-1"></a></span>
-<span id="cb162-11"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb162-12"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
-<span id="cb162-13"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb162-14"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb162-15"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb162-16"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb162-17"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb162-18"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
-<span id="cb162-19"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
-<span id="cb162-20"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-20" tabindex="-1"></a>  )</span>
-<span id="cb162-21"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-21" tabindex="-1"></a></span>
-<span id="cb162-22"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
-<span id="cb162-23"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb162-24"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
-<span id="cb162-25"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-25" tabindex="-1"></a></span>
-<span id="cb162-26"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-26" tabindex="-1"></a></span>
-<span id="cb162-27"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-27" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb162-28"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-28" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
-<span id="cb162-29"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-29" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svypoormed</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>)[<span class="dv">1</span>],</span>
-<span id="cb162-30"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-30" tabindex="-1"></a>  varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span>
-<span id="cb162-31"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-31" tabindex="-1"></a>))</span>
-<span id="cb162-32"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-32" tabindex="-1"></a></span>
-<span id="cb162-33"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-33" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb162-34"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-34" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
-<span id="cb162-35"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-35" tabindex="-1"></a>  <span class="fu">SE</span>(<span class="fu">svypoormed</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster))[<span class="dv">1</span>],</span>
-<span id="cb162-36"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-36" tabindex="-1"></a>  varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span>
-<span id="cb162-37"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb162-37" tabindex="-1"></a>))</span></code></pre></div>
+<div class="sourceCode" id="cb161"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb161-1"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
+<span id="cb161-2"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
+<span id="cb161-3"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
+<span id="cb161-4"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-4" tabindex="-1"></a></span>
+<span id="cb161-5"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
+<span id="cb161-6"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
+<span id="cb161-7"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-7" tabindex="-1"></a></span>
+<span id="cb161-8"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
+<span id="cb161-9"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
+<span id="cb161-10"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-10" tabindex="-1"></a></span>
+<span id="cb161-11"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb161-12"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
+<span id="cb161-13"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb161-14"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb161-15"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb161-16"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb161-17"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb161-18"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
+<span id="cb161-19"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
+<span id="cb161-20"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-20" tabindex="-1"></a>  )</span>
+<span id="cb161-21"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-21" tabindex="-1"></a></span>
+<span id="cb161-22"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
+<span id="cb161-23"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb161-24"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
+<span id="cb161-25"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-25" tabindex="-1"></a></span>
+<span id="cb161-26"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-26" tabindex="-1"></a></span>
+<span id="cb161-27"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-27" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb161-28"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-28" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
+<span id="cb161-29"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-29" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svypoormed</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>)[<span class="dv">1</span>],</span>
+<span id="cb161-30"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-30" tabindex="-1"></a>  varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span>
+<span id="cb161-31"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-31" tabindex="-1"></a>))</span>
+<span id="cb161-32"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-32" tabindex="-1"></a></span>
+<span id="cb161-33"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-33" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb161-34"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-34" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">all.equal</span>(</span>
+<span id="cb161-35"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-35" tabindex="-1"></a>  <span class="fu">SE</span>(<span class="fu">svypoormed</span>(<span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster))[<span class="dv">1</span>],</span>
+<span id="cb161-36"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-36" tabindex="-1"></a>  varpoord_poormed_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span>
+<span id="cb161-37"><a href="3.5-median-income-below-the-at-risk-of-poverty-threshold-svypoormed.html#cb161-37" tabindex="-1"></a>))</span></code></pre></div>
 <p>For additional usage examples of <code>svypoormed</code>, type <code>?convey::svypoormed</code> in the R console.</p>
 </div>
 </div>
diff --git a/docs/3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html b/docs/3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html
index 75bc61c..a7fa907 100644
--- a/docs/3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html
+++ b/docs/3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,13 +253,13 @@
 <div class="col-sm-12">
 <div id="foster-greer-thorbecke-class-svyfgt-svyfgtdec" class="section level2" number="3.6">
 <h2><span class="header-section-number">3.6</span> Foster-Greer-Thorbecke class (svyfgt, svyfgtdec)</h2>
-<div class="sourceCode" id="cb163"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb163-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb163-1" tabindex="-1"></a>✔️ used widely because encompasses interpretable measures</span>
-<span id="cb163-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb163-2" tabindex="-1"></a>✔️ allows an arbitrary poverty threshold</span>
-<span id="cb163-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb163-3" tabindex="-1"></a>✔️ can incorporate intensity and inequality among the poor</span>
-<span id="cb163-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb163-4" tabindex="-1"></a>✔️ when <span class="st">`</span><span class="at">g &gt;= 2</span><span class="st">`</span>, measure can be decomposed <span class="cf">in</span> interpretable measures of extension, intensity and inequality <span class="cf">in</span> poverty</span>
-<span id="cb163-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb163-5" tabindex="-1"></a>❌ scales are dependent on <span class="st">`</span><span class="at">g</span><span class="st">`</span></span>
-<span id="cb163-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb163-6" tabindex="-1"></a>❌ becomes increasingly difficult to interpret as <span class="st">`</span><span class="at">g</span><span class="st">`</span> parameter grows</span>
-<span id="cb163-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb163-7" tabindex="-1"></a>❌ no component that allows <span class="cf">for</span> time to exit poverty, unlike the watts index</span></code></pre></div>
+<div class="sourceCode" id="cb162"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb162-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb162-1" tabindex="-1"></a>✔️ used widely because encompasses interpretable measures</span>
+<span id="cb162-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb162-2" tabindex="-1"></a>✔️ allows an arbitrary poverty threshold</span>
+<span id="cb162-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb162-3" tabindex="-1"></a>✔️ can incorporate intensity and inequality among the poor</span>
+<span id="cb162-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb162-4" tabindex="-1"></a>✔️ when <span class="st">`</span><span class="at">g &gt;= 2</span><span class="st">`</span>, measure can be decomposed <span class="cf">in</span> interpretable measures of extension, intensity and inequality <span class="cf">in</span> poverty</span>
+<span id="cb162-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb162-5" tabindex="-1"></a>❌ scales are dependent on <span class="st">`</span><span class="at">g</span><span class="st">`</span></span>
+<span id="cb162-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb162-6" tabindex="-1"></a>❌ becomes increasingly difficult to interpret as <span class="st">`</span><span class="at">g</span><span class="st">`</span> parameter grows</span>
+<span id="cb162-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb162-7" tabindex="-1"></a>❌ no component that allows <span class="cf">for</span> time to exit poverty, unlike the watts index</span></code></pre></div>
 <p><span class="citation">Foster, Greer, and Thorbecke (<label for="tufte-mn-40" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-40" class="margin-toggle">1984<span class="marginnote">Foster, James, Joel Greer, and Erik Thorbecke. 1984. <span>“A Class of Decomposable Poverty Measures.”</span> <em>Econometrica</em> 52 (3): 761–66. <a href="http://www.jstor.org/stable/1913475">http://www.jstor.org/stable/1913475</a>.</span>)</span> proposed a family of indicators to measure poverty. This class of <span class="math inline">\(FGT\)</span> measures, can be defined as</p>
 <p><span class="math display">\[
 p=\frac{1}{N}\sum_{k\in U}h(y_{k},\theta ),
@@ -288,23 +288,23 @@ <h2><span class="header-section-number">3.6</span> Foster-Greer-Thorbecke class
 <p>The quantile and the mean involved in the definition of the threshold are estimated for the whole population. When <span class="math inline">\(\gamma=0\)</span> and <span class="math inline">\(\theta= .6*MED\)</span>, this measure is equal to the indicator ARPR computed by the function <code>svyarpr</code>. The linearization of the FGT(0) is presented in <span class="citation">Berger and Skinner (<label for="tufte-mn-43" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-43" class="margin-toggle">2003<span class="marginnote">Berger, Yves G., and Chris J. Skinner. 2003. <span>“Variance Estimation for a Low Income Proportion.”</span> <em>Journal of the Royal Statistical Society: Series C (Applied Statistics)</em> 52 (4): 457–68. <a href="https://doi.org/10.1111/1467-9876.00417">https://doi.org/10.1111/1467-9876.00417</a>.</span>)</span>.</p>
 <p>Next, we give some examples of the function <code>svyfgt</code> to estimate the values of the FGT poverty index.</p>
 <p>Consider first the poverty threshold fixed (<span class="math inline">\(\gamma=0\)</span>) in the value <span class="math inline">\(10000\)</span>. The headcount ratio (FGT0) is</p>
-<div class="sourceCode" id="cb164"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb164-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb164-1" tabindex="-1"></a><span class="fu">svyfgt</span>( <span class="sc">~</span> eqincome, des_eusilc, <span class="at">g =</span> <span class="dv">0</span>, <span class="at">abs_thresh =</span> <span class="dv">10000</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb163"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb163-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb163-1" tabindex="-1"></a><span class="fu">svyfgt</span>( <span class="sc">~</span> eqincome, des_eusilc, <span class="at">g =</span> <span class="dv">0</span>, <span class="at">abs_thresh =</span> <span class="dv">10000</span>)</span></code></pre></div>
 <pre><code>            fgt0     SE
 eqincome 0.11444 0.0027</code></pre>
 <p>The poverty gap ratio (FGT(1)) (<span class="math inline">\(\gamma=1\)</span>) index for the poverty threshold fixed at the same value is</p>
-<div class="sourceCode" id="cb166"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb166-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb166-1" tabindex="-1"></a><span class="fu">svyfgt</span>( <span class="sc">~</span> eqincome, des_eusilc, <span class="at">g =</span> <span class="dv">1</span>, <span class="at">abs_thresh =</span> <span class="dv">10000</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb165"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb165-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb165-1" tabindex="-1"></a><span class="fu">svyfgt</span>( <span class="sc">~</span> eqincome, des_eusilc, <span class="at">g =</span> <span class="dv">1</span>, <span class="at">abs_thresh =</span> <span class="dv">10000</span>)</span></code></pre></div>
 <pre><code>             fgt1     SE
 eqincome 0.032085 0.0011</code></pre>
 <p>To estimate the FGT(0) with the poverty threshold fixed at <span class="math inline">\(0.6* MED\)</span>, we first fix the argument <code>type_thresh="relq"</code> and then use the default values for <code>percent</code> and <code>order</code>:</p>
-<div class="sourceCode" id="cb168"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb168-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb168-1" tabindex="-1"></a><span class="fu">svyfgt</span>( <span class="sc">~</span> eqincome, des_eusilc, <span class="at">g =</span> <span class="dv">0</span>, <span class="at">type_thresh =</span> <span class="st">&quot;relq&quot;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb167"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb167-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb167-1" tabindex="-1"></a><span class="fu">svyfgt</span>( <span class="sc">~</span> eqincome, des_eusilc, <span class="at">g =</span> <span class="dv">0</span>, <span class="at">type_thresh =</span> <span class="st">&quot;relq&quot;</span>)</span></code></pre></div>
 <pre><code>            fgt0     SE
 eqincome 0.14444 0.0028</code></pre>
 <p>This matches the estimate obtained by:</p>
-<div class="sourceCode" id="cb170"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb170-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb170-1" tabindex="-1"></a><span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome, <span class="at">design =</span> des_eusilc, .<span class="dv">5</span>, .<span class="dv">6</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb169"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb169-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb169-1" tabindex="-1"></a><span class="fu">svyarpr</span>( <span class="sc">~</span> eqincome, <span class="at">design =</span> des_eusilc, .<span class="dv">5</span>, .<span class="dv">6</span>)</span></code></pre></div>
 <pre><code>            arpr     SE
 eqincome 0.14444 0.0028</code></pre>
 <p>To estimate the poverty gap ratio with the poverty threshold equal to <span class="math inline">\(0.6*MEAN\)</span>, we use:</p>
-<div class="sourceCode" id="cb172"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb172-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb172-1" tabindex="-1"></a><span class="fu">svyfgt</span>( <span class="sc">~</span> eqincome, des_eusilc, <span class="at">g =</span> <span class="dv">1</span>, <span class="at">type_thresh =</span> <span class="st">&quot;relm&quot;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb171"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb171-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb171-1" tabindex="-1"></a><span class="fu">svyfgt</span>( <span class="sc">~</span> eqincome, des_eusilc, <span class="at">g =</span> <span class="dv">1</span>, <span class="at">type_thresh =</span> <span class="st">&quot;relm&quot;</span>)</span></code></pre></div>
 <pre><code>             fgt1     SE
 eqincome 0.051187 0.0011</code></pre>
 <hr />
@@ -313,59 +313,59 @@ <h3><span class="header-section-number">3.6.1</span> Replication Example</h3>
 <p>In July 2006, <span class="citation">Jenkins (<label for="tufte-mn-44" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-44" class="margin-toggle">2008<span class="marginnote">Jenkins, Stephen. 2008. <span>“Estimation and Interpretation of Measures of Inequality, Poverty, and Social Welfare Using Stata.”</span> North American Stata Users' Group Meetings 2006. Stata Users Group. <a href="http://EconPapers.repec.org/RePEc:boc:asug06:16">http://EconPapers.repec.org/RePEc:boc:asug06:16</a>.</span>)</span> presented at the North American Stata Users’ Group Meetings on the stata Atkinson Index command. The example below reproduces those statistics.</p>
 <p>In order to match the presentation’s results using the <code>svyfgt</code> function from the <code>convey</code> library, the poverty threshold was considered absolute despite being directly estimated from the survey sample. This effectively treats the variance of the estimated poverty threshold as zero; <code>svyfgt</code> does not account for the uncertainty of the poverty threshold when the level has been stated as absolute with the <code>abs_thresh=</code> parameter. In general, we would instead recommend using either <code>relq</code> or <code>relm</code> in the <code>type_thresh=</code> parameter in order to account for the added uncertainty of the poverty threshold calculation. This example serves only to show that <code>svyfgt</code> behaves properly as compared to other software.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb174"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb174-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb174-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb174-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-3" tabindex="-1"></a></span>
-<span id="cb174-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb174-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb174-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-6" tabindex="-1"></a></span>
-<span id="cb174-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-7" tabindex="-1"></a><span class="co"># load the foreign library</span></span>
-<span id="cb174-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-8" tabindex="-1"></a><span class="fu">library</span>(foreign)</span>
-<span id="cb174-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-9" tabindex="-1"></a></span>
-<span id="cb174-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-10" tabindex="-1"></a><span class="co"># create a temporary file on the local disk</span></span>
-<span id="cb174-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-11" tabindex="-1"></a>tf <span class="ot">&lt;-</span> <span class="fu">tempfile</span>()</span>
-<span id="cb174-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-12" tabindex="-1"></a></span>
-<span id="cb174-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-13" tabindex="-1"></a><span class="co"># store the location of the presentation file</span></span>
-<span id="cb174-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-14" tabindex="-1"></a>presentation_zip <span class="ot">&lt;-</span></span>
-<span id="cb174-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-15" tabindex="-1"></a>  <span class="st">&quot;http://repec.org/nasug2006/nasug2006_jenkins.zip&quot;</span></span>
-<span id="cb174-16"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-16" tabindex="-1"></a></span>
-<span id="cb174-17"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-17" tabindex="-1"></a><span class="co"># download jenkins&#39; presentation to the temporary file</span></span>
-<span id="cb174-18"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-18" tabindex="-1"></a><span class="fu">download.file</span>(presentation_zip , tf , <span class="at">mode =</span> <span class="st">&#39;wb&#39;</span>)</span>
-<span id="cb174-19"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-19" tabindex="-1"></a></span>
-<span id="cb174-20"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-20" tabindex="-1"></a><span class="co"># unzip the contents of the archive</span></span>
-<span id="cb174-21"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-21" tabindex="-1"></a>presentation_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> <span class="fu">tempdir</span>())</span>
-<span id="cb174-22"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-22" tabindex="-1"></a></span>
-<span id="cb174-23"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-23" tabindex="-1"></a><span class="co"># load the institute for fiscal studies&#39; 1981, 1985, and 1991 data.frame objects</span></span>
-<span id="cb174-24"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-24" tabindex="-1"></a>x81 <span class="ot">&lt;-</span></span>
-<span id="cb174-25"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-25" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs81&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb174-26"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-26" tabindex="-1"></a>x85 <span class="ot">&lt;-</span></span>
-<span id="cb174-27"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-27" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs85&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb174-28"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-28" tabindex="-1"></a>x91 <span class="ot">&lt;-</span></span>
-<span id="cb174-29"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-29" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs91&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb174-30"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-30" tabindex="-1"></a></span>
-<span id="cb174-31"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-31" tabindex="-1"></a><span class="co"># </span><span class="al">NOTE</span><span class="co">: we recommend using ?convey::svyarpt rather than this unweighted calculation #</span></span>
-<span id="cb174-32"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-32" tabindex="-1"></a></span>
-<span id="cb174-33"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-33" tabindex="-1"></a><span class="co"># calculate 60% of the unweighted median income in 1981</span></span>
-<span id="cb174-34"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-34" tabindex="-1"></a>unwtd_arpt81 <span class="ot">&lt;-</span> <span class="fu">quantile</span>(x81<span class="sc">$</span>eybhc0 , <span class="fl">0.5</span>) <span class="sc">*</span> .<span class="dv">6</span></span>
-<span id="cb174-35"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-35" tabindex="-1"></a></span>
-<span id="cb174-36"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-36" tabindex="-1"></a><span class="co"># calculate 60% of the unweighted median income in 1985</span></span>
-<span id="cb174-37"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-37" tabindex="-1"></a>unwtd_arpt85 <span class="ot">&lt;-</span> <span class="fu">quantile</span>(x85<span class="sc">$</span>eybhc0 , <span class="fl">0.5</span>) <span class="sc">*</span> .<span class="dv">6</span></span>
-<span id="cb174-38"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-38" tabindex="-1"></a></span>
-<span id="cb174-39"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-39" tabindex="-1"></a><span class="co"># calculate 60% of the unweighted median income in 1991</span></span>
-<span id="cb174-40"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-40" tabindex="-1"></a>unwtd_arpt91 <span class="ot">&lt;-</span> <span class="fu">quantile</span>(x91<span class="sc">$</span>eybhc0 , <span class="fl">0.5</span>) <span class="sc">*</span> .<span class="dv">6</span></span>
-<span id="cb174-41"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-41" tabindex="-1"></a></span>
-<span id="cb174-42"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-42" tabindex="-1"></a><span class="co"># stack each of these three years of data into a single data.frame</span></span>
-<span id="cb174-43"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb174-43" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">rbind</span>(x81 , x85 , x91)</span></code></pre></div>
+<div class="sourceCode" id="cb173"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb173-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb173-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb173-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-3" tabindex="-1"></a></span>
+<span id="cb173-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb173-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb173-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-6" tabindex="-1"></a></span>
+<span id="cb173-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-7" tabindex="-1"></a><span class="co"># load the foreign library</span></span>
+<span id="cb173-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-8" tabindex="-1"></a><span class="fu">library</span>(foreign)</span>
+<span id="cb173-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-9" tabindex="-1"></a></span>
+<span id="cb173-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-10" tabindex="-1"></a><span class="co"># create a temporary file on the local disk</span></span>
+<span id="cb173-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-11" tabindex="-1"></a>tf <span class="ot">&lt;-</span> <span class="fu">tempfile</span>()</span>
+<span id="cb173-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-12" tabindex="-1"></a></span>
+<span id="cb173-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-13" tabindex="-1"></a><span class="co"># store the location of the presentation file</span></span>
+<span id="cb173-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-14" tabindex="-1"></a>presentation_zip <span class="ot">&lt;-</span></span>
+<span id="cb173-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-15" tabindex="-1"></a>  <span class="st">&quot;http://repec.org/nasug2006/nasug2006_jenkins.zip&quot;</span></span>
+<span id="cb173-16"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-16" tabindex="-1"></a></span>
+<span id="cb173-17"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-17" tabindex="-1"></a><span class="co"># download jenkins&#39; presentation to the temporary file</span></span>
+<span id="cb173-18"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-18" tabindex="-1"></a><span class="fu">download.file</span>(presentation_zip , tf , <span class="at">mode =</span> <span class="st">&#39;wb&#39;</span>)</span>
+<span id="cb173-19"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-19" tabindex="-1"></a></span>
+<span id="cb173-20"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-20" tabindex="-1"></a><span class="co"># unzip the contents of the archive</span></span>
+<span id="cb173-21"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-21" tabindex="-1"></a>presentation_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> <span class="fu">tempdir</span>())</span>
+<span id="cb173-22"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-22" tabindex="-1"></a></span>
+<span id="cb173-23"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-23" tabindex="-1"></a><span class="co"># load the institute for fiscal studies&#39; 1981, 1985, and 1991 data.frame objects</span></span>
+<span id="cb173-24"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-24" tabindex="-1"></a>x81 <span class="ot">&lt;-</span></span>
+<span id="cb173-25"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-25" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs81&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb173-26"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-26" tabindex="-1"></a>x85 <span class="ot">&lt;-</span></span>
+<span id="cb173-27"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-27" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs85&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb173-28"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-28" tabindex="-1"></a>x91 <span class="ot">&lt;-</span></span>
+<span id="cb173-29"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-29" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs91&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb173-30"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-30" tabindex="-1"></a></span>
+<span id="cb173-31"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-31" tabindex="-1"></a><span class="co"># </span><span class="al">NOTE</span><span class="co">: we recommend using ?convey::svyarpt rather than this unweighted calculation #</span></span>
+<span id="cb173-32"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-32" tabindex="-1"></a></span>
+<span id="cb173-33"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-33" tabindex="-1"></a><span class="co"># calculate 60% of the unweighted median income in 1981</span></span>
+<span id="cb173-34"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-34" tabindex="-1"></a>unwtd_arpt81 <span class="ot">&lt;-</span> <span class="fu">quantile</span>(x81<span class="sc">$</span>eybhc0 , <span class="fl">0.5</span>) <span class="sc">*</span> .<span class="dv">6</span></span>
+<span id="cb173-35"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-35" tabindex="-1"></a></span>
+<span id="cb173-36"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-36" tabindex="-1"></a><span class="co"># calculate 60% of the unweighted median income in 1985</span></span>
+<span id="cb173-37"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-37" tabindex="-1"></a>unwtd_arpt85 <span class="ot">&lt;-</span> <span class="fu">quantile</span>(x85<span class="sc">$</span>eybhc0 , <span class="fl">0.5</span>) <span class="sc">*</span> .<span class="dv">6</span></span>
+<span id="cb173-38"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-38" tabindex="-1"></a></span>
+<span id="cb173-39"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-39" tabindex="-1"></a><span class="co"># calculate 60% of the unweighted median income in 1991</span></span>
+<span id="cb173-40"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-40" tabindex="-1"></a>unwtd_arpt91 <span class="ot">&lt;-</span> <span class="fu">quantile</span>(x91<span class="sc">$</span>eybhc0 , <span class="fl">0.5</span>) <span class="sc">*</span> .<span class="dv">6</span></span>
+<span id="cb173-41"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-41" tabindex="-1"></a></span>
+<span id="cb173-42"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-42" tabindex="-1"></a><span class="co"># stack each of these three years of data into a single data.frame</span></span>
+<span id="cb173-43"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb173-43" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">rbind</span>(x81 , x85 , x91)</span></code></pre></div>
 <p>Replicate the author’s survey design statement from stata code..</p>
 <pre><code>. ge poor = (year==1981)*(x &lt; $z_81)+(year==1985)*(x &lt; $z_85)+(year==1991)*(x &lt; $z_91)
 . * account for clustering within HHs 
 . svyset hrn [pweight = wgt]</code></pre>
 <p>.. into R code:</p>
-<div class="sourceCode" id="cb176"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb176-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb176-1" tabindex="-1"></a><span class="co"># initiate a linearized survey design object</span></span>
-<span id="cb176-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb176-2" tabindex="-1"></a>y <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="sc">~</span> hrn , <span class="at">data =</span> x , <span class="at">weights =</span> <span class="sc">~</span> wgt)</span>
-<span id="cb176-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb176-3" tabindex="-1"></a></span>
-<span id="cb176-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb176-4" tabindex="-1"></a><span class="co"># immediately run the `convey_prep` function on the survey design</span></span>
-<span id="cb176-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb176-5" tabindex="-1"></a>z <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(y)</span></code></pre></div>
+<div class="sourceCode" id="cb175"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb175-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb175-1" tabindex="-1"></a><span class="co"># initiate a linearized survey design object</span></span>
+<span id="cb175-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb175-2" tabindex="-1"></a>y <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="sc">~</span> hrn , <span class="at">data =</span> x , <span class="at">weights =</span> <span class="sc">~</span> wgt)</span>
+<span id="cb175-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb175-3" tabindex="-1"></a></span>
+<span id="cb175-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb175-4" tabindex="-1"></a><span class="co"># immediately run the `convey_prep` function on the survey design</span></span>
+<span id="cb175-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb175-5" tabindex="-1"></a>z <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(y)</span></code></pre></div>
 <p>Replicate the author’s headcount ratio results with stata..</p>
 <pre><code>. svy: mean poor if year == 1981
 (running mean on estimation sample)
@@ -415,52 +415,52 @@ <h3><span class="header-section-number">3.6.1</span> Replication Example</h3>
         poor |   .2021312   .0062077      .1899615    .2143009
 --------------------------------------------------------------</code></pre>
 <p>..using R code:</p>
-<div class="sourceCode" id="cb178"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb178-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-1" tabindex="-1"></a>headcount_81 <span class="ot">&lt;-</span></span>
-<span id="cb178-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-2" tabindex="-1"></a>  <span class="fu">svyfgt</span>( <span class="sc">~</span> eybhc0 ,</span>
-<span id="cb178-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-3" tabindex="-1"></a>          <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>) ,</span>
-<span id="cb178-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-4" tabindex="-1"></a>          <span class="at">g =</span> <span class="dv">0</span> ,</span>
-<span id="cb178-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-5" tabindex="-1"></a>          <span class="at">abs_thresh =</span> unwtd_arpt81)</span>
-<span id="cb178-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-6" tabindex="-1"></a></span>
-<span id="cb178-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-7" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(headcount_81) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">14101</span>)</span>
-<span id="cb178-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-8" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">SE</span>(headcount_81) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">00449</span>)</span>
-<span id="cb178-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-9" tabindex="-1"></a></span>
-<span id="cb178-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-10" tabindex="-1"></a>headcount_81_ci <span class="ot">&lt;-</span></span>
-<span id="cb178-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-11" tabindex="-1"></a>  <span class="fu">confint</span>(headcount_81 , <span class="at">df =</span> <span class="fu">degf</span>(<span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>)))</span>
-<span id="cb178-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-12" tabindex="-1"></a></span>
-<span id="cb178-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-13" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_81_ci[<span class="dv">1</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">13222</span>)</span>
-<span id="cb178-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-14" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_81_ci[<span class="dv">2</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">14981</span>)</span>
-<span id="cb178-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-15" tabindex="-1"></a></span>
-<span id="cb178-16"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-16" tabindex="-1"></a>headcount_85 <span class="ot">&lt;-</span></span>
-<span id="cb178-17"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-17" tabindex="-1"></a>  <span class="fu">svyfgt</span>(<span class="sc">~</span> eybhc0 ,</span>
-<span id="cb178-18"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-18" tabindex="-1"></a>         <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1985</span>) ,</span>
-<span id="cb178-19"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-19" tabindex="-1"></a>         <span class="at">g =</span> <span class="dv">0</span> ,</span>
-<span id="cb178-20"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-20" tabindex="-1"></a>         <span class="at">abs_thresh =</span> unwtd_arpt85)</span>
-<span id="cb178-21"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-21" tabindex="-1"></a></span>
-<span id="cb178-22"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-22" tabindex="-1"></a></span>
-<span id="cb178-23"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-23" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(headcount_85) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">13764</span>)</span>
-<span id="cb178-24"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-24" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">SE</span>(headcount_85) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">00465</span>)</span>
-<span id="cb178-25"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-25" tabindex="-1"></a></span>
-<span id="cb178-26"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-26" tabindex="-1"></a>headcount_85_ci <span class="ot">&lt;-</span></span>
-<span id="cb178-27"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-27" tabindex="-1"></a>  <span class="fu">confint</span>(headcount_85 , <span class="at">df =</span> <span class="fu">degf</span>(<span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1985</span>)))</span>
-<span id="cb178-28"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-28" tabindex="-1"></a></span>
-<span id="cb178-29"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-29" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_85_ci[<span class="dv">1</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">12852</span>)</span>
-<span id="cb178-30"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-30" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_85_ci[<span class="dv">2</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">14677</span>)</span>
-<span id="cb178-31"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-31" tabindex="-1"></a></span>
-<span id="cb178-32"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-32" tabindex="-1"></a>headcount_91 <span class="ot">&lt;-</span></span>
-<span id="cb178-33"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-33" tabindex="-1"></a>  <span class="fu">svyfgt</span>(<span class="sc">~</span> eybhc0 ,</span>
-<span id="cb178-34"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-34" tabindex="-1"></a>         <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1991</span>) ,</span>
-<span id="cb178-35"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-35" tabindex="-1"></a>         <span class="at">g =</span> <span class="dv">0</span> ,</span>
-<span id="cb178-36"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-36" tabindex="-1"></a>         <span class="at">abs_thresh =</span> unwtd_arpt91)</span>
-<span id="cb178-37"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-37" tabindex="-1"></a></span>
-<span id="cb178-38"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-38" tabindex="-1"></a></span>
-<span id="cb178-39"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-39" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(headcount_91) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">20213</span>)</span>
-<span id="cb178-40"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-40" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">SE</span>(headcount_91) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">00621</span>)</span>
-<span id="cb178-41"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-41" tabindex="-1"></a></span>
-<span id="cb178-42"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-42" tabindex="-1"></a>headcount_91_ci <span class="ot">&lt;-</span></span>
-<span id="cb178-43"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-43" tabindex="-1"></a>  <span class="fu">confint</span>(headcount_91 , <span class="at">df =</span> <span class="fu">degf</span>(<span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1991</span>)))</span>
-<span id="cb178-44"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-44" tabindex="-1"></a></span>
-<span id="cb178-45"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-45" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_91_ci[<span class="dv">1</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">18996</span>)</span>
-<span id="cb178-46"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb178-46" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_91_ci[<span class="dv">2</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">21430</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb177"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb177-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-1" tabindex="-1"></a>headcount_81 <span class="ot">&lt;-</span></span>
+<span id="cb177-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-2" tabindex="-1"></a>  <span class="fu">svyfgt</span>( <span class="sc">~</span> eybhc0 ,</span>
+<span id="cb177-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-3" tabindex="-1"></a>          <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>) ,</span>
+<span id="cb177-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-4" tabindex="-1"></a>          <span class="at">g =</span> <span class="dv">0</span> ,</span>
+<span id="cb177-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-5" tabindex="-1"></a>          <span class="at">abs_thresh =</span> unwtd_arpt81)</span>
+<span id="cb177-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-6" tabindex="-1"></a></span>
+<span id="cb177-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-7" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(headcount_81) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">14101</span>)</span>
+<span id="cb177-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-8" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">SE</span>(headcount_81) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">00449</span>)</span>
+<span id="cb177-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-9" tabindex="-1"></a></span>
+<span id="cb177-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-10" tabindex="-1"></a>headcount_81_ci <span class="ot">&lt;-</span></span>
+<span id="cb177-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-11" tabindex="-1"></a>  <span class="fu">confint</span>(headcount_81 , <span class="at">df =</span> <span class="fu">degf</span>(<span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>)))</span>
+<span id="cb177-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-12" tabindex="-1"></a></span>
+<span id="cb177-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-13" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_81_ci[<span class="dv">1</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">13222</span>)</span>
+<span id="cb177-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-14" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_81_ci[<span class="dv">2</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">14981</span>)</span>
+<span id="cb177-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-15" tabindex="-1"></a></span>
+<span id="cb177-16"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-16" tabindex="-1"></a>headcount_85 <span class="ot">&lt;-</span></span>
+<span id="cb177-17"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-17" tabindex="-1"></a>  <span class="fu">svyfgt</span>(<span class="sc">~</span> eybhc0 ,</span>
+<span id="cb177-18"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-18" tabindex="-1"></a>         <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1985</span>) ,</span>
+<span id="cb177-19"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-19" tabindex="-1"></a>         <span class="at">g =</span> <span class="dv">0</span> ,</span>
+<span id="cb177-20"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-20" tabindex="-1"></a>         <span class="at">abs_thresh =</span> unwtd_arpt85)</span>
+<span id="cb177-21"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-21" tabindex="-1"></a></span>
+<span id="cb177-22"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-22" tabindex="-1"></a></span>
+<span id="cb177-23"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-23" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(headcount_85) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">13764</span>)</span>
+<span id="cb177-24"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-24" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">SE</span>(headcount_85) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">00465</span>)</span>
+<span id="cb177-25"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-25" tabindex="-1"></a></span>
+<span id="cb177-26"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-26" tabindex="-1"></a>headcount_85_ci <span class="ot">&lt;-</span></span>
+<span id="cb177-27"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-27" tabindex="-1"></a>  <span class="fu">confint</span>(headcount_85 , <span class="at">df =</span> <span class="fu">degf</span>(<span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1985</span>)))</span>
+<span id="cb177-28"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-28" tabindex="-1"></a></span>
+<span id="cb177-29"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-29" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_85_ci[<span class="dv">1</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">12852</span>)</span>
+<span id="cb177-30"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-30" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_85_ci[<span class="dv">2</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">14677</span>)</span>
+<span id="cb177-31"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-31" tabindex="-1"></a></span>
+<span id="cb177-32"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-32" tabindex="-1"></a>headcount_91 <span class="ot">&lt;-</span></span>
+<span id="cb177-33"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-33" tabindex="-1"></a>  <span class="fu">svyfgt</span>(<span class="sc">~</span> eybhc0 ,</span>
+<span id="cb177-34"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-34" tabindex="-1"></a>         <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1991</span>) ,</span>
+<span id="cb177-35"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-35" tabindex="-1"></a>         <span class="at">g =</span> <span class="dv">0</span> ,</span>
+<span id="cb177-36"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-36" tabindex="-1"></a>         <span class="at">abs_thresh =</span> unwtd_arpt91)</span>
+<span id="cb177-37"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-37" tabindex="-1"></a></span>
+<span id="cb177-38"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-38" tabindex="-1"></a></span>
+<span id="cb177-39"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-39" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(headcount_91) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">20213</span>)</span>
+<span id="cb177-40"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-40" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">SE</span>(headcount_91) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">00621</span>)</span>
+<span id="cb177-41"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-41" tabindex="-1"></a></span>
+<span id="cb177-42"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-42" tabindex="-1"></a>headcount_91_ci <span class="ot">&lt;-</span></span>
+<span id="cb177-43"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-43" tabindex="-1"></a>  <span class="fu">confint</span>(headcount_91 , <span class="at">df =</span> <span class="fu">degf</span>(<span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1991</span>)))</span>
+<span id="cb177-44"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-44" tabindex="-1"></a></span>
+<span id="cb177-45"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-45" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_91_ci[<span class="dv">1</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">18996</span>)</span>
+<span id="cb177-46"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb177-46" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(headcount_91_ci[<span class="dv">2</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">21430</span>)</span></code></pre></div>
 <p>Confirm this replication applies for the normalized poverty gap as well, comparing stata code..</p>
 <pre><code>. ge ngap = poor*($z_81- x)/$z_81 if year == 1981
 
@@ -480,199 +480,199 @@ <h3><span class="header-section-number">3.6.1</span> Replication Example</h3>
         ngap |   .0271577   .0013502      .0245109    .0298044
 --------------------------------------------------------------</code></pre>
 <p>..to R code:</p>
-<div class="sourceCode" id="cb180"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb180-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-1" tabindex="-1"></a>norm_pov_81 <span class="ot">&lt;-</span></span>
-<span id="cb180-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-2" tabindex="-1"></a>  <span class="fu">svyfgt</span>( <span class="sc">~</span> eybhc0 ,</span>
-<span id="cb180-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-3" tabindex="-1"></a>          <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>) ,</span>
-<span id="cb180-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-4" tabindex="-1"></a>          <span class="at">g =</span> <span class="dv">1</span> ,</span>
-<span id="cb180-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-5" tabindex="-1"></a>          <span class="at">abs_thresh =</span> unwtd_arpt81)</span>
-<span id="cb180-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-6" tabindex="-1"></a></span>
-<span id="cb180-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-7" tabindex="-1"></a></span>
-<span id="cb180-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-8" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(norm_pov_81) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">02716</span>)</span>
-<span id="cb180-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-9" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">SE</span>(norm_pov_81) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">00135</span>)</span>
-<span id="cb180-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-10" tabindex="-1"></a></span>
-<span id="cb180-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-11" tabindex="-1"></a>norm_pov_81_ci <span class="ot">&lt;-</span></span>
-<span id="cb180-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-12" tabindex="-1"></a>  <span class="fu">confint</span>(norm_pov_81 , <span class="at">df =</span> <span class="fu">degf</span>(<span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>)))</span>
-<span id="cb180-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-13" tabindex="-1"></a></span>
-<span id="cb180-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-14" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(norm_pov_81_ci[<span class="dv">1</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">02451</span>)</span>
-<span id="cb180-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-15" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(norm_pov_81_ci[<span class="dv">2</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">02980</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb179"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb179-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-1" tabindex="-1"></a>norm_pov_81 <span class="ot">&lt;-</span></span>
+<span id="cb179-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-2" tabindex="-1"></a>  <span class="fu">svyfgt</span>( <span class="sc">~</span> eybhc0 ,</span>
+<span id="cb179-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-3" tabindex="-1"></a>          <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>) ,</span>
+<span id="cb179-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-4" tabindex="-1"></a>          <span class="at">g =</span> <span class="dv">1</span> ,</span>
+<span id="cb179-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-5" tabindex="-1"></a>          <span class="at">abs_thresh =</span> unwtd_arpt81)</span>
+<span id="cb179-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-6" tabindex="-1"></a></span>
+<span id="cb179-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-7" tabindex="-1"></a></span>
+<span id="cb179-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-8" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">coef</span>(norm_pov_81) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">02716</span>)</span>
+<span id="cb179-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-9" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">SE</span>(norm_pov_81) , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">00135</span>)</span>
+<span id="cb179-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-10" tabindex="-1"></a></span>
+<span id="cb179-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-11" tabindex="-1"></a>norm_pov_81_ci <span class="ot">&lt;-</span></span>
+<span id="cb179-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-12" tabindex="-1"></a>  <span class="fu">confint</span>(norm_pov_81 , <span class="at">df =</span> <span class="fu">degf</span>(<span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>)))</span>
+<span id="cb179-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-13" tabindex="-1"></a></span>
+<span id="cb179-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-14" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(norm_pov_81_ci[<span class="dv">1</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">02451</span>)</span>
+<span id="cb179-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb179-15" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(norm_pov_81_ci[<span class="dv">2</span>] , <span class="dv">5</span>) <span class="sc">==</span> .<span class="dv">02980</span>)</span></code></pre></div>
 </div>
 <div id="monte-carlo-simulation" class="section level3" number="3.6.2">
 <h3><span class="header-section-number">3.6.2</span> Monte Carlo Simulation</h3>
 <p>To provide a example for our code, we proceed with a Monte Carlo experiment.
 Using the <code>eusilcP</code> data from the <code>simPop</code> package <span class="citation">(<label for="tufte-mn-45" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-45" class="margin-toggle">Templ et al. 2017<span class="marginnote">Templ, Matthias, Bernhard Meindl, Alexander Kowarik, and Olivier Dupriez. 2017. <span>“Simulation of Synthetic Complex Data: The <span>R</span> Package <span class="nocase">simPop</span>.”</span> <em>Journal of Statistical Software</em> 79 (10): 1–38. <a href="https://doi.org/10.18637/jss.v079.i10">https://doi.org/10.18637/jss.v079.i10</a>.</span>)</span>, we can compute the actual values of the FGT components for that population:</p>
-<div class="sourceCode" id="cb181"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb181-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
-<span id="cb181-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-2" tabindex="-1"></a><span class="fu">library</span>(sampling)</span>
-<span id="cb181-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-3" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb181-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-4" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb181-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-5" tabindex="-1"></a><span class="fu">library</span>(parallel)</span>
-<span id="cb181-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-6" tabindex="-1"></a></span>
-<span id="cb181-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-7" tabindex="-1"></a><span class="co"># load pseudo population data</span></span>
-<span id="cb181-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-8" tabindex="-1"></a><span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
-<span id="cb181-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-9" tabindex="-1"></a></span>
-<span id="cb181-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-10" tabindex="-1"></a><span class="co"># compute population value of the FGT(2) index decomposition</span></span>
-<span id="cb181-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-11" tabindex="-1"></a>inc.all <span class="ot">&lt;-</span> eusilcP<span class="sc">$</span>eqIncome</span>
-<span id="cb181-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-12" tabindex="-1"></a>gfun <span class="ot">&lt;-</span> <span class="cf">function</span>(y , thresh)</span>
-<span id="cb181-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-13" tabindex="-1"></a>  (thresh <span class="sc">-</span> y) <span class="sc">/</span> thresh</span>
-<span id="cb181-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-14" tabindex="-1"></a>hfun <span class="ot">&lt;-</span></span>
-<span id="cb181-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-15" tabindex="-1"></a>  <span class="cf">function</span>(y , thresh , g)</span>
-<span id="cb181-16"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-16" tabindex="-1"></a>    (((thresh <span class="sc">-</span> y) <span class="sc">/</span> thresh) <span class="sc">^</span> g) <span class="sc">*</span> (y <span class="sc">&lt;=</span> thresh)</span>
-<span id="cb181-17"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-17" tabindex="-1"></a>fgt2 <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">hfun</span>(inc.all , <span class="dv">10000</span> , <span class="dv">2</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb181-18"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-18" tabindex="-1"></a>fgt1 <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">hfun</span>(inc.all , <span class="dv">10000</span> , <span class="dv">1</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb181-19"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-19" tabindex="-1"></a>fgt0 <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">hfun</span>(inc.all , <span class="dv">10000</span> , <span class="dv">0</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb181-20"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-20" tabindex="-1"></a>igr.fgt <span class="ot">&lt;-</span></span>
-<span id="cb181-21"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-21" tabindex="-1"></a>  <span class="fu">mean</span>(<span class="fu">hfun</span>(inc.all , <span class="dv">10000</span> , <span class="dv">1</span>)[inc.all <span class="sc">&lt;=</span> <span class="dv">10000</span>] , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb181-22"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-22" tabindex="-1"></a>gei.poor <span class="ot">&lt;-</span></span>
-<span id="cb181-23"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-23" tabindex="-1"></a>  convey<span class="sc">:::</span><span class="fu">CalcGEI</span>(<span class="fu">gfun</span>(inc.all , <span class="dv">10000</span>) , <span class="fu">ifelse</span>(inc.all <span class="sc">&lt;</span> <span class="dv">10000</span> , <span class="dv">1</span> , <span class="dv">0</span>) , <span class="dv">2</span>)</span>
-<span id="cb181-24"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-24" tabindex="-1"></a>theta.pop <span class="ot">&lt;-</span></span>
-<span id="cb181-25"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-25" tabindex="-1"></a>  <span class="fu">c</span>(</span>
-<span id="cb181-26"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-26" tabindex="-1"></a>    <span class="st">&quot;fgt2&quot;</span> <span class="ot">=</span> fgt2 ,</span>
-<span id="cb181-27"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-27" tabindex="-1"></a>    <span class="st">&quot;fgt0&quot;</span> <span class="ot">=</span>  fgt0 ,</span>
-<span id="cb181-28"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-28" tabindex="-1"></a>    <span class="st">&quot;fgt1&quot;</span> <span class="ot">=</span>  fgt1 ,</span>
-<span id="cb181-29"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-29" tabindex="-1"></a>    <span class="st">&quot;igr&quot;</span> <span class="ot">=</span> igr.fgt ,</span>
-<span id="cb181-30"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-30" tabindex="-1"></a>    <span class="st">&quot;gei(poor;epsilon=2)&quot;</span> <span class="ot">=</span>  gei.poor</span>
-<span id="cb181-31"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-31" tabindex="-1"></a>  )</span>
-<span id="cb181-32"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb181-32" tabindex="-1"></a>theta.pop</span></code></pre></div>
+<div class="sourceCode" id="cb180"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb180-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
+<span id="cb180-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-2" tabindex="-1"></a><span class="fu">library</span>(sampling)</span>
+<span id="cb180-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-3" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb180-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-4" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb180-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-5" tabindex="-1"></a><span class="fu">library</span>(parallel)</span>
+<span id="cb180-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-6" tabindex="-1"></a></span>
+<span id="cb180-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-7" tabindex="-1"></a><span class="co"># load pseudo population data</span></span>
+<span id="cb180-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-8" tabindex="-1"></a><span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
+<span id="cb180-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-9" tabindex="-1"></a></span>
+<span id="cb180-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-10" tabindex="-1"></a><span class="co"># compute population value of the FGT(2) index decomposition</span></span>
+<span id="cb180-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-11" tabindex="-1"></a>inc.all <span class="ot">&lt;-</span> eusilcP<span class="sc">$</span>eqIncome</span>
+<span id="cb180-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-12" tabindex="-1"></a>gfun <span class="ot">&lt;-</span> <span class="cf">function</span>(y , thresh)</span>
+<span id="cb180-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-13" tabindex="-1"></a>  (thresh <span class="sc">-</span> y) <span class="sc">/</span> thresh</span>
+<span id="cb180-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-14" tabindex="-1"></a>hfun <span class="ot">&lt;-</span></span>
+<span id="cb180-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-15" tabindex="-1"></a>  <span class="cf">function</span>(y , thresh , g)</span>
+<span id="cb180-16"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-16" tabindex="-1"></a>    (((thresh <span class="sc">-</span> y) <span class="sc">/</span> thresh) <span class="sc">^</span> g) <span class="sc">*</span> (y <span class="sc">&lt;=</span> thresh)</span>
+<span id="cb180-17"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-17" tabindex="-1"></a>fgt2 <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">hfun</span>(inc.all , <span class="dv">10000</span> , <span class="dv">2</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb180-18"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-18" tabindex="-1"></a>fgt1 <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">hfun</span>(inc.all , <span class="dv">10000</span> , <span class="dv">1</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb180-19"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-19" tabindex="-1"></a>fgt0 <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">hfun</span>(inc.all , <span class="dv">10000</span> , <span class="dv">0</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb180-20"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-20" tabindex="-1"></a>igr.fgt <span class="ot">&lt;-</span></span>
+<span id="cb180-21"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-21" tabindex="-1"></a>  <span class="fu">mean</span>(<span class="fu">hfun</span>(inc.all , <span class="dv">10000</span> , <span class="dv">1</span>)[inc.all <span class="sc">&lt;=</span> <span class="dv">10000</span>] , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb180-22"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-22" tabindex="-1"></a>gei.poor <span class="ot">&lt;-</span></span>
+<span id="cb180-23"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-23" tabindex="-1"></a>  convey<span class="sc">:::</span><span class="fu">CalcGEI</span>(<span class="fu">gfun</span>(inc.all , <span class="dv">10000</span>) , <span class="fu">ifelse</span>(inc.all <span class="sc">&lt;</span> <span class="dv">10000</span> , <span class="dv">1</span> , <span class="dv">0</span>) , <span class="dv">2</span>)</span>
+<span id="cb180-24"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-24" tabindex="-1"></a>theta.pop <span class="ot">&lt;-</span></span>
+<span id="cb180-25"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-25" tabindex="-1"></a>  <span class="fu">c</span>(</span>
+<span id="cb180-26"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-26" tabindex="-1"></a>    <span class="st">&quot;fgt2&quot;</span> <span class="ot">=</span> fgt2 ,</span>
+<span id="cb180-27"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-27" tabindex="-1"></a>    <span class="st">&quot;fgt0&quot;</span> <span class="ot">=</span>  fgt0 ,</span>
+<span id="cb180-28"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-28" tabindex="-1"></a>    <span class="st">&quot;fgt1&quot;</span> <span class="ot">=</span>  fgt1 ,</span>
+<span id="cb180-29"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-29" tabindex="-1"></a>    <span class="st">&quot;igr&quot;</span> <span class="ot">=</span> igr.fgt ,</span>
+<span id="cb180-30"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-30" tabindex="-1"></a>    <span class="st">&quot;gei(poor;epsilon=2)&quot;</span> <span class="ot">=</span>  gei.poor</span>
+<span id="cb180-31"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-31" tabindex="-1"></a>  )</span>
+<span id="cb180-32"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb180-32" tabindex="-1"></a>theta.pop</span></code></pre></div>
 <pre><code>##                fgt2                fgt0                fgt1                 igr 
 ##          0.01571192          0.11412691          0.03259544          0.28560699 
 ## gei(poor;epsilon=2) 
 ##          0.34386588</code></pre>
 <p>Now, to study the distribution of the estimator under a particular sampling design, we select 5000 samples under one-stage cluster sampling of 100 households using the <code>cluster</code> function from the <code>sampling</code> package <span class="citation">(<label for="tufte-mn-46" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-46" class="margin-toggle">Tillé and Matei 2021<span class="marginnote">Tillé, Yves, and Alina Matei. 2021. <em>Sampling: Survey Sampling</em>. <a href="https://CRAN.R-project.org/package=sampling">https://CRAN.R-project.org/package=sampling</a>.</span>)</span>, and use the <code>svyfgtdec</code> function to estimate the FGT components for each of those samples:</p>
-<div class="sourceCode" id="cb183"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb183-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-1" tabindex="-1"></a><span class="co"># define the number of monte carlo replicates</span></span>
-<span id="cb183-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-2" tabindex="-1"></a>mc.rep <span class="ot">&lt;-</span> 5000L</span>
-<span id="cb183-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-3" tabindex="-1"></a></span>
-<span id="cb183-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-4" tabindex="-1"></a></span>
-<span id="cb183-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-5" tabindex="-1"></a></span>
-<span id="cb183-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-6" tabindex="-1"></a><span class="co"># simulation function</span></span>
-<span id="cb183-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-7" tabindex="-1"></a>fgtdec_sim_fun <span class="ot">&lt;-</span> <span class="cf">function</span>(this.iter) {</span>
-<span id="cb183-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-8" tabindex="-1"></a>  <span class="fu">set.seed</span>(this.iter)</span>
-<span id="cb183-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-9" tabindex="-1"></a>  </span>
-<span id="cb183-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-10" tabindex="-1"></a>  <span class="fu">library</span>(sampling)</span>
-<span id="cb183-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-11" tabindex="-1"></a>  <span class="fu">library</span>(survey)</span>
-<span id="cb183-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-12" tabindex="-1"></a>  <span class="fu">library</span>(convey)</span>
-<span id="cb183-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-13" tabindex="-1"></a>  </span>
-<span id="cb183-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-14" tabindex="-1"></a>  <span class="co"># load pseudo population data</span></span>
-<span id="cb183-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-15" tabindex="-1"></a>  <span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
-<span id="cb183-16"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-16" tabindex="-1"></a>  </span>
-<span id="cb183-17"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-17" tabindex="-1"></a>  </span>
-<span id="cb183-18"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-18" tabindex="-1"></a>  <span class="co"># compute size-like variable for PPS sampling design</span></span>
-<span id="cb183-19"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-19" tabindex="-1"></a>  eusilcP<span class="sc">$</span>aux <span class="ot">&lt;-</span></span>
-<span id="cb183-20"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-20" tabindex="-1"></a>    <span class="fu">log</span>(<span class="fu">ifelse</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;=</span> <span class="dv">1000</span> , eusilcP<span class="sc">$</span>eqIncome , <span class="dv">1000</span>))</span>
-<span id="cb183-21"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-21" tabindex="-1"></a>  </span>
-<span id="cb183-22"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-22" tabindex="-1"></a>  </span>
-<span id="cb183-23"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-23" tabindex="-1"></a>  <span class="co"># select sample</span></span>
-<span id="cb183-24"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-24" tabindex="-1"></a>  tt <span class="ot">&lt;-</span></span>
-<span id="cb183-25"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-25" tabindex="-1"></a>    sampling<span class="sc">::</span><span class="fu">cluster</span>(</span>
-<span id="cb183-26"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-26" tabindex="-1"></a>      <span class="at">data =</span> eusilcP[<span class="fu">sample.int</span>(<span class="fu">nrow</span>(eusilcP) , <span class="fu">nrow</span>(eusilcP) , <span class="at">replace =</span> <span class="cn">FALSE</span>) , ] ,</span>
-<span id="cb183-27"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-27" tabindex="-1"></a>      <span class="at">clustername =</span> <span class="st">&quot;hid&quot;</span> ,</span>
-<span id="cb183-28"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-28" tabindex="-1"></a>      <span class="at">size =</span> 1000L ,</span>
-<span id="cb183-29"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-29" tabindex="-1"></a>      <span class="at">method =</span> <span class="st">&quot;systematic&quot;</span> ,</span>
-<span id="cb183-30"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-30" tabindex="-1"></a>      <span class="at">pik =</span> eusilcP<span class="sc">$</span>aux</span>
-<span id="cb183-31"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-31" tabindex="-1"></a>    )</span>
-<span id="cb183-32"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-32" tabindex="-1"></a>  </span>
-<span id="cb183-33"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-33" tabindex="-1"></a>  <span class="co"># collect data</span></span>
-<span id="cb183-34"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-34" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">getdata</span>(eusilcP , tt)</span>
-<span id="cb183-35"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-35" tabindex="-1"></a>  </span>
-<span id="cb183-36"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-36" tabindex="-1"></a>  <span class="co"># create survey design object</span></span>
-<span id="cb183-37"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-37" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span></span>
-<span id="cb183-38"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-38" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
-<span id="cb183-39"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-39" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> hid ,</span>
-<span id="cb183-40"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-40" tabindex="-1"></a>      <span class="at">probs =</span> <span class="sc">~</span> Prob ,</span>
-<span id="cb183-41"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-41" tabindex="-1"></a>      <span class="at">data =</span> this.sample ,</span>
-<span id="cb183-42"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-42" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
-<span id="cb183-43"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-43" tabindex="-1"></a>    )</span>
-<span id="cb183-44"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-44" tabindex="-1"></a>  </span>
-<span id="cb183-45"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-45" tabindex="-1"></a>  <span class="co"># prepare for convey functions</span></span>
-<span id="cb183-46"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-46" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(this.desobj)</span>
-<span id="cb183-47"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-47" tabindex="-1"></a>  </span>
-<span id="cb183-48"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-48" tabindex="-1"></a>  <span class="co"># compute estimates</span></span>
-<span id="cb183-49"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-49" tabindex="-1"></a>  <span class="fu">svyfgtdec</span>( <span class="sc">~</span> eqIncome , this.desobj , <span class="at">abs_thresh =</span> <span class="dv">10000</span> , <span class="at">g =</span> <span class="dv">2</span>)</span>
-<span id="cb183-50"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-50" tabindex="-1"></a>  </span>
-<span id="cb183-51"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-51" tabindex="-1"></a>}</span>
-<span id="cb183-52"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-52" tabindex="-1"></a></span>
-<span id="cb183-53"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-53" tabindex="-1"></a><span class="co"># run replications</span></span>
-<span id="cb183-54"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-54" tabindex="-1"></a>cl <span class="ot">&lt;-</span> <span class="fu">makeCluster</span>(<span class="fu">detectCores</span>() <span class="sc">-</span> <span class="dv">1</span>)</span>
-<span id="cb183-55"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-55" tabindex="-1"></a></span>
-<span id="cb183-56"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-56" tabindex="-1"></a>fgtdec.estimate.list <span class="ot">&lt;-</span></span>
-<span id="cb183-57"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-57" tabindex="-1"></a>  <span class="fu">clusterApply</span>(cl, <span class="fu">seq_len</span>(mc.rep) , fgtdec_sim_fun)</span>
-<span id="cb183-58"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-58" tabindex="-1"></a></span>
-<span id="cb183-59"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-59" tabindex="-1"></a><span class="fu">stopCluster</span>(cl)</span></code></pre></div>
+<div class="sourceCode" id="cb182"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb182-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-1" tabindex="-1"></a><span class="co"># define the number of monte carlo replicates</span></span>
+<span id="cb182-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-2" tabindex="-1"></a>mc.rep <span class="ot">&lt;-</span> 5000L</span>
+<span id="cb182-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-3" tabindex="-1"></a></span>
+<span id="cb182-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-4" tabindex="-1"></a></span>
+<span id="cb182-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-5" tabindex="-1"></a></span>
+<span id="cb182-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-6" tabindex="-1"></a><span class="co"># simulation function</span></span>
+<span id="cb182-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-7" tabindex="-1"></a>fgtdec_sim_fun <span class="ot">&lt;-</span> <span class="cf">function</span>(this.iter) {</span>
+<span id="cb182-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-8" tabindex="-1"></a>  <span class="fu">set.seed</span>(this.iter)</span>
+<span id="cb182-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-9" tabindex="-1"></a>  </span>
+<span id="cb182-10"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-10" tabindex="-1"></a>  <span class="fu">library</span>(sampling)</span>
+<span id="cb182-11"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-11" tabindex="-1"></a>  <span class="fu">library</span>(survey)</span>
+<span id="cb182-12"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-12" tabindex="-1"></a>  <span class="fu">library</span>(convey)</span>
+<span id="cb182-13"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-13" tabindex="-1"></a>  </span>
+<span id="cb182-14"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-14" tabindex="-1"></a>  <span class="co"># load pseudo population data</span></span>
+<span id="cb182-15"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-15" tabindex="-1"></a>  <span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
+<span id="cb182-16"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-16" tabindex="-1"></a>  </span>
+<span id="cb182-17"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-17" tabindex="-1"></a>  </span>
+<span id="cb182-18"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-18" tabindex="-1"></a>  <span class="co"># compute size-like variable for PPS sampling design</span></span>
+<span id="cb182-19"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-19" tabindex="-1"></a>  eusilcP<span class="sc">$</span>aux <span class="ot">&lt;-</span></span>
+<span id="cb182-20"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-20" tabindex="-1"></a>    <span class="fu">log</span>(<span class="fu">ifelse</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;=</span> <span class="dv">1000</span> , eusilcP<span class="sc">$</span>eqIncome , <span class="dv">1000</span>))</span>
+<span id="cb182-21"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-21" tabindex="-1"></a>  </span>
+<span id="cb182-22"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-22" tabindex="-1"></a>  </span>
+<span id="cb182-23"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-23" tabindex="-1"></a>  <span class="co"># select sample</span></span>
+<span id="cb182-24"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-24" tabindex="-1"></a>  tt <span class="ot">&lt;-</span></span>
+<span id="cb182-25"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-25" tabindex="-1"></a>    sampling<span class="sc">::</span><span class="fu">cluster</span>(</span>
+<span id="cb182-26"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-26" tabindex="-1"></a>      <span class="at">data =</span> eusilcP[<span class="fu">sample.int</span>(<span class="fu">nrow</span>(eusilcP) , <span class="fu">nrow</span>(eusilcP) , <span class="at">replace =</span> <span class="cn">FALSE</span>) , ] ,</span>
+<span id="cb182-27"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-27" tabindex="-1"></a>      <span class="at">clustername =</span> <span class="st">&quot;hid&quot;</span> ,</span>
+<span id="cb182-28"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-28" tabindex="-1"></a>      <span class="at">size =</span> 1000L ,</span>
+<span id="cb182-29"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-29" tabindex="-1"></a>      <span class="at">method =</span> <span class="st">&quot;systematic&quot;</span> ,</span>
+<span id="cb182-30"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-30" tabindex="-1"></a>      <span class="at">pik =</span> eusilcP<span class="sc">$</span>aux</span>
+<span id="cb182-31"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-31" tabindex="-1"></a>    )</span>
+<span id="cb182-32"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-32" tabindex="-1"></a>  </span>
+<span id="cb182-33"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-33" tabindex="-1"></a>  <span class="co"># collect data</span></span>
+<span id="cb182-34"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-34" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">getdata</span>(eusilcP , tt)</span>
+<span id="cb182-35"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-35" tabindex="-1"></a>  </span>
+<span id="cb182-36"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-36" tabindex="-1"></a>  <span class="co"># create survey design object</span></span>
+<span id="cb182-37"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-37" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span></span>
+<span id="cb182-38"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-38" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
+<span id="cb182-39"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-39" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> hid ,</span>
+<span id="cb182-40"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-40" tabindex="-1"></a>      <span class="at">probs =</span> <span class="sc">~</span> Prob ,</span>
+<span id="cb182-41"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-41" tabindex="-1"></a>      <span class="at">data =</span> this.sample ,</span>
+<span id="cb182-42"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-42" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
+<span id="cb182-43"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-43" tabindex="-1"></a>    )</span>
+<span id="cb182-44"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-44" tabindex="-1"></a>  </span>
+<span id="cb182-45"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-45" tabindex="-1"></a>  <span class="co"># prepare for convey functions</span></span>
+<span id="cb182-46"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-46" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(this.desobj)</span>
+<span id="cb182-47"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-47" tabindex="-1"></a>  </span>
+<span id="cb182-48"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-48" tabindex="-1"></a>  <span class="co"># compute estimates</span></span>
+<span id="cb182-49"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-49" tabindex="-1"></a>  <span class="fu">svyfgtdec</span>( <span class="sc">~</span> eqIncome , this.desobj , <span class="at">abs_thresh =</span> <span class="dv">10000</span> , <span class="at">g =</span> <span class="dv">2</span>)</span>
+<span id="cb182-50"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-50" tabindex="-1"></a>  </span>
+<span id="cb182-51"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-51" tabindex="-1"></a>}</span>
+<span id="cb182-52"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-52" tabindex="-1"></a></span>
+<span id="cb182-53"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-53" tabindex="-1"></a><span class="co"># run replications</span></span>
+<span id="cb182-54"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-54" tabindex="-1"></a>cl <span class="ot">&lt;-</span> <span class="fu">makeCluster</span>(<span class="fu">detectCores</span>() <span class="sc">-</span> <span class="dv">1</span>)</span>
+<span id="cb182-55"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-55" tabindex="-1"></a></span>
+<span id="cb182-56"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-56" tabindex="-1"></a>fgtdec.estimate.list <span class="ot">&lt;-</span></span>
+<span id="cb182-57"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-57" tabindex="-1"></a>  <span class="fu">clusterApply</span>(cl, <span class="fu">seq_len</span>(mc.rep) , fgtdec_sim_fun)</span>
+<span id="cb182-58"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-58" tabindex="-1"></a></span>
+<span id="cb182-59"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb182-59" tabindex="-1"></a><span class="fu">stopCluster</span>(cl)</span></code></pre></div>
 <p>The PRB of each component is estimated using the code below. Notice that PRBs are relatively small, with absolute values below 1%, with the largest bias in the GEI index component.</p>
-<div class="sourceCode" id="cb184"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb184-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb184-1" tabindex="-1"></a><span class="co"># repeat true population values</span></span>
-<span id="cb184-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb184-2" tabindex="-1"></a>(theta.pop)</span></code></pre></div>
+<div class="sourceCode" id="cb183"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb183-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-1" tabindex="-1"></a><span class="co"># repeat true population values</span></span>
+<span id="cb183-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb183-2" tabindex="-1"></a>(theta.pop)</span></code></pre></div>
 <pre><code>##                fgt2                fgt0                fgt1                 igr 
 ##          0.01571192          0.11412691          0.03259544          0.28560699 
 ## gei(poor;epsilon=2) 
 ##          0.34386588</code></pre>
-<div class="sourceCode" id="cb186"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb186-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb186-1" tabindex="-1"></a><span class="co"># estimate the expected values of the components estimators</span></span>
-<span id="cb186-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb186-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
-<span id="cb186-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb186-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(fgtdec.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb185"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb185-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb185-1" tabindex="-1"></a><span class="co"># estimate the expected values of the components estimators</span></span>
+<span id="cb185-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb185-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
+<span id="cb185-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb185-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(fgtdec.estimate.list , coef)))</span></code></pre></div>
 <pre><code>##                fgt2                fgt0                fgt1                 igr 
 ##          0.01577844          0.11432776          0.03269125          0.28591312 
 ## gei(poor;epsilon=2) 
 ##          0.34234370</code></pre>
-<div class="sourceCode" id="cb188"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb188-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb188-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
-<span id="cb188-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb188-2" tabindex="-1"></a>(percentage_relative_bias <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb187"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb187-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb187-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
+<span id="cb187-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb187-2" tabindex="-1"></a>(percentage_relative_bias <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
 <pre><code>##                fgt2                fgt0                fgt1                 igr 
 ##           0.4233956           0.1759893           0.2939132           0.1071867 
 ## gei(poor;epsilon=2) 
 ##          -0.4426679</code></pre>
-<div class="sourceCode" id="cb190"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb190-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb190-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(percentage_relative_bias) <span class="sc">&lt;</span> <span class="dv">1</span>) </span></code></pre></div>
+<div class="sourceCode" id="cb189"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb189-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb189-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(percentage_relative_bias) <span class="sc">&lt;</span> <span class="dv">1</span>) </span></code></pre></div>
 <p>For the variance estimators, we estimate the PRB using the code below.
 Note that the bias is still relatively small, with absolute values of the PRB below 5%.</p>
-<div class="sourceCode" id="cb191"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb191-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb191-1" tabindex="-1"></a><span class="co"># estimate the variance of the components estimators</span></span>
-<span id="cb191-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb191-2" tabindex="-1"></a><span class="co"># using the empirical variance of the estimates</span></span>
-<span id="cb191-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb191-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span></span>
-<span id="cb191-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb191-4" tabindex="-1"></a>   <span class="fu">diag</span>(<span class="fu">var</span>(<span class="fu">t</span>(</span>
-<span id="cb191-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb191-5" tabindex="-1"></a>     <span class="fu">sapply</span>(fgtdec.estimate.list , coef)</span>
-<span id="cb191-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb191-6" tabindex="-1"></a>   ))))</span></code></pre></div>
+<div class="sourceCode" id="cb190"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb190-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb190-1" tabindex="-1"></a><span class="co"># estimate the variance of the components estimators</span></span>
+<span id="cb190-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb190-2" tabindex="-1"></a><span class="co"># using the empirical variance of the estimates</span></span>
+<span id="cb190-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb190-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span></span>
+<span id="cb190-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb190-4" tabindex="-1"></a>   <span class="fu">diag</span>(<span class="fu">var</span>(<span class="fu">t</span>(</span>
+<span id="cb190-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb190-5" tabindex="-1"></a>     <span class="fu">sapply</span>(fgtdec.estimate.list , coef)</span>
+<span id="cb190-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb190-6" tabindex="-1"></a>   ))))</span></code></pre></div>
 <pre><code>##                fgt2                fgt0                fgt1                 igr 
 ##        6.447720e-06        1.015546e-04        1.468049e-05        4.753320e-04 
 ## gei(poor;epsilon=2) 
 ##        1.841360e-03</code></pre>
-<div class="sourceCode" id="cb193"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb193-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb193-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Watts index variance estimator</span></span>
-<span id="cb193-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb193-2" tabindex="-1"></a><span class="co"># using the (estimated) expected value of the variance estimates</span></span>
-<span id="cb193-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb193-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span></span>
-<span id="cb193-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb193-4" tabindex="-1"></a>    <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(fgtdec.estimate.list , <span class="cf">function</span>(z)</span>
-<span id="cb193-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb193-5" tabindex="-1"></a>      <span class="fu">diag</span>(<span class="fu">vcov</span>(</span>
-<span id="cb193-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb193-6" tabindex="-1"></a>        z</span>
-<span id="cb193-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb193-7" tabindex="-1"></a>      )))))</span></code></pre></div>
+<div class="sourceCode" id="cb192"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb192-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb192-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Watts index variance estimator</span></span>
+<span id="cb192-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb192-2" tabindex="-1"></a><span class="co"># using the (estimated) expected value of the variance estimates</span></span>
+<span id="cb192-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb192-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span></span>
+<span id="cb192-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb192-4" tabindex="-1"></a>    <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(fgtdec.estimate.list , <span class="cf">function</span>(z)</span>
+<span id="cb192-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb192-5" tabindex="-1"></a>      <span class="fu">diag</span>(<span class="fu">vcov</span>(</span>
+<span id="cb192-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb192-6" tabindex="-1"></a>        z</span>
+<span id="cb192-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb192-7" tabindex="-1"></a>      )))))</span></code></pre></div>
 <pre><code>##                fgt2                fgt0                fgt1                 igr 
 ##        6.462904e-06        1.014859e-04        1.473047e-05        4.923412e-04 
 ## gei(poor;epsilon=2) 
 ##        1.911158e-03</code></pre>
-<div class="sourceCode" id="cb195"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb195-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb195-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimators</span></span>
-<span id="cb195-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb195-2" tabindex="-1"></a>(percentage_relative_bias_variance <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span>  (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb194"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb194-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb194-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimators</span></span>
+<span id="cb194-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb194-2" tabindex="-1"></a>(percentage_relative_bias_variance <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span>  (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
 <pre><code>##                fgt2                fgt0                fgt1                 igr 
 ##          0.23548684         -0.06759586          0.34047392          3.57838870 
 ## gei(poor;epsilon=2) 
 ##          3.79052600</code></pre>
-<div class="sourceCode" id="cb197"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb197-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb197-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(percentage_relative_bias_variance) <span class="sc">&lt;</span> <span class="dv">5</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb196"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb196-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb196-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(percentage_relative_bias_variance) <span class="sc">&lt;</span> <span class="dv">5</span>)</span></code></pre></div>
 <p>Regarding the MSE of the decomposition estimator, the squared bias accounts for less than 0.1% of the MSE.
 This means that, with a good estimate of the variance, we should be able to have a good approximation for the MSE.</p>
-<div class="sourceCode" id="cb198"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb198-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb198-1" tabindex="-1"></a><span class="co"># estimate MSE</span></span>
-<span id="cb198-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb198-2" tabindex="-1"></a>theta.bias2 <span class="ot">&lt;-</span> (theta.exp <span class="sc">-</span> theta.pop) <span class="sc">^</span> <span class="dv">2</span></span>
-<span id="cb198-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb198-3" tabindex="-1"></a>(theta.mse <span class="ot">&lt;-</span> theta.bias2 <span class="sc">+</span> vartheta.popest)</span></code></pre></div>
+<div class="sourceCode" id="cb197"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb197-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb197-1" tabindex="-1"></a><span class="co"># estimate MSE</span></span>
+<span id="cb197-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb197-2" tabindex="-1"></a>theta.bias2 <span class="ot">&lt;-</span> (theta.exp <span class="sc">-</span> theta.pop) <span class="sc">^</span> <span class="dv">2</span></span>
+<span id="cb197-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb197-3" tabindex="-1"></a>(theta.mse <span class="ot">&lt;-</span> theta.bias2 <span class="sc">+</span> vartheta.popest)</span></code></pre></div>
 <pre><code>##                fgt2                fgt0                fgt1                 igr 
 ##        6.452146e-06        1.015949e-04        1.468967e-05        4.754257e-04 
 ## gei(poor;epsilon=2) 
 ##        1.843678e-03</code></pre>
-<div class="sourceCode" id="cb200"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb200-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb200-1" tabindex="-1"></a><span class="co"># squared bias component of the MSE</span></span>
-<span id="cb200-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb200-2" tabindex="-1"></a>( squared_bias_over_mse <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.bias2 <span class="sc">/</span> theta.mse) )</span></code></pre></div>
+<div class="sourceCode" id="cb199"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb199-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb199-1" tabindex="-1"></a><span class="co"># squared bias component of the MSE</span></span>
+<span id="cb199-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb199-2" tabindex="-1"></a>( squared_bias_over_mse <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.bias2 <span class="sc">/</span> theta.mse) )</span></code></pre></div>
 <pre><code>##                fgt2                fgt0                fgt1                 igr 
 ##          0.06858780          0.03970787          0.06247986          0.01971227 
 ## gei(poor;epsilon=2) 
 ##          0.12567511</code></pre>
-<div class="sourceCode" id="cb202"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb202-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-1" tabindex="-1"></a><span class="fu">stopifnot</span>( squared_bias_over_mse <span class="sc">&lt;</span> <span class="dv">1</span> )</span></code></pre></div>
+<div class="sourceCode" id="cb201"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb201-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb201-1" tabindex="-1"></a><span class="fu">stopifnot</span>( squared_bias_over_mse <span class="sc">&lt;</span> <span class="dv">1</span> )</span></code></pre></div>
 <p>The CIs based on the normal approximation work reasonably well for all components. The code below shows that the coverage rates are close to the 95% nominal coverage rate.</p>
-<div class="sourceCode" id="cb203"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb203-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb203-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Watts index</span></span>
-<span id="cb203-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb203-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
-<span id="cb203-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb203-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
-<span id="cb203-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb203-4" tabindex="-1"></a>  <span class="fu">sapply</span>(fgtdec.estimate.list, <span class="cf">function</span>(this.stat)</span>
-<span id="cb203-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb203-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
-<span id="cb203-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb203-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop)</span>
-<span id="cb203-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb203-7" tabindex="-1"></a></span>
-<span id="cb203-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb203-8" tabindex="-1"></a><span class="co"># evaluate empirical coverage</span></span>
-<span id="cb203-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb203-9" tabindex="-1"></a><span class="fu">stopifnot</span>( <span class="fu">abs</span>( <span class="fu">rowMeans</span>(est.coverage) <span class="sc">-</span> <span class="fl">0.95</span> ) <span class="sc">&lt;</span> <span class="fl">0.015</span> )</span></code></pre></div>
+<div class="sourceCode" id="cb202"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb202-1"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Watts index</span></span>
+<span id="cb202-2"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
+<span id="cb202-3"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
+<span id="cb202-4"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-4" tabindex="-1"></a>  <span class="fu">sapply</span>(fgtdec.estimate.list, <span class="cf">function</span>(this.stat)</span>
+<span id="cb202-5"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
+<span id="cb202-6"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop)</span>
+<span id="cb202-7"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-7" tabindex="-1"></a></span>
+<span id="cb202-8"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-8" tabindex="-1"></a><span class="co"># evaluate empirical coverage</span></span>
+<span id="cb202-9"><a href="3.6-foster-greer-thorbecke-class-svyfgt-svyfgtdec.html#cb202-9" tabindex="-1"></a><span class="fu">stopifnot</span>( <span class="fu">abs</span>( <span class="fu">rowMeans</span>(est.coverage) <span class="sc">-</span> <span class="fl">0.95</span> ) <span class="sc">&lt;</span> <span class="fl">0.015</span> )</span></code></pre></div>
 <p>For additional usage examples of <code>svyfgt</code> and <code>svyfgtdec</code>, type <code>?convey::svyfgt</code> or <code>?convey::svyfgtdec</code> in the R console.</p>
 </div>
 </div>
diff --git a/docs/3.7-watts-poverty-measure-svywatts-svywattsdec.html b/docs/3.7-watts-poverty-measure-svywatts-svywattsdec.html
index ecf22f9..5c04561 100644
--- a/docs/3.7-watts-poverty-measure-svywatts-svywattsdec.html
+++ b/docs/3.7-watts-poverty-measure-svywatts-svywattsdec.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,12 +253,12 @@
 <div class="col-sm-12">
 <div id="watts-poverty-measure-svywatts-svywattsdec" class="section level2" number="3.7">
 <h2><span class="header-section-number">3.7</span> Watts poverty measure (svywatts, svywattsdec)</h2>
-<div class="sourceCode" id="cb204"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb204-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-1" tabindex="-1"></a>✔️ time to exit poverty interpretation<span class="sc">:</span> watts score divided by a growth rate</span>
-<span id="cb204-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-2" tabindex="-1"></a>✔️ sensitive to intensity and inequality among the poor</span>
-<span id="cb204-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-3" tabindex="-1"></a>✔️ can be decomposed into interpretable measures</span>
-<span id="cb204-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-4" tabindex="-1"></a>❌ not defined <span class="cf">for</span> individuals with zero or negative incomes</span>
-<span id="cb204-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-5" tabindex="-1"></a>❌ interpretation is not very straightforward</span>
-<span id="cb204-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-6" tabindex="-1"></a>❌ less common than the FGT measures nowadays</span></code></pre></div>
+<div class="sourceCode" id="cb203"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb203-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb203-1" tabindex="-1"></a>✔️ time to exit poverty interpretation<span class="sc">:</span> watts score divided by a growth rate</span>
+<span id="cb203-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb203-2" tabindex="-1"></a>✔️ sensitive to intensity and inequality among the poor</span>
+<span id="cb203-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb203-3" tabindex="-1"></a>✔️ can be decomposed into interpretable measures</span>
+<span id="cb203-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb203-4" tabindex="-1"></a>❌ not defined <span class="cf">for</span> individuals with zero or negative incomes</span>
+<span id="cb203-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb203-5" tabindex="-1"></a>❌ interpretation is not very straightforward</span>
+<span id="cb203-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb203-6" tabindex="-1"></a>❌ less common than the FGT measures nowadays</span></code></pre></div>
 <p>The measure proposed in <span class="citation">Watts (<label for="tufte-mn-47" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-47" class="margin-toggle">1968<span class="marginnote">Watts, Harold W. 1968. <span>“An Economic Definition of Poverty.”</span> Discussion Papers 5. Institute For Research on Poverty. <a href="https://www.irp.wisc.edu/publications/dps/pdfs/dp568.pdf">https://www.irp.wisc.edu/publications/dps/pdfs/dp568.pdf</a>.</span>)</span> satisfies a number of desirable poverty measurement axioms and is known to be one of the first distribution-sensitive poverty measures, as noted by <span class="citation">Haughton and Khandker (<label for="tufte-mn-48" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-48" class="margin-toggle">2009<span class="marginnote">Haughton, Jonathan, and Shahidur Khandker. 2009. <em>Handbook on Poverty and Inequality</em>. World Bank Training Series. World Bank Publications. <a href="https://openknowledge.worldbank.org/bitstream/handle/10986/11985/9780821376133.pdf">https://openknowledge.worldbank.org/bitstream/handle/10986/11985/9780821376133.pdf</a>.</span>)</span>. It is defined as:</p>
 <p><span class="math display">\[
 Watts = \frac{1}{N} \sum_{i \in U} \log{ \bigg( \frac{y_i}{\theta} \bigg) \delta ( y_i \leqslant \theta) }.
@@ -285,294 +285,294 @@ <h2><span class="header-section-number">3.7</span> Watts poverty measure (svywat
 <h3><span class="header-section-number">3.7.1</span> Monte Carlo Simulation</h3>
 <p>To provide a example for our code, we proceed with a Monte Carlo experiment.
 Using the <code>eusilcP</code> data from the <code>simPop</code> package <span class="citation">(<label for="tufte-mn-52" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-52" class="margin-toggle">Templ et al. 2017<span class="marginnote">Templ, Matthias, Bernhard Meindl, Alexander Kowarik, and Olivier Dupriez. 2017. <span>“Simulation of Synthetic Complex Data: The <span>R</span> Package <span class="nocase">simPop</span>.”</span> <em>Journal of Statistical Software</em> 79 (10): 1–38. <a href="https://doi.org/10.18637/jss.v079.i10">https://doi.org/10.18637/jss.v079.i10</a>.</span>)</span>, we can compute the actual value of the Watts index for that population:</p>
-<div class="sourceCode" id="cb205"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb205-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
-<span id="cb205-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-2" tabindex="-1"></a><span class="fu">library</span>(sampling)</span>
-<span id="cb205-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-3" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb205-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-4" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb205-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-5" tabindex="-1"></a><span class="fu">library</span>(parallel)</span>
-<span id="cb205-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-6" tabindex="-1"></a></span>
-<span id="cb205-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-7" tabindex="-1"></a><span class="co"># load pseudo population data</span></span>
-<span id="cb205-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-8" tabindex="-1"></a><span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
-<span id="cb205-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-9" tabindex="-1"></a></span>
-<span id="cb205-10"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-10" tabindex="-1"></a><span class="co"># compute population value of the Watts index decomposition</span></span>
-<span id="cb205-11"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-11" tabindex="-1"></a>inc.pos <span class="ot">&lt;-</span> eusilcP<span class="sc">$</span>eqIncome[eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;</span> <span class="dv">0</span>]</span>
-<span id="cb205-12"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-12" tabindex="-1"></a>(theta.pop <span class="ot">&lt;-</span></span>
-<span id="cb205-13"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb205-13" tabindex="-1"></a>    <span class="fu">mean</span>(<span class="fu">ifelse</span>(inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span> , <span class="fu">log</span>(<span class="dv">10000</span> <span class="sc">/</span>  inc.pos) , <span class="dv">0</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb204"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb204-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
+<span id="cb204-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-2" tabindex="-1"></a><span class="fu">library</span>(sampling)</span>
+<span id="cb204-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-3" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb204-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-4" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb204-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-5" tabindex="-1"></a><span class="fu">library</span>(parallel)</span>
+<span id="cb204-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-6" tabindex="-1"></a></span>
+<span id="cb204-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-7" tabindex="-1"></a><span class="co"># load pseudo population data</span></span>
+<span id="cb204-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-8" tabindex="-1"></a><span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
+<span id="cb204-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-9" tabindex="-1"></a></span>
+<span id="cb204-10"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-10" tabindex="-1"></a><span class="co"># compute population value of the Watts index decomposition</span></span>
+<span id="cb204-11"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-11" tabindex="-1"></a>inc.pos <span class="ot">&lt;-</span> eusilcP<span class="sc">$</span>eqIncome[eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;</span> <span class="dv">0</span>]</span>
+<span id="cb204-12"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-12" tabindex="-1"></a>(theta.pop <span class="ot">&lt;-</span></span>
+<span id="cb204-13"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb204-13" tabindex="-1"></a>    <span class="fu">mean</span>(<span class="fu">ifelse</span>(inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span> , <span class="fu">log</span>(<span class="dv">10000</span> <span class="sc">/</span>  inc.pos) , <span class="dv">0</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>))</span></code></pre></div>
 <pre><code>## [1] 0.05025374</code></pre>
 <p>Now, to study the distribution of the estimator under a particular sampling design, we select 5000 samples under one-stage cluster sampling of 100 households using the <code>cluster</code> function from the <code>sampling</code> package <span class="citation">(<label for="tufte-mn-53" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-53" class="margin-toggle">Tillé and Matei 2021<span class="marginnote">Tillé, Yves, and Alina Matei. 2021. <em>Sampling: Survey Sampling</em>. <a href="https://CRAN.R-project.org/package=sampling">https://CRAN.R-project.org/package=sampling</a>.</span>)</span>, and use the <code>svywatts</code> function to estimate the Watts index for each of those samples:</p>
-<div class="sourceCode" id="cb207"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb207-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-1" tabindex="-1"></a><span class="co"># define the number of monte carlo replicates</span></span>
-<span id="cb207-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-2" tabindex="-1"></a>mc.rep <span class="ot">&lt;-</span> 5000L</span>
-<span id="cb207-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-3" tabindex="-1"></a></span>
-<span id="cb207-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-4" tabindex="-1"></a></span>
-<span id="cb207-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-5" tabindex="-1"></a><span class="co"># simulation function</span></span>
-<span id="cb207-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-6" tabindex="-1"></a>watts_sim_fun <span class="ot">&lt;-</span> <span class="cf">function</span>(this.iter) {</span>
-<span id="cb207-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-7" tabindex="-1"></a>  <span class="fu">set.seed</span>(this.iter)</span>
-<span id="cb207-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-8" tabindex="-1"></a>  </span>
-<span id="cb207-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-9" tabindex="-1"></a>  <span class="fu">library</span>(survey)</span>
-<span id="cb207-10"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-10" tabindex="-1"></a>  <span class="fu">library</span>(convey)</span>
-<span id="cb207-11"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-11" tabindex="-1"></a>  <span class="fu">library</span>(sampling)</span>
-<span id="cb207-12"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-12" tabindex="-1"></a>  </span>
-<span id="cb207-13"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-13" tabindex="-1"></a>  </span>
-<span id="cb207-14"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-14" tabindex="-1"></a>  <span class="co"># load pseudo population data</span></span>
-<span id="cb207-15"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-15" tabindex="-1"></a>  <span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
-<span id="cb207-16"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-16" tabindex="-1"></a>  </span>
-<span id="cb207-17"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-17" tabindex="-1"></a>  <span class="co"># compute size-like variable for PPS sampling design</span></span>
-<span id="cb207-18"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-18" tabindex="-1"></a>  eusilcP<span class="sc">$</span>aux <span class="ot">&lt;-</span></span>
-<span id="cb207-19"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-19" tabindex="-1"></a>    <span class="fu">log</span>(<span class="fu">ifelse</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;=</span> <span class="dv">1000</span> , eusilcP<span class="sc">$</span>eqIncome , <span class="dv">1000</span>))</span>
-<span id="cb207-20"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-20" tabindex="-1"></a>  </span>
-<span id="cb207-21"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-21" tabindex="-1"></a>  <span class="co"># select sample</span></span>
-<span id="cb207-22"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-22" tabindex="-1"></a>  tt <span class="ot">&lt;-</span></span>
-<span id="cb207-23"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-23" tabindex="-1"></a>    sampling<span class="sc">::</span><span class="fu">cluster</span>(</span>
-<span id="cb207-24"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-24" tabindex="-1"></a>      <span class="at">data =</span> eusilcP[<span class="fu">sample.int</span>(<span class="fu">nrow</span>(eusilcP) , <span class="fu">nrow</span>(eusilcP) , <span class="at">replace =</span> <span class="cn">FALSE</span>) ,] ,</span>
-<span id="cb207-25"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-25" tabindex="-1"></a>      <span class="at">clustername =</span> <span class="st">&quot;hid&quot;</span> ,</span>
-<span id="cb207-26"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-26" tabindex="-1"></a>      <span class="at">size =</span> 1000L ,</span>
-<span id="cb207-27"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-27" tabindex="-1"></a>      <span class="at">method =</span> <span class="st">&quot;systematic&quot;</span> ,</span>
-<span id="cb207-28"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-28" tabindex="-1"></a>      <span class="at">pik =</span> eusilcP<span class="sc">$</span>aux</span>
-<span id="cb207-29"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-29" tabindex="-1"></a>    )</span>
-<span id="cb207-30"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-30" tabindex="-1"></a>  </span>
-<span id="cb207-31"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-31" tabindex="-1"></a>  <span class="co"># collect data</span></span>
-<span id="cb207-32"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-32" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">getdata</span>(eusilcP , tt)</span>
-<span id="cb207-33"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-33" tabindex="-1"></a>  </span>
-<span id="cb207-34"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-34" tabindex="-1"></a>  <span class="co"># create survey design object</span></span>
-<span id="cb207-35"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-35" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span></span>
-<span id="cb207-36"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-36" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
-<span id="cb207-37"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-37" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> hid ,</span>
-<span id="cb207-38"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-38" tabindex="-1"></a>      <span class="at">probs =</span> <span class="sc">~</span> Prob ,</span>
-<span id="cb207-39"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-39" tabindex="-1"></a>      <span class="at">data =</span> this.sample ,</span>
-<span id="cb207-40"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-40" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
-<span id="cb207-41"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-41" tabindex="-1"></a>    )</span>
-<span id="cb207-42"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-42" tabindex="-1"></a>  </span>
-<span id="cb207-43"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-43" tabindex="-1"></a>  <span class="co"># prepare for convey functions</span></span>
-<span id="cb207-44"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-44" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(this.desobj)</span>
-<span id="cb207-45"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-45" tabindex="-1"></a>  </span>
-<span id="cb207-46"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-46" tabindex="-1"></a>  <span class="co"># filter positive incomes</span></span>
-<span id="cb207-47"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-47" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">subset</span>(this.desobj , eqIncome <span class="sc">&gt;</span> <span class="dv">0</span>)</span>
-<span id="cb207-48"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-48" tabindex="-1"></a>  </span>
-<span id="cb207-49"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-49" tabindex="-1"></a>  <span class="co"># compute estimates</span></span>
-<span id="cb207-50"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-50" tabindex="-1"></a>  <span class="fu">svywatts</span>( <span class="sc">~</span> eqIncome , this.desobj , <span class="at">abs_thresh =</span> <span class="dv">10000</span>)</span>
-<span id="cb207-51"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-51" tabindex="-1"></a>  </span>
-<span id="cb207-52"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-52" tabindex="-1"></a>}</span>
-<span id="cb207-53"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-53" tabindex="-1"></a></span>
-<span id="cb207-54"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-54" tabindex="-1"></a><span class="co"># run replications</span></span>
-<span id="cb207-55"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-55" tabindex="-1"></a>cl <span class="ot">&lt;-</span> <span class="fu">makeCluster</span>(<span class="fu">detectCores</span>() <span class="sc">-</span> <span class="dv">1</span>)</span>
-<span id="cb207-56"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-56" tabindex="-1"></a></span>
-<span id="cb207-57"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-57" tabindex="-1"></a>watts.estimate.list <span class="ot">&lt;-</span></span>
-<span id="cb207-58"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-58" tabindex="-1"></a>  <span class="fu">clusterApply</span>(cl, <span class="fu">seq_len</span>(mc.rep) , watts_sim_fun)</span>
-<span id="cb207-59"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-59" tabindex="-1"></a></span>
-<span id="cb207-60"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-60" tabindex="-1"></a><span class="fu">stopCluster</span>(cl)</span></code></pre></div>
+<div class="sourceCode" id="cb206"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb206-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-1" tabindex="-1"></a><span class="co"># define the number of monte carlo replicates</span></span>
+<span id="cb206-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-2" tabindex="-1"></a>mc.rep <span class="ot">&lt;-</span> 5000L</span>
+<span id="cb206-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-3" tabindex="-1"></a></span>
+<span id="cb206-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-4" tabindex="-1"></a></span>
+<span id="cb206-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-5" tabindex="-1"></a><span class="co"># simulation function</span></span>
+<span id="cb206-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-6" tabindex="-1"></a>watts_sim_fun <span class="ot">&lt;-</span> <span class="cf">function</span>(this.iter) {</span>
+<span id="cb206-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-7" tabindex="-1"></a>  <span class="fu">set.seed</span>(this.iter)</span>
+<span id="cb206-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-8" tabindex="-1"></a>  </span>
+<span id="cb206-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-9" tabindex="-1"></a>  <span class="fu">library</span>(survey)</span>
+<span id="cb206-10"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-10" tabindex="-1"></a>  <span class="fu">library</span>(convey)</span>
+<span id="cb206-11"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-11" tabindex="-1"></a>  <span class="fu">library</span>(sampling)</span>
+<span id="cb206-12"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-12" tabindex="-1"></a>  </span>
+<span id="cb206-13"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-13" tabindex="-1"></a>  </span>
+<span id="cb206-14"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-14" tabindex="-1"></a>  <span class="co"># load pseudo population data</span></span>
+<span id="cb206-15"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-15" tabindex="-1"></a>  <span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
+<span id="cb206-16"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-16" tabindex="-1"></a>  </span>
+<span id="cb206-17"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-17" tabindex="-1"></a>  <span class="co"># compute size-like variable for PPS sampling design</span></span>
+<span id="cb206-18"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-18" tabindex="-1"></a>  eusilcP<span class="sc">$</span>aux <span class="ot">&lt;-</span></span>
+<span id="cb206-19"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-19" tabindex="-1"></a>    <span class="fu">log</span>(<span class="fu">ifelse</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;=</span> <span class="dv">1000</span> , eusilcP<span class="sc">$</span>eqIncome , <span class="dv">1000</span>))</span>
+<span id="cb206-20"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-20" tabindex="-1"></a>  </span>
+<span id="cb206-21"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-21" tabindex="-1"></a>  <span class="co"># select sample</span></span>
+<span id="cb206-22"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-22" tabindex="-1"></a>  tt <span class="ot">&lt;-</span></span>
+<span id="cb206-23"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-23" tabindex="-1"></a>    sampling<span class="sc">::</span><span class="fu">cluster</span>(</span>
+<span id="cb206-24"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-24" tabindex="-1"></a>      <span class="at">data =</span> eusilcP[<span class="fu">sample.int</span>(<span class="fu">nrow</span>(eusilcP) , <span class="fu">nrow</span>(eusilcP) , <span class="at">replace =</span> <span class="cn">FALSE</span>) ,] ,</span>
+<span id="cb206-25"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-25" tabindex="-1"></a>      <span class="at">clustername =</span> <span class="st">&quot;hid&quot;</span> ,</span>
+<span id="cb206-26"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-26" tabindex="-1"></a>      <span class="at">size =</span> 1000L ,</span>
+<span id="cb206-27"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-27" tabindex="-1"></a>      <span class="at">method =</span> <span class="st">&quot;systematic&quot;</span> ,</span>
+<span id="cb206-28"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-28" tabindex="-1"></a>      <span class="at">pik =</span> eusilcP<span class="sc">$</span>aux</span>
+<span id="cb206-29"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-29" tabindex="-1"></a>    )</span>
+<span id="cb206-30"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-30" tabindex="-1"></a>  </span>
+<span id="cb206-31"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-31" tabindex="-1"></a>  <span class="co"># collect data</span></span>
+<span id="cb206-32"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-32" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">getdata</span>(eusilcP , tt)</span>
+<span id="cb206-33"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-33" tabindex="-1"></a>  </span>
+<span id="cb206-34"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-34" tabindex="-1"></a>  <span class="co"># create survey design object</span></span>
+<span id="cb206-35"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-35" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span></span>
+<span id="cb206-36"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-36" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
+<span id="cb206-37"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-37" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> hid ,</span>
+<span id="cb206-38"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-38" tabindex="-1"></a>      <span class="at">probs =</span> <span class="sc">~</span> Prob ,</span>
+<span id="cb206-39"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-39" tabindex="-1"></a>      <span class="at">data =</span> this.sample ,</span>
+<span id="cb206-40"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-40" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
+<span id="cb206-41"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-41" tabindex="-1"></a>    )</span>
+<span id="cb206-42"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-42" tabindex="-1"></a>  </span>
+<span id="cb206-43"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-43" tabindex="-1"></a>  <span class="co"># prepare for convey functions</span></span>
+<span id="cb206-44"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-44" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(this.desobj)</span>
+<span id="cb206-45"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-45" tabindex="-1"></a>  </span>
+<span id="cb206-46"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-46" tabindex="-1"></a>  <span class="co"># filter positive incomes</span></span>
+<span id="cb206-47"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-47" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">subset</span>(this.desobj , eqIncome <span class="sc">&gt;</span> <span class="dv">0</span>)</span>
+<span id="cb206-48"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-48" tabindex="-1"></a>  </span>
+<span id="cb206-49"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-49" tabindex="-1"></a>  <span class="co"># compute estimates</span></span>
+<span id="cb206-50"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-50" tabindex="-1"></a>  <span class="fu">svywatts</span>( <span class="sc">~</span> eqIncome , this.desobj , <span class="at">abs_thresh =</span> <span class="dv">10000</span>)</span>
+<span id="cb206-51"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-51" tabindex="-1"></a>  </span>
+<span id="cb206-52"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-52" tabindex="-1"></a>}</span>
+<span id="cb206-53"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-53" tabindex="-1"></a></span>
+<span id="cb206-54"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-54" tabindex="-1"></a><span class="co"># run replications</span></span>
+<span id="cb206-55"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-55" tabindex="-1"></a>cl <span class="ot">&lt;-</span> <span class="fu">makeCluster</span>(<span class="fu">detectCores</span>() <span class="sc">-</span> <span class="dv">1</span>)</span>
+<span id="cb206-56"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-56" tabindex="-1"></a></span>
+<span id="cb206-57"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-57" tabindex="-1"></a>watts.estimate.list <span class="ot">&lt;-</span></span>
+<span id="cb206-58"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-58" tabindex="-1"></a>  <span class="fu">clusterApply</span>(cl, <span class="fu">seq_len</span>(mc.rep) , watts_sim_fun)</span>
+<span id="cb206-59"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-59" tabindex="-1"></a></span>
+<span id="cb206-60"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb206-60" tabindex="-1"></a><span class="fu">stopCluster</span>(cl)</span></code></pre></div>
 <p>Then, we evaluate the Percentage Relative Bias (PRB) of the Watts index estimator. Under this scenario, the PRB of the Watts index estimator is 0.3772%.</p>
-<div class="sourceCode" id="cb208"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb208-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb208-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Watts index estimator</span></span>
-<span id="cb208-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb208-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
-<span id="cb208-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb208-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(watts.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb207"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb207-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Watts index estimator</span></span>
+<span id="cb207-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
+<span id="cb207-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb207-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(watts.estimate.list , coef)))</span></code></pre></div>
 <pre><code>## [1] 0.05044329</code></pre>
-<div class="sourceCode" id="cb210"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb210-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb210-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
-<span id="cb210-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb210-2" tabindex="-1"></a>(percentage_relative_bias <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>) )</span></code></pre></div>
+<div class="sourceCode" id="cb209"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb209-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb209-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
+<span id="cb209-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb209-2" tabindex="-1"></a>(percentage_relative_bias <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>) )</span></code></pre></div>
 <pre><code>## [1] 0.377195</code></pre>
-<div class="sourceCode" id="cb212"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb212-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb212-1" tabindex="-1"></a><span class="fu">stopifnot</span>( <span class="fu">round</span>( percentage_relative_bias , <span class="dv">4</span> ) <span class="sc">==</span> <span class="fl">0.3772</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb211"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb211-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb211-1" tabindex="-1"></a><span class="fu">stopifnot</span>( <span class="fu">round</span>( percentage_relative_bias , <span class="dv">4</span> ) <span class="sc">==</span> <span class="fl">0.3772</span>)</span></code></pre></div>
 <p>For the variance estimator, we have:</p>
-<div class="sourceCode" id="cb213"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb213-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb213-1" tabindex="-1"></a><span class="co"># estimate the variance of the Watts index estimator</span></span>
-<span id="cb213-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb213-2" tabindex="-1"></a><span class="co"># using the empirical variance of the estimates</span></span>
-<span id="cb213-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb213-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span> <span class="fu">var</span>(<span class="fu">sapply</span>(watts.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb212"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb212-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb212-1" tabindex="-1"></a><span class="co"># estimate the variance of the Watts index estimator</span></span>
+<span id="cb212-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb212-2" tabindex="-1"></a><span class="co"># using the empirical variance of the estimates</span></span>
+<span id="cb212-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb212-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span> <span class="fu">var</span>(<span class="fu">sapply</span>(watts.estimate.list , coef)))</span></code></pre></div>
 <pre><code>## [1] 6.141434e-05</code></pre>
-<div class="sourceCode" id="cb215"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb215-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb215-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Watts index variance estimator</span></span>
-<span id="cb215-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb215-2" tabindex="-1"></a><span class="co"># using the (estimated) expected value of the variance estimates</span></span>
-<span id="cb215-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb215-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(watts.estimate.list , vcov)))</span></code></pre></div>
+<div class="sourceCode" id="cb214"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb214-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb214-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Watts index variance estimator</span></span>
+<span id="cb214-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb214-2" tabindex="-1"></a><span class="co"># using the (estimated) expected value of the variance estimates</span></span>
+<span id="cb214-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb214-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(watts.estimate.list , vcov)))</span></code></pre></div>
 <pre><code>## [1] 6.100902e-05</code></pre>
-<div class="sourceCode" id="cb217"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb217-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb217-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimator</span></span>
-<span id="cb217-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb217-2" tabindex="-1"></a>(percentage_relative_bias_variance <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span>  (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb216"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb216-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb216-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimator</span></span>
+<span id="cb216-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb216-2" tabindex="-1"></a>(percentage_relative_bias_variance <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span>  (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
 <pre><code>## [1] -0.6599717</code></pre>
-<div class="sourceCode" id="cb219"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb219-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb219-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(percentage_relative_bias_variance, <span class="dv">4</span>) <span class="sc">==</span> <span class="sc">-</span><span class="fl">0.6600</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb218"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb218-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb218-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(percentage_relative_bias_variance, <span class="dv">4</span>) <span class="sc">==</span> <span class="sc">-</span><span class="fl">0.6600</span>)</span></code></pre></div>
 <p>Under this scenario, the PRB of the Watts index variance estimator is -0.6600%.</p>
 <p>Our simulations show that the Squared Bias of this estimator accounts for less than 0.1% of its Mean Squared Error:</p>
-<div class="sourceCode" id="cb220"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb220-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb220-1" tabindex="-1"></a>theta.bias2 <span class="ot">&lt;-</span> (theta.exp <span class="sc">-</span> theta.pop) <span class="sc">^</span> <span class="dv">2</span></span>
-<span id="cb220-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb220-2" tabindex="-1"></a>theta.mse <span class="ot">&lt;-</span> theta.bias2 <span class="sc">+</span> vartheta.popest</span>
-<span id="cb220-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb220-3" tabindex="-1"></a>(squared_bias_over_mse <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.bias2 <span class="sc">/</span> theta.mse))</span></code></pre></div>
+<div class="sourceCode" id="cb219"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb219-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb219-1" tabindex="-1"></a>theta.bias2 <span class="ot">&lt;-</span> (theta.exp <span class="sc">-</span> theta.pop) <span class="sc">^</span> <span class="dv">2</span></span>
+<span id="cb219-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb219-2" tabindex="-1"></a>theta.mse <span class="ot">&lt;-</span> theta.bias2 <span class="sc">+</span> vartheta.popest</span>
+<span id="cb219-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb219-3" tabindex="-1"></a>(squared_bias_over_mse <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.bias2 <span class="sc">/</span> theta.mse))</span></code></pre></div>
 <pre><code>## [1] 0.05847158</code></pre>
-<div class="sourceCode" id="cb222"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb222-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-1" tabindex="-1"></a><span class="fu">stopifnot</span>(squared_bias_over_mse <span class="sc">&lt;</span> <span class="fl">0.1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb221"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb221-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb221-1" tabindex="-1"></a><span class="fu">stopifnot</span>(squared_bias_over_mse <span class="sc">&lt;</span> <span class="fl">0.1</span>)</span></code></pre></div>
 <p>Next, we evaluate the Percentage Coverage Rate (PCR). In theory, under repeated sampling, the estimated 95% CIs should cover the population parameter approximately 95% of the time. We can evaluate that using:</p>
-<div class="sourceCode" id="cb223"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb223-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb223-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Watts index</span></span>
-<span id="cb223-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb223-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
-<span id="cb223-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb223-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
-<span id="cb223-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb223-4" tabindex="-1"></a>  <span class="fu">sapply</span>(watts.estimate.list, <span class="cf">function</span>(this.stat)</span>
-<span id="cb223-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb223-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
-<span id="cb223-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb223-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop)</span>
-<span id="cb223-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb223-7" tabindex="-1"></a></span>
-<span id="cb223-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb223-8" tabindex="-1"></a><span class="co"># evaluate empirical coverage</span></span>
-<span id="cb223-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb223-9" tabindex="-1"></a>(empirical_coverage <span class="ot">&lt;-</span> <span class="fu">mean</span>(est.coverage))</span></code></pre></div>
+<div class="sourceCode" id="cb222"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb222-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Watts index</span></span>
+<span id="cb222-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
+<span id="cb222-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
+<span id="cb222-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-4" tabindex="-1"></a>  <span class="fu">sapply</span>(watts.estimate.list, <span class="cf">function</span>(this.stat)</span>
+<span id="cb222-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
+<span id="cb222-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop)</span>
+<span id="cb222-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-7" tabindex="-1"></a></span>
+<span id="cb222-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-8" tabindex="-1"></a><span class="co"># evaluate empirical coverage</span></span>
+<span id="cb222-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb222-9" tabindex="-1"></a>(empirical_coverage <span class="ot">&lt;-</span> <span class="fu">mean</span>(est.coverage))</span></code></pre></div>
 <pre><code>## [1] 0.9268</code></pre>
-<div class="sourceCode" id="cb225"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb225-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(empirical_coverage  <span class="sc">-</span> <span class="fl">0.95</span>) <span class="sc">&lt;</span> <span class="fl">0.025</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb224"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb224-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb224-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(empirical_coverage  <span class="sc">-</span> <span class="fl">0.95</span>) <span class="sc">&lt;</span> <span class="fl">0.025</span>)</span></code></pre></div>
 <p>Our coverages are not too far from the nominal coverage level of 95%.</p>
 <p>For the Watts index decomposition, we start by computing the (true) population values of the components:</p>
-<div class="sourceCode" id="cb226"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb226-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-1" tabindex="-1"></a><span class="co"># compute population value of the Watts index decomposition</span></span>
-<span id="cb226-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-2" tabindex="-1"></a>inc.pos <span class="ot">&lt;-</span> eusilcP<span class="sc">$</span>eqIncome[eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;</span> <span class="dv">0</span>]</span>
-<span id="cb226-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-3" tabindex="-1"></a>wdec1 <span class="ot">&lt;-</span></span>
-<span id="cb226-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-4" tabindex="-1"></a>  <span class="fu">mean</span>(<span class="fu">ifelse</span>(inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span> , <span class="fu">log</span>(<span class="dv">10000</span> <span class="sc">/</span>  inc.pos) , <span class="dv">0</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb226-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-5" tabindex="-1"></a>wdec2 <span class="ot">&lt;-</span> <span class="fu">mean</span>(inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span> , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb226-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-6" tabindex="-1"></a>mu.poor <span class="ot">&lt;-</span> <span class="fu">mean</span>(inc.pos [inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span>])</span>
-<span id="cb226-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-7" tabindex="-1"></a>wdec3 <span class="ot">&lt;-</span> <span class="fu">log</span>(<span class="dv">10000</span> <span class="sc">/</span> mu.poor)</span>
-<span id="cb226-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-8" tabindex="-1"></a>wdec4 <span class="ot">&lt;-</span></span>
-<span id="cb226-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-9" tabindex="-1"></a>  <span class="sc">-</span><span class="fu">mean</span>(<span class="fu">log</span>(inc.pos[inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span>] <span class="sc">/</span> mu.poor) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb226-10"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-10" tabindex="-1"></a>theta.pop <span class="ot">&lt;-</span></span>
-<span id="cb226-11"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-11" tabindex="-1"></a>  <span class="fu">c</span>(</span>
-<span id="cb226-12"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-12" tabindex="-1"></a>    <span class="st">&quot;watts&quot;</span> <span class="ot">=</span> wdec1 ,</span>
-<span id="cb226-13"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-13" tabindex="-1"></a>    <span class="st">&quot;fgt0&quot;</span> <span class="ot">=</span>  wdec2 ,</span>
-<span id="cb226-14"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-14" tabindex="-1"></a>    <span class="st">&quot;watts pov. gap ratio&quot;</span> <span class="ot">=</span> wdec3 ,</span>
-<span id="cb226-15"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-15" tabindex="-1"></a>    <span class="st">&quot;theil(poor)&quot;</span> <span class="ot">=</span>  wdec4</span>
-<span id="cb226-16"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-16" tabindex="-1"></a>  )</span>
-<span id="cb226-17"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb226-17" tabindex="-1"></a>theta.pop</span></code></pre></div>
+<div class="sourceCode" id="cb225"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb225-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-1" tabindex="-1"></a><span class="co"># compute population value of the Watts index decomposition</span></span>
+<span id="cb225-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-2" tabindex="-1"></a>inc.pos <span class="ot">&lt;-</span> eusilcP<span class="sc">$</span>eqIncome[eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;</span> <span class="dv">0</span>]</span>
+<span id="cb225-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-3" tabindex="-1"></a>wdec1 <span class="ot">&lt;-</span></span>
+<span id="cb225-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-4" tabindex="-1"></a>  <span class="fu">mean</span>(<span class="fu">ifelse</span>(inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span> , <span class="fu">log</span>(<span class="dv">10000</span> <span class="sc">/</span>  inc.pos) , <span class="dv">0</span>) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb225-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-5" tabindex="-1"></a>wdec2 <span class="ot">&lt;-</span> <span class="fu">mean</span>(inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span> , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb225-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-6" tabindex="-1"></a>mu.poor <span class="ot">&lt;-</span> <span class="fu">mean</span>(inc.pos [inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span>])</span>
+<span id="cb225-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-7" tabindex="-1"></a>wdec3 <span class="ot">&lt;-</span> <span class="fu">log</span>(<span class="dv">10000</span> <span class="sc">/</span> mu.poor)</span>
+<span id="cb225-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-8" tabindex="-1"></a>wdec4 <span class="ot">&lt;-</span></span>
+<span id="cb225-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-9" tabindex="-1"></a>  <span class="sc">-</span><span class="fu">mean</span>(<span class="fu">log</span>(inc.pos[inc.pos <span class="sc">&lt;=</span> <span class="dv">10000</span>] <span class="sc">/</span> mu.poor) , <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb225-10"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-10" tabindex="-1"></a>theta.pop <span class="ot">&lt;-</span></span>
+<span id="cb225-11"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-11" tabindex="-1"></a>  <span class="fu">c</span>(</span>
+<span id="cb225-12"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-12" tabindex="-1"></a>    <span class="st">&quot;watts&quot;</span> <span class="ot">=</span> wdec1 ,</span>
+<span id="cb225-13"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-13" tabindex="-1"></a>    <span class="st">&quot;fgt0&quot;</span> <span class="ot">=</span>  wdec2 ,</span>
+<span id="cb225-14"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-14" tabindex="-1"></a>    <span class="st">&quot;watts pov. gap ratio&quot;</span> <span class="ot">=</span> wdec3 ,</span>
+<span id="cb225-15"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-15" tabindex="-1"></a>    <span class="st">&quot;theil(poor)&quot;</span> <span class="ot">=</span>  wdec4</span>
+<span id="cb225-16"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-16" tabindex="-1"></a>  )</span>
+<span id="cb225-17"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb225-17" tabindex="-1"></a>theta.pop</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##           0.05025374           0.11399096           0.33497664 
 ##          theil(poor) 
 ##           0.10588056</code></pre>
 <p>Then, using the same sampling strategy of the <code>svywatts</code>, we compute the <code>svywattsdec</code> for each sample:</p>
-<div class="sourceCode" id="cb228"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb228-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-1" tabindex="-1"></a><span class="co"># simulation function</span></span>
-<span id="cb228-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-2" tabindex="-1"></a>wattsdec_sim_fun <span class="ot">&lt;-</span> <span class="cf">function</span>(this.iter) {</span>
-<span id="cb228-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-3" tabindex="-1"></a>  </span>
-<span id="cb228-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-4" tabindex="-1"></a>  <span class="fu">set.seed</span>(this.iter)</span>
-<span id="cb228-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-5" tabindex="-1"></a>  </span>
-<span id="cb228-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-6" tabindex="-1"></a>  <span class="fu">library</span>(survey)</span>
-<span id="cb228-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-7" tabindex="-1"></a>  <span class="fu">library</span>(convey)</span>
-<span id="cb228-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-8" tabindex="-1"></a>  <span class="fu">library</span>(sampling)</span>
-<span id="cb228-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-9" tabindex="-1"></a>  </span>
-<span id="cb228-10"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-10" tabindex="-1"></a>  </span>
-<span id="cb228-11"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-11" tabindex="-1"></a>  <span class="co"># load pseudo population data</span></span>
-<span id="cb228-12"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-12" tabindex="-1"></a>  <span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
-<span id="cb228-13"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-13" tabindex="-1"></a>  </span>
-<span id="cb228-14"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-14" tabindex="-1"></a>  <span class="co"># compute size-like variable for PPS sampling design</span></span>
-<span id="cb228-15"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-15" tabindex="-1"></a>  eusilcP<span class="sc">$</span>aux <span class="ot">&lt;-</span></span>
-<span id="cb228-16"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-16" tabindex="-1"></a>    <span class="fu">log</span>(<span class="fu">ifelse</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;=</span> <span class="dv">1000</span> , eusilcP<span class="sc">$</span>eqIncome , <span class="dv">1000</span>))</span>
-<span id="cb228-17"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-17" tabindex="-1"></a>  </span>
-<span id="cb228-18"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-18" tabindex="-1"></a>  <span class="co"># select sample</span></span>
-<span id="cb228-19"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-19" tabindex="-1"></a>  tt <span class="ot">&lt;-</span></span>
-<span id="cb228-20"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-20" tabindex="-1"></a>    sampling<span class="sc">::</span><span class="fu">cluster</span>(</span>
-<span id="cb228-21"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-21" tabindex="-1"></a>      <span class="at">data =</span> eusilcP[<span class="fu">sample.int</span>(<span class="fu">nrow</span>(eusilcP) , <span class="fu">nrow</span>(eusilcP) , <span class="at">replace =</span> <span class="cn">FALSE</span>) , ] ,</span>
-<span id="cb228-22"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-22" tabindex="-1"></a>      <span class="at">clustername =</span> <span class="st">&quot;hid&quot;</span> ,</span>
-<span id="cb228-23"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-23" tabindex="-1"></a>      <span class="at">size =</span> 1000L ,</span>
-<span id="cb228-24"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-24" tabindex="-1"></a>      <span class="at">method =</span> <span class="st">&quot;systematic&quot;</span> ,</span>
-<span id="cb228-25"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-25" tabindex="-1"></a>      <span class="at">pik =</span> eusilcP<span class="sc">$</span>aux</span>
-<span id="cb228-26"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-26" tabindex="-1"></a>    )</span>
-<span id="cb228-27"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-27" tabindex="-1"></a>  </span>
-<span id="cb228-28"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-28" tabindex="-1"></a>  <span class="co"># collect data</span></span>
-<span id="cb228-29"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-29" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">getdata</span>(eusilcP , tt)</span>
-<span id="cb228-30"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-30" tabindex="-1"></a>  </span>
-<span id="cb228-31"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-31" tabindex="-1"></a>  <span class="co"># create survey design object</span></span>
-<span id="cb228-32"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-32" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span></span>
-<span id="cb228-33"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-33" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
-<span id="cb228-34"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-34" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> hid ,</span>
-<span id="cb228-35"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-35" tabindex="-1"></a>      <span class="at">probs =</span> <span class="sc">~</span> Prob ,</span>
-<span id="cb228-36"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-36" tabindex="-1"></a>      <span class="at">data =</span> this.sample ,</span>
-<span id="cb228-37"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-37" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
-<span id="cb228-38"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-38" tabindex="-1"></a>    )</span>
-<span id="cb228-39"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-39" tabindex="-1"></a>  </span>
-<span id="cb228-40"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-40" tabindex="-1"></a>  <span class="co"># prepare for convey functions</span></span>
-<span id="cb228-41"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-41" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(this.desobj)</span>
-<span id="cb228-42"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-42" tabindex="-1"></a>  </span>
-<span id="cb228-43"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-43" tabindex="-1"></a>  <span class="co"># filter positive incomes</span></span>
-<span id="cb228-44"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-44" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">subset</span>(this.desobj , eqIncome <span class="sc">&gt;</span> <span class="dv">0</span>)</span>
-<span id="cb228-45"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-45" tabindex="-1"></a>  </span>
-<span id="cb228-46"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-46" tabindex="-1"></a>  <span class="co"># compute estimates</span></span>
-<span id="cb228-47"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-47" tabindex="-1"></a>  <span class="fu">svywattsdec</span>(<span class="sc">~</span> eqIncome , this.desobj , <span class="at">abs_thresh =</span> <span class="dv">10000</span>)</span>
-<span id="cb228-48"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-48" tabindex="-1"></a>  </span>
-<span id="cb228-49"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-49" tabindex="-1"></a>}</span>
-<span id="cb228-50"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-50" tabindex="-1"></a></span>
-<span id="cb228-51"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-51" tabindex="-1"></a><span class="co"># run replications</span></span>
-<span id="cb228-52"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-52" tabindex="-1"></a>cl <span class="ot">&lt;-</span> <span class="fu">makeCluster</span>(<span class="fu">detectCores</span>() <span class="sc">-</span> <span class="dv">1</span>)</span>
-<span id="cb228-53"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-53" tabindex="-1"></a></span>
-<span id="cb228-54"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-54" tabindex="-1"></a>wattsdec.estimate.list <span class="ot">&lt;-</span></span>
-<span id="cb228-55"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-55" tabindex="-1"></a>  <span class="fu">clusterApply</span>(cl, <span class="fu">seq_len</span>(mc.rep) , wattsdec_sim_fun)</span>
-<span id="cb228-56"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-56" tabindex="-1"></a></span>
-<span id="cb228-57"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-57" tabindex="-1"></a><span class="fu">stopCluster</span>(cl)</span></code></pre></div>
+<div class="sourceCode" id="cb227"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb227-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-1" tabindex="-1"></a><span class="co"># simulation function</span></span>
+<span id="cb227-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-2" tabindex="-1"></a>wattsdec_sim_fun <span class="ot">&lt;-</span> <span class="cf">function</span>(this.iter) {</span>
+<span id="cb227-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-3" tabindex="-1"></a>  </span>
+<span id="cb227-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-4" tabindex="-1"></a>  <span class="fu">set.seed</span>(this.iter)</span>
+<span id="cb227-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-5" tabindex="-1"></a>  </span>
+<span id="cb227-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-6" tabindex="-1"></a>  <span class="fu">library</span>(survey)</span>
+<span id="cb227-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-7" tabindex="-1"></a>  <span class="fu">library</span>(convey)</span>
+<span id="cb227-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-8" tabindex="-1"></a>  <span class="fu">library</span>(sampling)</span>
+<span id="cb227-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-9" tabindex="-1"></a>  </span>
+<span id="cb227-10"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-10" tabindex="-1"></a>  </span>
+<span id="cb227-11"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-11" tabindex="-1"></a>  <span class="co"># load pseudo population data</span></span>
+<span id="cb227-12"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-12" tabindex="-1"></a>  <span class="fu">data</span>(<span class="st">&quot;eusilcP&quot;</span> , <span class="at">package =</span> <span class="st">&quot;simPop&quot;</span>)</span>
+<span id="cb227-13"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-13" tabindex="-1"></a>  </span>
+<span id="cb227-14"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-14" tabindex="-1"></a>  <span class="co"># compute size-like variable for PPS sampling design</span></span>
+<span id="cb227-15"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-15" tabindex="-1"></a>  eusilcP<span class="sc">$</span>aux <span class="ot">&lt;-</span></span>
+<span id="cb227-16"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-16" tabindex="-1"></a>    <span class="fu">log</span>(<span class="fu">ifelse</span>(eusilcP<span class="sc">$</span>eqIncome <span class="sc">&gt;=</span> <span class="dv">1000</span> , eusilcP<span class="sc">$</span>eqIncome , <span class="dv">1000</span>))</span>
+<span id="cb227-17"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-17" tabindex="-1"></a>  </span>
+<span id="cb227-18"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-18" tabindex="-1"></a>  <span class="co"># select sample</span></span>
+<span id="cb227-19"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-19" tabindex="-1"></a>  tt <span class="ot">&lt;-</span></span>
+<span id="cb227-20"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-20" tabindex="-1"></a>    sampling<span class="sc">::</span><span class="fu">cluster</span>(</span>
+<span id="cb227-21"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-21" tabindex="-1"></a>      <span class="at">data =</span> eusilcP[<span class="fu">sample.int</span>(<span class="fu">nrow</span>(eusilcP) , <span class="fu">nrow</span>(eusilcP) , <span class="at">replace =</span> <span class="cn">FALSE</span>) , ] ,</span>
+<span id="cb227-22"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-22" tabindex="-1"></a>      <span class="at">clustername =</span> <span class="st">&quot;hid&quot;</span> ,</span>
+<span id="cb227-23"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-23" tabindex="-1"></a>      <span class="at">size =</span> 1000L ,</span>
+<span id="cb227-24"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-24" tabindex="-1"></a>      <span class="at">method =</span> <span class="st">&quot;systematic&quot;</span> ,</span>
+<span id="cb227-25"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-25" tabindex="-1"></a>      <span class="at">pik =</span> eusilcP<span class="sc">$</span>aux</span>
+<span id="cb227-26"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-26" tabindex="-1"></a>    )</span>
+<span id="cb227-27"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-27" tabindex="-1"></a>  </span>
+<span id="cb227-28"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-28" tabindex="-1"></a>  <span class="co"># collect data</span></span>
+<span id="cb227-29"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-29" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">getdata</span>(eusilcP , tt)</span>
+<span id="cb227-30"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-30" tabindex="-1"></a>  </span>
+<span id="cb227-31"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-31" tabindex="-1"></a>  <span class="co"># create survey design object</span></span>
+<span id="cb227-32"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-32" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span></span>
+<span id="cb227-33"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-33" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
+<span id="cb227-34"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-34" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> hid ,</span>
+<span id="cb227-35"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-35" tabindex="-1"></a>      <span class="at">probs =</span> <span class="sc">~</span> Prob ,</span>
+<span id="cb227-36"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-36" tabindex="-1"></a>      <span class="at">data =</span> this.sample ,</span>
+<span id="cb227-37"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-37" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
+<span id="cb227-38"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-38" tabindex="-1"></a>    )</span>
+<span id="cb227-39"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-39" tabindex="-1"></a>  </span>
+<span id="cb227-40"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-40" tabindex="-1"></a>  <span class="co"># prepare for convey functions</span></span>
+<span id="cb227-41"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-41" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(this.desobj)</span>
+<span id="cb227-42"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-42" tabindex="-1"></a>  </span>
+<span id="cb227-43"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-43" tabindex="-1"></a>  <span class="co"># filter positive incomes</span></span>
+<span id="cb227-44"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-44" tabindex="-1"></a>  this.desobj <span class="ot">&lt;-</span> <span class="fu">subset</span>(this.desobj , eqIncome <span class="sc">&gt;</span> <span class="dv">0</span>)</span>
+<span id="cb227-45"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-45" tabindex="-1"></a>  </span>
+<span id="cb227-46"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-46" tabindex="-1"></a>  <span class="co"># compute estimates</span></span>
+<span id="cb227-47"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-47" tabindex="-1"></a>  <span class="fu">svywattsdec</span>(<span class="sc">~</span> eqIncome , this.desobj , <span class="at">abs_thresh =</span> <span class="dv">10000</span>)</span>
+<span id="cb227-48"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-48" tabindex="-1"></a>  </span>
+<span id="cb227-49"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-49" tabindex="-1"></a>}</span>
+<span id="cb227-50"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-50" tabindex="-1"></a></span>
+<span id="cb227-51"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-51" tabindex="-1"></a><span class="co"># run replications</span></span>
+<span id="cb227-52"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-52" tabindex="-1"></a>cl <span class="ot">&lt;-</span> <span class="fu">makeCluster</span>(<span class="fu">detectCores</span>() <span class="sc">-</span> <span class="dv">1</span>)</span>
+<span id="cb227-53"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-53" tabindex="-1"></a></span>
+<span id="cb227-54"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-54" tabindex="-1"></a>wattsdec.estimate.list <span class="ot">&lt;-</span></span>
+<span id="cb227-55"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-55" tabindex="-1"></a>  <span class="fu">clusterApply</span>(cl, <span class="fu">seq_len</span>(mc.rep) , wattsdec_sim_fun)</span>
+<span id="cb227-56"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-56" tabindex="-1"></a></span>
+<span id="cb227-57"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb227-57" tabindex="-1"></a><span class="fu">stopCluster</span>(cl)</span></code></pre></div>
 <p>The PRB of each component is estimated using the code below. Notice that PRBs are relatively small, with absolute values below 1%, with the largest bias in the Theil index component.</p>
-<div class="sourceCode" id="cb229"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb229-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb229-1" tabindex="-1"></a><span class="co"># repeat true population values</span></span>
-<span id="cb229-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb229-2" tabindex="-1"></a>(theta.pop)</span></code></pre></div>
+<div class="sourceCode" id="cb228"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb228-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-1" tabindex="-1"></a><span class="co"># repeat true population values</span></span>
+<span id="cb228-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb228-2" tabindex="-1"></a>(theta.pop)</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##           0.05025374           0.11399096           0.33497664 
 ##          theil(poor) 
 ##           0.10588056</code></pre>
-<div class="sourceCode" id="cb231"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb231-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb231-1" tabindex="-1"></a><span class="co"># estimate the expected values of the components estimators</span></span>
-<span id="cb231-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb231-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
-<span id="cb231-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb231-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(wattsdec.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb230"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb230-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb230-1" tabindex="-1"></a><span class="co"># estimate the expected values of the components estimators</span></span>
+<span id="cb230-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb230-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
+<span id="cb230-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb230-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(wattsdec.estimate.list , coef)))</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##           0.05044329           0.11418992           0.33584759 
 ##          theil(poor) 
 ##           0.10584416</code></pre>
-<div class="sourceCode" id="cb233"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb233-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb233-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
-<span id="cb233-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb233-2" tabindex="-1"></a>(percentage_relative_bias <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb232"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb232-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb232-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
+<span id="cb232-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb232-2" tabindex="-1"></a>(percentage_relative_bias <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##           0.37719501           0.17453750           0.26000223 
 ##          theil(poor) 
 ##          -0.03437576</code></pre>
-<div class="sourceCode" id="cb235"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb235-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb235-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(percentage_relative_bias) <span class="sc">&lt;</span> <span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb234"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb234-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb234-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(percentage_relative_bias) <span class="sc">&lt;</span> <span class="dv">1</span>)</span></code></pre></div>
 <p>For the variance estimators, we estimate the PRB using the code below.
 Note that the bias of the variance estimators is still relatively small, with absolute value of the Watts variance estimator’s PRB below 1% and all four components variance estimators below 5%.</p>
-<div class="sourceCode" id="cb236"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb236-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb236-1" tabindex="-1"></a><span class="co"># estimate the variance of the components estimators</span></span>
-<span id="cb236-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb236-2" tabindex="-1"></a><span class="co"># using the empirical variance of the estimates</span></span>
-<span id="cb236-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb236-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span></span>
-<span id="cb236-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb236-4" tabindex="-1"></a>   <span class="fu">diag</span>(<span class="fu">var</span>(<span class="fu">t</span>(</span>
-<span id="cb236-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb236-5" tabindex="-1"></a>     <span class="fu">sapply</span>(wattsdec.estimate.list , coef)</span>
-<span id="cb236-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb236-6" tabindex="-1"></a>   ))))</span></code></pre></div>
+<div class="sourceCode" id="cb235"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb235-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb235-1" tabindex="-1"></a><span class="co"># estimate the variance of the components estimators</span></span>
+<span id="cb235-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb235-2" tabindex="-1"></a><span class="co"># using the empirical variance of the estimates</span></span>
+<span id="cb235-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb235-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span></span>
+<span id="cb235-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb235-4" tabindex="-1"></a>   <span class="fu">diag</span>(<span class="fu">var</span>(<span class="fu">t</span>(</span>
+<span id="cb235-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb235-5" tabindex="-1"></a>     <span class="fu">sapply</span>(wattsdec.estimate.list , coef)</span>
+<span id="cb235-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb235-6" tabindex="-1"></a>   ))))</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##         6.141434e-05         1.015260e-04         9.241259e-04 
 ##          theil(poor) 
 ##         1.108525e-03</code></pre>
-<div class="sourceCode" id="cb238"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb238-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb238-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Watts index variance estimator</span></span>
-<span id="cb238-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb238-2" tabindex="-1"></a><span class="co"># using the (estimated) expected value of the variance estimates</span></span>
-<span id="cb238-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb238-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span></span>
-<span id="cb238-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb238-4" tabindex="-1"></a>    <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(wattsdec.estimate.list , <span class="cf">function</span>(z)</span>
-<span id="cb238-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb238-5" tabindex="-1"></a>      <span class="fu">diag</span>(<span class="fu">vcov</span>(</span>
-<span id="cb238-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb238-6" tabindex="-1"></a>        z</span>
-<span id="cb238-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb238-7" tabindex="-1"></a>      )))))</span></code></pre></div>
+<div class="sourceCode" id="cb237"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb237-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb237-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Watts index variance estimator</span></span>
+<span id="cb237-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb237-2" tabindex="-1"></a><span class="co"># using the (estimated) expected value of the variance estimates</span></span>
+<span id="cb237-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb237-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span></span>
+<span id="cb237-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb237-4" tabindex="-1"></a>    <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(wattsdec.estimate.list , <span class="cf">function</span>(z)</span>
+<span id="cb237-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb237-5" tabindex="-1"></a>      <span class="fu">diag</span>(<span class="fu">vcov</span>(</span>
+<span id="cb237-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb237-6" tabindex="-1"></a>        z</span>
+<span id="cb237-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb237-7" tabindex="-1"></a>      )))))</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##         6.100902e-05         1.013968e-04         9.613831e-04 
 ##          theil(poor) 
 ##         1.070018e-03</code></pre>
-<div class="sourceCode" id="cb240"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb240-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb240-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimators</span></span>
-<span id="cb240-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb240-2" tabindex="-1"></a>(percentage_relative_bias <span class="ot">&lt;-</span></span>
-<span id="cb240-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb240-3" tabindex="-1"></a>    <span class="dv">100</span> <span class="sc">*</span>  (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb239"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb239-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb239-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimators</span></span>
+<span id="cb239-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb239-2" tabindex="-1"></a>(percentage_relative_bias <span class="ot">&lt;-</span></span>
+<span id="cb239-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb239-3" tabindex="-1"></a>    <span class="dv">100</span> <span class="sc">*</span>  (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##           -0.6599717           -0.1273107            4.0316155 
 ##          theil(poor) 
 ##           -3.4736907</code></pre>
-<div class="sourceCode" id="cb242"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb242-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb242-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(percentage_relative_bias[<span class="dv">1</span>]) <span class="sc">&lt;</span> <span class="dv">1</span> <span class="sc">&amp;</span> <span class="fu">all</span>(<span class="fu">abs</span>(percentage_relative_bias) <span class="sc">&lt;</span> <span class="dv">5</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb241"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb241-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb241-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(percentage_relative_bias[<span class="dv">1</span>]) <span class="sc">&lt;</span> <span class="dv">1</span> <span class="sc">&amp;</span> <span class="fu">all</span>(<span class="fu">abs</span>(percentage_relative_bias) <span class="sc">&lt;</span> <span class="dv">5</span>))</span></code></pre></div>
 <p>Regarding the MSE, the squared bias accounts for less than 0.1% of the MSE.
 This means that, with a good estimate of the variance, we should be able to have a good approximation for the MSE.</p>
-<div class="sourceCode" id="cb243"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb243-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb243-1" tabindex="-1"></a><span class="co"># estimate MSE</span></span>
-<span id="cb243-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb243-2" tabindex="-1"></a>theta.bias2 <span class="ot">&lt;-</span> (theta.exp <span class="sc">-</span> theta.pop) <span class="sc">^</span> <span class="dv">2</span></span>
-<span id="cb243-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb243-3" tabindex="-1"></a>(theta.mse <span class="ot">&lt;-</span> theta.bias2 <span class="sc">+</span> vartheta.popest)</span></code></pre></div>
+<div class="sourceCode" id="cb242"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb242-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb242-1" tabindex="-1"></a><span class="co"># estimate MSE</span></span>
+<span id="cb242-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb242-2" tabindex="-1"></a>theta.bias2 <span class="ot">&lt;-</span> (theta.exp <span class="sc">-</span> theta.pop) <span class="sc">^</span> <span class="dv">2</span></span>
+<span id="cb242-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb242-3" tabindex="-1"></a>(theta.mse <span class="ot">&lt;-</span> theta.bias2 <span class="sc">+</span> vartheta.popest)</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##         6.145027e-05         1.015656e-04         9.248844e-04 
 ##          theil(poor) 
 ##         1.108526e-03</code></pre>
-<div class="sourceCode" id="cb245"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb245-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb245-1" tabindex="-1"></a><span class="co"># squared bias component of the MSE</span></span>
-<span id="cb245-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb245-2" tabindex="-1"></a>(squared_bias_over_mse <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.bias2 <span class="sc">/</span> theta.mse))</span></code></pre></div>
+<div class="sourceCode" id="cb244"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb244-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb244-1" tabindex="-1"></a><span class="co"># squared bias component of the MSE</span></span>
+<span id="cb244-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb244-2" tabindex="-1"></a>(squared_bias_over_mse <span class="ot">&lt;-</span> <span class="dv">100</span> <span class="sc">*</span> (theta.bias2 <span class="sc">/</span> theta.mse))</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##         0.0584715789         0.0389737000         0.0820154610 
 ##          theil(poor) 
 ##         0.0001195063</code></pre>
-<div class="sourceCode" id="cb247"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb247-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-1" tabindex="-1"></a><span class="fu">stopifnot</span>(squared_bias_over_mse <span class="sc">&lt;</span> <span class="fl">0.1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb246"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb246-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb246-1" tabindex="-1"></a><span class="fu">stopifnot</span>(squared_bias_over_mse <span class="sc">&lt;</span> <span class="fl">0.1</span>)</span></code></pre></div>
 <p>However, the CIs based on the normal approximation might not work very well for some components. The code below shows that coverage rate for the Theil index component differs significantly from the 95% nominal coverage rate.</p>
-<div class="sourceCode" id="cb248"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb248-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb248-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Watts index</span></span>
-<span id="cb248-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb248-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
-<span id="cb248-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb248-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
-<span id="cb248-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb248-4" tabindex="-1"></a>  <span class="fu">sapply</span>(wattsdec.estimate.list, <span class="cf">function</span>(this.stat)</span>
-<span id="cb248-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb248-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
-<span id="cb248-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb248-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop)</span>
-<span id="cb248-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb248-7" tabindex="-1"></a></span>
-<span id="cb248-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb248-8" tabindex="-1"></a><span class="co"># evaluate empirical coverage</span></span>
-<span id="cb248-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb248-9" tabindex="-1"></a>(empirical_coverage <span class="ot">&lt;-</span> <span class="fu">rowMeans</span>(est.coverage))</span></code></pre></div>
+<div class="sourceCode" id="cb247"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb247-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Watts index</span></span>
+<span id="cb247-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
+<span id="cb247-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
+<span id="cb247-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-4" tabindex="-1"></a>  <span class="fu">sapply</span>(wattsdec.estimate.list, <span class="cf">function</span>(this.stat)</span>
+<span id="cb247-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
+<span id="cb247-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop)</span>
+<span id="cb247-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-7" tabindex="-1"></a></span>
+<span id="cb247-8"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-8" tabindex="-1"></a><span class="co"># evaluate empirical coverage</span></span>
+<span id="cb247-9"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb247-9" tabindex="-1"></a>(empirical_coverage <span class="ot">&lt;-</span> <span class="fu">rowMeans</span>(est.coverage))</span></code></pre></div>
 <pre><code>##                watts                 fgt0 watts pov. gap ratio 
 ##               0.9268               0.9494               0.9476 
 ##          theil(poor) 
 ##               0.8452</code></pre>
-<div class="sourceCode" id="cb250"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb250-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb250-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(empirical_coverage <span class="sc">-</span> <span class="fl">0.95</span>) <span class="sc">&lt;</span> <span class="fl">0.15</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb249"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb249-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb249-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">abs</span>(empirical_coverage <span class="sc">-</span> <span class="fl">0.95</span>) <span class="sc">&lt;</span> <span class="fl">0.15</span>)</span></code></pre></div>
 <p>One of the reasons for this is that the sample might not be large enough for the CLT to hold. The distribution of the estimator shows substantial asymmetry, which would be a problem for the normal approximation.</p>
-<div class="sourceCode" id="cb251"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb251-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb251-1" tabindex="-1"></a><span class="fu">hist</span>(</span>
-<span id="cb251-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb251-2" tabindex="-1"></a>  <span class="fu">sapply</span>(wattsdec.estimate.list , coef)[<span class="dv">4</span>, ] ,</span>
-<span id="cb251-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb251-3" tabindex="-1"></a>  <span class="at">main =</span> <span class="st">&quot;Histogram of Theil component estimator&quot;</span> ,</span>
-<span id="cb251-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb251-4" tabindex="-1"></a>  <span class="at">xlim =</span> <span class="fu">c</span>(<span class="dv">0</span>, .<span class="dv">30</span>) ,</span>
-<span id="cb251-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb251-5" tabindex="-1"></a>  <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span> , <span class="dv">1500</span>) ,</span>
-<span id="cb251-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb251-6" tabindex="-1"></a>  <span class="at">xlab =</span> <span class="st">&quot;Estimate&quot;</span></span>
-<span id="cb251-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb251-7" tabindex="-1"></a>)</span></code></pre></div>
+<div class="sourceCode" id="cb250"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb250-1"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb250-1" tabindex="-1"></a><span class="fu">hist</span>(</span>
+<span id="cb250-2"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb250-2" tabindex="-1"></a>  <span class="fu">sapply</span>(wattsdec.estimate.list , coef)[<span class="dv">4</span>, ] ,</span>
+<span id="cb250-3"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb250-3" tabindex="-1"></a>  <span class="at">main =</span> <span class="st">&quot;Histogram of Theil component estimator&quot;</span> ,</span>
+<span id="cb250-4"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb250-4" tabindex="-1"></a>  <span class="at">xlim =</span> <span class="fu">c</span>(<span class="dv">0</span>, .<span class="dv">30</span>) ,</span>
+<span id="cb250-5"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb250-5" tabindex="-1"></a>  <span class="at">ylim =</span> <span class="fu">c</span>(<span class="dv">0</span> , <span class="dv">1500</span>) ,</span>
+<span id="cb250-6"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb250-6" tabindex="-1"></a>  <span class="at">xlab =</span> <span class="st">&quot;Estimate&quot;</span></span>
+<span id="cb250-7"><a href="3.7-watts-poverty-measure-svywatts-svywattsdec.html#cb250-7" tabindex="-1"></a>)</span></code></pre></div>
 <p><img src="context_files/figure-html/unnamed-chunk-74-1.png" width="672"  /></p>
 <p>For additional usage examples of <code>svywatts</code> and <code>svywattsdec</code>, type <code>?convey::svywatts</code> or <code>?convey::svywattsdec</code> in the R console.</p>
 
diff --git a/docs/4-inequality.html b/docs/4-inequality.html
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+++ b/docs/4-inequality.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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+++ b/docs/4.10-entropy-based-measures.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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+<meta name="date" content="2023-11-07" />
 
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diff --git a/docs/4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html b/docs/4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html
index 312c137..ab4727f 100644
--- a/docs/4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html
+++ b/docs/4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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@@ -253,12 +253,12 @@
 <div class="col-sm-12">
 <div id="generalized-entropy-and-decomposition-svygei-svygeidec" class="section level2" number="4.11">
 <h2><span class="header-section-number">4.11</span> Generalized Entropy and Decomposition (svygei, svygeidec)</h2>
-<div class="sourceCode" id="cb366"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb366-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-1" tabindex="-1"></a>✔️ flexible inequality<span class="sc">-</span>aversion parameter <span class="sc">--</span> varying its epsilon parameter can highlight the effect of inequality <span class="cf">in</span> different parts of the income distribution</span>
-<span id="cb366-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-2" tabindex="-1"></a>✔️ can be group<span class="sc">-</span>decomposed into within<span class="sc">-</span>inequality and between<span class="sc">-</span>inequality</span>
-<span id="cb366-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-3" tabindex="-1"></a>✔️ this parameter can also <span class="fu">be</span> (somewhat) tuned to be less affected by outliers</span>
-<span id="cb366-4"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-4" tabindex="-1"></a>❌ does not handle zero or negative incomes</span>
-<span id="cb366-5"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-5" tabindex="-1"></a>❌ hard to interpret</span>
-<span id="cb366-6"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-6" tabindex="-1"></a>❌ can be very sensitive to outliers</span></code></pre></div>
+<div class="sourceCode" id="cb365"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb365-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb365-1" tabindex="-1"></a>✔️ flexible inequality<span class="sc">-</span>aversion parameter <span class="sc">--</span> varying its epsilon parameter can highlight the effect of inequality <span class="cf">in</span> different parts of the income distribution</span>
+<span id="cb365-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb365-2" tabindex="-1"></a>✔️ can be group<span class="sc">-</span>decomposed into within<span class="sc">-</span>inequality and between<span class="sc">-</span>inequality</span>
+<span id="cb365-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb365-3" tabindex="-1"></a>✔️ this parameter can also <span class="fu">be</span> (somewhat) tuned to be less affected by outliers</span>
+<span id="cb365-4"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb365-4" tabindex="-1"></a>❌ does not handle zero or negative incomes</span>
+<span id="cb365-5"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb365-5" tabindex="-1"></a>❌ hard to interpret</span>
+<span id="cb365-6"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb365-6" tabindex="-1"></a>❌ can be very sensitive to outliers</span></code></pre></div>
 <p>Using a generalization of the information function, now defined as:</p>
 <p><span class="math display">\[
 g(f) = \frac{1}{\alpha-1} [ 1 - f^{\alpha - 1} ]
@@ -294,38 +294,38 @@ <h2><span class="header-section-number">4.11</span> Generalized Entropy and Deco
 <h3><span class="header-section-number">4.11.1</span> Replication Example</h3>
 <p>In July 2006, <span class="citation">Jenkins (<label for="tufte-mn-97" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-97" class="margin-toggle">2008<span class="marginnote">Jenkins, Stephen. 2008. <span>“Estimation and Interpretation of Measures of Inequality, Poverty, and Social Welfare Using Stata.”</span> North American Stata Users' Group Meetings 2006. Stata Users Group. <a href="http://EconPapers.repec.org/RePEc:boc:asug06:16">http://EconPapers.repec.org/RePEc:boc:asug06:16</a>.</span>)</span> presented at the North American Stata Users’ Group Meetings on the stata Generalized Entropy Index command. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb367"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb367-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb367-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb367-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-3" tabindex="-1"></a></span>
-<span id="cb367-4"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb367-5"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb367-6"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-6" tabindex="-1"></a></span>
-<span id="cb367-7"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-7" tabindex="-1"></a><span class="co"># load the foreign library</span></span>
-<span id="cb367-8"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-8" tabindex="-1"></a><span class="fu">library</span>(foreign)</span>
-<span id="cb367-9"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-9" tabindex="-1"></a></span>
-<span id="cb367-10"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-10" tabindex="-1"></a><span class="co"># create a temporary file on the local disk</span></span>
-<span id="cb367-11"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-11" tabindex="-1"></a>tf <span class="ot">&lt;-</span> <span class="fu">tempfile</span>()</span>
-<span id="cb367-12"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-12" tabindex="-1"></a></span>
-<span id="cb367-13"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-13" tabindex="-1"></a><span class="co"># store the location of the presentation file</span></span>
-<span id="cb367-14"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-14" tabindex="-1"></a>presentation_zip <span class="ot">&lt;-</span></span>
-<span id="cb367-15"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-15" tabindex="-1"></a>  <span class="st">&quot;http://repec.org/nasug2006/nasug2006_jenkins.zip&quot;</span></span>
-<span id="cb367-16"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-16" tabindex="-1"></a></span>
-<span id="cb367-17"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-17" tabindex="-1"></a><span class="co"># download jenkins&#39; presentation to the temporary file</span></span>
-<span id="cb367-18"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-18" tabindex="-1"></a><span class="fu">download.file</span>(presentation_zip , tf , <span class="at">mode =</span> <span class="st">&#39;wb&#39;</span>)</span>
-<span id="cb367-19"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-19" tabindex="-1"></a></span>
-<span id="cb367-20"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-20" tabindex="-1"></a><span class="co"># unzip the contents of the archive</span></span>
-<span id="cb367-21"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-21" tabindex="-1"></a>presentation_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> <span class="fu">tempdir</span>())</span>
-<span id="cb367-22"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-22" tabindex="-1"></a></span>
-<span id="cb367-23"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-23" tabindex="-1"></a><span class="co"># load the institute for fiscal studies&#39; 1981, 1985, and 1991 data.frame objects</span></span>
-<span id="cb367-24"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-24" tabindex="-1"></a>x81 <span class="ot">&lt;-</span></span>
-<span id="cb367-25"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-25" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs81&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb367-26"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-26" tabindex="-1"></a>x85 <span class="ot">&lt;-</span></span>
-<span id="cb367-27"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-27" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs85&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb367-28"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-28" tabindex="-1"></a>x91 <span class="ot">&lt;-</span></span>
-<span id="cb367-29"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-29" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs91&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb367-30"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-30" tabindex="-1"></a></span>
-<span id="cb367-31"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-31" tabindex="-1"></a><span class="co"># stack each of these three years of data into a single data.frame</span></span>
-<span id="cb367-32"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb367-32" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">rbind</span>(x81 , x85 , x91)</span></code></pre></div>
+<div class="sourceCode" id="cb366"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb366-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb366-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb366-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-3" tabindex="-1"></a></span>
+<span id="cb366-4"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb366-5"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb366-6"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-6" tabindex="-1"></a></span>
+<span id="cb366-7"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-7" tabindex="-1"></a><span class="co"># load the foreign library</span></span>
+<span id="cb366-8"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-8" tabindex="-1"></a><span class="fu">library</span>(foreign)</span>
+<span id="cb366-9"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-9" tabindex="-1"></a></span>
+<span id="cb366-10"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-10" tabindex="-1"></a><span class="co"># create a temporary file on the local disk</span></span>
+<span id="cb366-11"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-11" tabindex="-1"></a>tf <span class="ot">&lt;-</span> <span class="fu">tempfile</span>()</span>
+<span id="cb366-12"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-12" tabindex="-1"></a></span>
+<span id="cb366-13"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-13" tabindex="-1"></a><span class="co"># store the location of the presentation file</span></span>
+<span id="cb366-14"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-14" tabindex="-1"></a>presentation_zip <span class="ot">&lt;-</span></span>
+<span id="cb366-15"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-15" tabindex="-1"></a>  <span class="st">&quot;http://repec.org/nasug2006/nasug2006_jenkins.zip&quot;</span></span>
+<span id="cb366-16"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-16" tabindex="-1"></a></span>
+<span id="cb366-17"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-17" tabindex="-1"></a><span class="co"># download jenkins&#39; presentation to the temporary file</span></span>
+<span id="cb366-18"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-18" tabindex="-1"></a><span class="fu">download.file</span>(presentation_zip , tf , <span class="at">mode =</span> <span class="st">&#39;wb&#39;</span>)</span>
+<span id="cb366-19"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-19" tabindex="-1"></a></span>
+<span id="cb366-20"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-20" tabindex="-1"></a><span class="co"># unzip the contents of the archive</span></span>
+<span id="cb366-21"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-21" tabindex="-1"></a>presentation_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> <span class="fu">tempdir</span>())</span>
+<span id="cb366-22"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-22" tabindex="-1"></a></span>
+<span id="cb366-23"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-23" tabindex="-1"></a><span class="co"># load the institute for fiscal studies&#39; 1981, 1985, and 1991 data.frame objects</span></span>
+<span id="cb366-24"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-24" tabindex="-1"></a>x81 <span class="ot">&lt;-</span></span>
+<span id="cb366-25"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-25" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs81&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb366-26"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-26" tabindex="-1"></a>x85 <span class="ot">&lt;-</span></span>
+<span id="cb366-27"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-27" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs85&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb366-28"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-28" tabindex="-1"></a>x91 <span class="ot">&lt;-</span></span>
+<span id="cb366-29"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-29" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs91&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb366-30"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-30" tabindex="-1"></a></span>
+<span id="cb366-31"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-31" tabindex="-1"></a><span class="co"># stack each of these three years of data into a single data.frame</span></span>
+<span id="cb366-32"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb366-32" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">rbind</span>(x81 , x85 , x91)</span></code></pre></div>
 <p>Replicate the author’s survey design statement from stata code..</p>
 <pre><code>. * account for clustering within HHs 
 . version 8: svyset [pweight = wgt], psu(hrn)
@@ -333,11 +333,11 @@ <h3><span class="header-section-number">4.11.1</span> Replication Example</h3>
 psu is hrn
 construct an</code></pre>
 <p>.. into R code:</p>
-<div class="sourceCode" id="cb369"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb369-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb369-1" tabindex="-1"></a><span class="co"># initiate a linearized survey design object</span></span>
-<span id="cb369-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb369-2" tabindex="-1"></a>y <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="sc">~</span> hrn , <span class="at">data =</span> x , <span class="at">weights =</span> <span class="sc">~</span> wgt)</span>
-<span id="cb369-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb369-3" tabindex="-1"></a></span>
-<span id="cb369-4"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb369-4" tabindex="-1"></a><span class="co"># immediately run the `convey_prep` function on the survey design</span></span>
-<span id="cb369-5"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb369-5" tabindex="-1"></a>z <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(y)</span></code></pre></div>
+<div class="sourceCode" id="cb368"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb368-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb368-1" tabindex="-1"></a><span class="co"># initiate a linearized survey design object</span></span>
+<span id="cb368-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb368-2" tabindex="-1"></a>y <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="sc">~</span> hrn , <span class="at">data =</span> x , <span class="at">weights =</span> <span class="sc">~</span> wgt)</span>
+<span id="cb368-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb368-3" tabindex="-1"></a></span>
+<span id="cb368-4"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb368-4" tabindex="-1"></a><span class="co"># immediately run the `convey_prep` function on the survey design</span></span>
+<span id="cb368-5"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb368-5" tabindex="-1"></a>z <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(y)</span></code></pre></div>
 <p>Replicate the author’s subset statement and each of his svygei results..</p>
 <pre><code>. svygei x if year == 1981
  
@@ -359,21 +359,21 @@ <h3><span class="header-section-number">4.11.1</span> Replication Example</h3>
 GE(3)    |  .1739994   .00662015    26.28    0.000      .1610242   .1869747
 ---------------------------------------------------------------------------</code></pre>
 <p>..using R code:</p>
-<div class="sourceCode" id="cb371"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb371-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb371-1" tabindex="-1"></a>z81 <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>)</span>
-<span id="cb371-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb371-2" tabindex="-1"></a></span>
-<span id="cb371-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb371-3" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="sc">-</span><span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb370"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb370-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb370-1" tabindex="-1"></a>z81 <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>)</span>
+<span id="cb370-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb370-2" tabindex="-1"></a></span>
+<span id="cb370-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb370-3" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="sc">-</span><span class="dv">1</span>)</span></code></pre></div>
 <pre><code>##            gei     SE
 ## eybhc0 0.19021 0.0247</code></pre>
-<div class="sourceCode" id="cb373"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb373-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb373-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="dv">0</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb372"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb372-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb372-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="dv">0</span>)</span></code></pre></div>
 <pre><code>##            gei     SE
 ## eybhc0 0.11429 0.0028</code></pre>
-<div class="sourceCode" id="cb375"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb375-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb375-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb374"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb374-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb374-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>))</span></code></pre></div>
 <pre><code>##            gei     SE
 ## eybhc0 0.11169 0.0023</code></pre>
-<div class="sourceCode" id="cb377"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb377-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb377-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb376"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb376-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb376-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
 <pre><code>##            gei     SE
 ## eybhc0 0.12879 0.0033</code></pre>
-<div class="sourceCode" id="cb379"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb379-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb379-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="dv">3</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb378"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb378-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb378-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="dv">3</span>)</span></code></pre></div>
 <pre><code>##          gei     SE
 ## eybhc0 0.174 0.0066</code></pre>
 <p>Confirm this replication applies for subsetted objects as well. Compare stata output..</p>
@@ -395,83 +395,83 @@ <h3><span class="header-section-number">4.11.1</span> Replication Example</h3>
 GE(3)    |  .2609507   .01850689    14.10    0.000      .2246779   .2972235
 ---------------------------------------------------------------------------</code></pre>
 <p>..to R code:</p>
-<div class="sourceCode" id="cb382"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb382-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb382-1" tabindex="-1"></a>z85 <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1985</span>)</span>
-<span id="cb382-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb382-2" tabindex="-1"></a></span>
-<span id="cb382-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb382-3" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>) , <span class="at">epsilon =</span> <span class="sc">-</span><span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb381"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb381-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb381-1" tabindex="-1"></a>z85 <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1985</span>)</span>
+<span id="cb381-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb381-2" tabindex="-1"></a></span>
+<span id="cb381-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb381-3" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>) , <span class="at">epsilon =</span> <span class="sc">-</span><span class="dv">1</span>)</span></code></pre></div>
 <pre><code>##            gei     SE
 ## eybhc0 0.16024 0.0094</code></pre>
-<div class="sourceCode" id="cb384"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb384-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb384-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>) , <span class="at">epsilon =</span> <span class="dv">0</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb383"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb383-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb383-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>) , <span class="at">epsilon =</span> <span class="dv">0</span>)</span></code></pre></div>
 <pre><code>##            gei     SE
 ## eybhc0 0.12762 0.0033</code></pre>
-<div class="sourceCode" id="cb386"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb386-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb386-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb385"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb385-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb385-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>))</span></code></pre></div>
 <pre><code>##            gei     SE
 ## eybhc0 0.13372 0.0041</code></pre>
-<div class="sourceCode" id="cb388"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb388-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb388-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>) , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb387"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb387-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb387-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>) , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
 <pre><code>##            gei     SE
 ## eybhc0 0.16764 0.0073</code></pre>
-<div class="sourceCode" id="cb390"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb390-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb390-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>) , <span class="at">epsilon =</span> <span class="dv">3</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb389"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb389-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb389-1" tabindex="-1"></a><span class="fu">svygei</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z85 , eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>) , <span class="at">epsilon =</span> <span class="dv">3</span>)</span></code></pre></div>
 <pre><code>##            gei     SE
 ## eybhc0 0.26095 0.0185</code></pre>
 <p>Replicate the author’s decomposition by population subgroup (work status) shown on PDF page 57..</p>
-<div class="sourceCode" id="cb392"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb392-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-1" tabindex="-1"></a><span class="co"># define work status (PDF page 22)</span></span>
-<span id="cb392-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-2" tabindex="-1"></a>z <span class="ot">&lt;-</span></span>
-<span id="cb392-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-3" tabindex="-1"></a>  <span class="fu">update</span>(z , <span class="at">wkstatus =</span> <span class="fu">c</span>(<span class="dv">1</span> , <span class="dv">1</span> , <span class="dv">1</span> , <span class="dv">1</span> , <span class="dv">2</span> , <span class="dv">3</span> , <span class="dv">2</span> , <span class="dv">2</span>)[<span class="fu">as.numeric</span>(esbu)])</span>
-<span id="cb392-4"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-4" tabindex="-1"></a>z <span class="ot">&lt;-</span></span>
-<span id="cb392-5"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-5" tabindex="-1"></a>  <span class="fu">update</span>(z , <span class="at">wkstatus =</span> <span class="fu">factor</span>(wkstatus , <span class="at">labels =</span> <span class="fu">c</span>(<span class="st">&quot;1+ ft working&quot;</span> , <span class="st">&quot;no ft working&quot;</span> , <span class="st">&quot;elderly&quot;</span>)))</span>
-<span id="cb392-6"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-6" tabindex="-1"></a></span>
-<span id="cb392-7"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-7" tabindex="-1"></a><span class="co"># subset to 1991 and remove records with zero income</span></span>
-<span id="cb392-8"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-8" tabindex="-1"></a>z91 <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1991</span> <span class="sc">&amp;</span> eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>)</span>
-<span id="cb392-9"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-9" tabindex="-1"></a></span>
-<span id="cb392-10"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-10" tabindex="-1"></a><span class="co"># population share</span></span>
-<span id="cb392-11"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb392-11" tabindex="-1"></a><span class="fu">svymean</span>( <span class="sc">~</span> wkstatus, z91)</span></code></pre></div>
+<div class="sourceCode" id="cb391"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb391-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-1" tabindex="-1"></a><span class="co"># define work status (PDF page 22)</span></span>
+<span id="cb391-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-2" tabindex="-1"></a>z <span class="ot">&lt;-</span></span>
+<span id="cb391-3"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-3" tabindex="-1"></a>  <span class="fu">update</span>(z , <span class="at">wkstatus =</span> <span class="fu">c</span>(<span class="dv">1</span> , <span class="dv">1</span> , <span class="dv">1</span> , <span class="dv">1</span> , <span class="dv">2</span> , <span class="dv">3</span> , <span class="dv">2</span> , <span class="dv">2</span>)[<span class="fu">as.numeric</span>(esbu)])</span>
+<span id="cb391-4"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-4" tabindex="-1"></a>z <span class="ot">&lt;-</span></span>
+<span id="cb391-5"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-5" tabindex="-1"></a>  <span class="fu">update</span>(z , <span class="at">wkstatus =</span> <span class="fu">factor</span>(wkstatus , <span class="at">labels =</span> <span class="fu">c</span>(<span class="st">&quot;1+ ft working&quot;</span> , <span class="st">&quot;no ft working&quot;</span> , <span class="st">&quot;elderly&quot;</span>)))</span>
+<span id="cb391-6"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-6" tabindex="-1"></a></span>
+<span id="cb391-7"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-7" tabindex="-1"></a><span class="co"># subset to 1991 and remove records with zero income</span></span>
+<span id="cb391-8"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-8" tabindex="-1"></a>z91 <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1991</span> <span class="sc">&amp;</span> eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>)</span>
+<span id="cb391-9"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-9" tabindex="-1"></a></span>
+<span id="cb391-10"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-10" tabindex="-1"></a><span class="co"># population share</span></span>
+<span id="cb391-11"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb391-11" tabindex="-1"></a><span class="fu">svymean</span>( <span class="sc">~</span> wkstatus, z91)</span></code></pre></div>
 <pre><code>##                          mean     SE
 ## wkstatus1+ ft working 0.61724 0.0067
 ## wkstatusno ft working 0.20607 0.0059
 ## wkstatuselderly       0.17669 0.0046</code></pre>
-<div class="sourceCode" id="cb394"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb394-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb394-1" tabindex="-1"></a><span class="co"># mean</span></span>
-<span id="cb394-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb394-2" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, svymean)</span></code></pre></div>
+<div class="sourceCode" id="cb393"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb393-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb393-1" tabindex="-1"></a><span class="co"># mean</span></span>
+<span id="cb393-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb393-2" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, svymean)</span></code></pre></div>
 <pre><code>##                    wkstatus   eybhc0       se
 ## 1+ ft working 1+ ft working 278.8040 3.703790
 ## no ft working no ft working 151.6317 3.153968
 ## elderly             elderly 176.6045 4.661740</code></pre>
-<div class="sourceCode" id="cb396"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb396-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb396-1" tabindex="-1"></a><span class="co"># subgroup indices: ge_k</span></span>
-<span id="cb396-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb396-2" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0 , <span class="sc">~</span> wkstatus , z91 , svygei , <span class="at">epsilon =</span> <span class="sc">-</span><span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb395"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb395-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb395-1" tabindex="-1"></a><span class="co"># subgroup indices: ge_k</span></span>
+<span id="cb395-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb395-2" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0 , <span class="sc">~</span> wkstatus , z91 , svygei , <span class="at">epsilon =</span> <span class="sc">-</span><span class="dv">1</span>)</span></code></pre></div>
 <pre><code>##                    wkstatus     eybhc0          se
 ## 1+ ft working 1+ ft working  0.2300708  0.02853959
 ## no ft working no ft working 10.9231761 10.65482557
 ## elderly             elderly  0.1932164  0.02571991</code></pre>
-<div class="sourceCode" id="cb398"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb398-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb398-1" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0 , <span class="sc">~</span> wkstatus , z91 , svygei , <span class="at">epsilon =</span> <span class="dv">0</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb397"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb397-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb397-1" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0 , <span class="sc">~</span> wkstatus , z91 , svygei , <span class="at">epsilon =</span> <span class="dv">0</span>)</span></code></pre></div>
 <pre><code>##                    wkstatus    eybhc0          se
 ## 1+ ft working 1+ ft working 0.1536921 0.006955506
 ## no ft working no ft working 0.1836835 0.014740510
 ## elderly             elderly 0.1653658 0.016409770</code></pre>
-<div class="sourceCode" id="cb400"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb400-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb400-1" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0 , <span class="sc">~</span> wkstatus , z91 , svygei , <span class="at">epsilon =</span> <span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb399"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb399-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb399-1" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0 , <span class="sc">~</span> wkstatus , z91 , svygei , <span class="at">epsilon =</span> <span class="dv">1</span>)</span></code></pre></div>
 <pre><code>##                    wkstatus    eybhc0          se
 ## 1+ ft working 1+ ft working 0.1598558 0.008327994
 ## no ft working no ft working 0.1889909 0.016766120
 ## elderly             elderly 0.2023862 0.027787224</code></pre>
-<div class="sourceCode" id="cb402"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb402-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb402-1" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0 , <span class="sc">~</span> wkstatus , z91 , svygei , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb401"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb401-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb401-1" tabindex="-1"></a><span class="fu">svyby</span>( <span class="sc">~</span> eybhc0 , <span class="sc">~</span> wkstatus , z91 , svygei , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
 <pre><code>##                    wkstatus    eybhc0         se
 ## 1+ ft working 1+ ft working 0.2130664 0.01546521
 ## no ft working no ft working 0.2846345 0.06016394
 ## elderly             elderly 0.3465088 0.07362898</code></pre>
-<div class="sourceCode" id="cb404"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb404-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb404-1" tabindex="-1"></a><span class="co"># GE decomposition</span></span>
-<span id="cb404-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb404-2" tabindex="-1"></a><span class="fu">svygeidec</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, <span class="at">epsilon =</span> <span class="sc">-</span><span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb403"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb403-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb403-1" tabindex="-1"></a><span class="co"># GE decomposition</span></span>
+<span id="cb403-2"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb403-2" tabindex="-1"></a><span class="fu">svygeidec</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, <span class="at">epsilon =</span> <span class="sc">-</span><span class="dv">1</span>)</span></code></pre></div>
 <pre><code>##         gei decomposition     SE
 ## total            3.682893 3.3999
 ## within           3.646572 3.3998
 ## between          0.036321 0.0028</code></pre>
-<div class="sourceCode" id="cb406"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb406-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb406-1" tabindex="-1"></a><span class="fu">svygeidec</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, <span class="at">epsilon =</span> <span class="dv">0</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb405"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb405-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb405-1" tabindex="-1"></a><span class="fu">svygeidec</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, <span class="at">epsilon =</span> <span class="dv">0</span>)</span></code></pre></div>
 <pre><code>##         gei decomposition     SE
 ## total            0.195236 0.0065
 ## within           0.161935 0.0061
 ## between          0.033301 0.0025</code></pre>
-<div class="sourceCode" id="cb408"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb408-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb408-1" tabindex="-1"></a><span class="fu">svygeidec</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, <span class="at">epsilon =</span> <span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb407"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb407-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb407-1" tabindex="-1"></a><span class="fu">svygeidec</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, <span class="at">epsilon =</span> <span class="dv">1</span>)</span></code></pre></div>
 <pre><code>##         gei decomposition     SE
 ## total            0.200390 0.0079
 ## within           0.169396 0.0076
 ## between          0.030994 0.0022</code></pre>
-<div class="sourceCode" id="cb410"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb410-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb410-1" tabindex="-1"></a><span class="fu">svygeidec</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb409"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb409-1"><a href="4.11-generalized-entropy-and-decomposition-svygei-svygeidec.html#cb409-1" tabindex="-1"></a><span class="fu">svygeidec</span>( <span class="sc">~</span> eybhc0, <span class="sc">~</span> wkstatus, z91, <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
 <pre><code>##         gei decomposition     SE
 ## total            0.274325 0.0167
 ## within           0.245067 0.0164
diff --git a/docs/4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html b/docs/4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html
index afbed33..7629715 100644
--- a/docs/4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html
+++ b/docs/4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,12 +253,12 @@
 <div class="col-sm-12">
 <div id="j-divergence-and-decomposition-svyjdiv-svyjdivdec" class="section level2" number="4.12">
 <h2><span class="header-section-number">4.12</span> J-Divergence and Decomposition (svyjdiv, svyjdivdec)</h2>
-<div class="sourceCode" id="cb412"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb412-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb412-1" tabindex="-1"></a>✔️ can be interpreted <span class="cf">in</span> terms of GEI indices</span>
-<span id="cb412-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb412-2" tabindex="-1"></a>✔️ can be group<span class="sc">-</span>decomposed into within<span class="sc">-</span>inequality and between<span class="sc">-</span>inequality</span>
-<span id="cb412-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb412-3" tabindex="-1"></a>✔️ does not need <span class="fu">to</span> (explicitly) choose inequality aversion parameters</span>
-<span id="cb412-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb412-4" tabindex="-1"></a>❌ does not handle zero or negative incomes</span>
-<span id="cb412-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb412-5" tabindex="-1"></a>❌ hard to interpret</span>
-<span id="cb412-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb412-6" tabindex="-1"></a>❌ the decomposition interpretation is not exactly the same as the GEI, but very similar</span></code></pre></div>
+<div class="sourceCode" id="cb411"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb411-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb411-1" tabindex="-1"></a>✔️ can be interpreted <span class="cf">in</span> terms of GEI indices</span>
+<span id="cb411-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb411-2" tabindex="-1"></a>✔️ can be group<span class="sc">-</span>decomposed into within<span class="sc">-</span>inequality and between<span class="sc">-</span>inequality</span>
+<span id="cb411-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb411-3" tabindex="-1"></a>✔️ does not need <span class="fu">to</span> (explicitly) choose inequality aversion parameters</span>
+<span id="cb411-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb411-4" tabindex="-1"></a>❌ does not handle zero or negative incomes</span>
+<span id="cb411-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb411-5" tabindex="-1"></a>❌ hard to interpret</span>
+<span id="cb411-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb411-6" tabindex="-1"></a>❌ the decomposition interpretation is not exactly the same as the GEI, but very similar</span></code></pre></div>
 <p>The J-divergence measure <span class="citation">(<label for="tufte-mn-98" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-98" class="margin-toggle">Rohde 2016<span class="marginnote">Rohde, Nicholas. 2016. <span>“J-Divergence Measurements of Economic Inequality.”</span> <em>Journal of the Royal Statistical Society: Series A (Statistics in Society)</em> 179 (3): 847–70. <a href="https://doi.org/10.1111/rssa.12153">https://doi.org/10.1111/rssa.12153</a>.</span>)</span> can be seen as the sum of <span class="math inline">\(GE_0\)</span> and <span class="math inline">\(GE_1\)</span>, satisfying axioms that, individually, those two indices do not. The J-divergence measure is defined as:</p>
 <p><span class="math display">\[
 J = \frac{1}{N} \sum_{i \in U} \bigg( \frac{ y_i }{ \mu } -1 \bigg) \ln \bigg( \frac{y_i}{\mu} \bigg)
@@ -275,136 +275,136 @@ <h2><span class="header-section-number">4.12</span> J-Divergence and Decompositi
 <div id="monte-carlo-simulation-2" class="section level3" number="4.12.1">
 <h3><span class="header-section-number">4.12.1</span> Monte Carlo Simulation</h3>
 <p>First, we should check that the finite-population values make sense. The J-divergence can be seen as the sum of <span class="math inline">\(GE^{(0)}\)</span> and <span class="math inline">\(GE^{(1)}\)</span>. So, taking the starting population from the <code>svyzenga</code> section of this text, we have:</p>
-<div class="sourceCode" id="cb413"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb413-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb413-1" tabindex="-1"></a><span class="co"># compute finite population J-divergence</span></span>
-<span id="cb413-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb413-2" tabindex="-1"></a>(jdivt.pop <span class="ot">&lt;-</span></span>
-<span id="cb413-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb413-3" tabindex="-1"></a>   (convey<span class="sc">:::</span><span class="fu">CalcJDiv</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>))))</span></code></pre></div>
+<div class="sourceCode" id="cb412"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb412-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb412-1" tabindex="-1"></a><span class="co"># compute finite population J-divergence</span></span>
+<span id="cb412-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb412-2" tabindex="-1"></a>(jdivt.pop <span class="ot">&lt;-</span></span>
+<span id="cb412-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb412-3" tabindex="-1"></a>   (convey<span class="sc">:::</span><span class="fu">CalcJDiv</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>))))</span></code></pre></div>
 <pre><code>## [1] 0.4332649</code></pre>
-<div class="sourceCode" id="cb415"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb415-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb415-1" tabindex="-1"></a><span class="co"># compute finite population GE indices</span></span>
-<span id="cb415-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb415-2" tabindex="-1"></a>(gei0.pop <span class="ot">&lt;-</span></span>
-<span id="cb415-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb415-3" tabindex="-1"></a>    convey<span class="sc">:::</span><span class="fu">CalcGEI</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>) , <span class="dv">0</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb414"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb414-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb414-1" tabindex="-1"></a><span class="co"># compute finite population GE indices</span></span>
+<span id="cb414-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb414-2" tabindex="-1"></a>(gei0.pop <span class="ot">&lt;-</span></span>
+<span id="cb414-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb414-3" tabindex="-1"></a>    convey<span class="sc">:::</span><span class="fu">CalcGEI</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>) , <span class="dv">0</span>))</span></code></pre></div>
 <pre><code>## [1] 0.2215037</code></pre>
-<div class="sourceCode" id="cb417"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb417-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb417-1" tabindex="-1"></a>(gei1.pop <span class="ot">&lt;-</span></span>
-<span id="cb417-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb417-2" tabindex="-1"></a>    convey<span class="sc">:::</span><span class="fu">CalcGEI</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>) , <span class="dv">1</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb416"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb416-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb416-1" tabindex="-1"></a>(gei1.pop <span class="ot">&lt;-</span></span>
+<span id="cb416-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb416-2" tabindex="-1"></a>    convey<span class="sc">:::</span><span class="fu">CalcGEI</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>) , <span class="dv">1</span>))</span></code></pre></div>
 <pre><code>## [1] 0.2117612</code></pre>
-<div class="sourceCode" id="cb419"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb419-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb419-1" tabindex="-1"></a><span class="co"># check equality; should be true</span></span>
-<span id="cb419-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb419-2" tabindex="-1"></a><span class="fu">all.equal</span>(jdivt.pop , gei0.pop <span class="sc">+</span> gei1.pop)</span></code></pre></div>
+<div class="sourceCode" id="cb418"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb418-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb418-1" tabindex="-1"></a><span class="co"># check equality; should be true</span></span>
+<span id="cb418-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb418-2" tabindex="-1"></a><span class="fu">all.equal</span>(jdivt.pop , gei0.pop <span class="sc">+</span> gei1.pop)</span></code></pre></div>
 <pre><code>## [1] TRUE</code></pre>
 <p>As expected, the J-divergence matches the sum of GEs in the finite population. And as we’ve checked the GE measures before, the J-divergence computation function seems safe.</p>
 <p>In order to assess the estimators implemented in <code>svyjdiv</code> and <code>svyjdivdec</code>, we can run a Monte Carlo experiment. Using the same samples we used in the <code>svyzenga</code> replication example, we have:</p>
-<div class="sourceCode" id="cb421"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb421-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-1" tabindex="-1"></a><span class="co"># estimate J-divergence with each sample</span></span>
-<span id="cb421-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-2" tabindex="-1"></a>jdiv.estimate.list <span class="ot">&lt;-</span></span>
-<span id="cb421-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-3" tabindex="-1"></a>  <span class="fu">lapply</span>(survey.list ,</span>
-<span id="cb421-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-4" tabindex="-1"></a>         <span class="cf">function</span>(this.sample) {</span>
-<span id="cb421-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-5" tabindex="-1"></a>           <span class="fu">svyjdiv</span>( <span class="sc">~</span> x ,</span>
-<span id="cb421-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-6" tabindex="-1"></a>                    <span class="fu">subset</span>(this.sample , x <span class="sc">&gt;</span> <span class="dv">0</span>) ,</span>
-<span id="cb421-7"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-7" tabindex="-1"></a>                    <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb421-8"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-8" tabindex="-1"></a>         })</span>
-<span id="cb421-9"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-9" tabindex="-1"></a></span>
-<span id="cb421-10"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-10" tabindex="-1"></a><span class="co"># compute the (finite population overall) J-divergence</span></span>
-<span id="cb421-11"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-11" tabindex="-1"></a>(theta.pop <span class="ot">&lt;-</span></span>
-<span id="cb421-12"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb421-12" tabindex="-1"></a>    convey<span class="sc">:::</span><span class="fu">CalcJDiv</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>)))</span></code></pre></div>
+<div class="sourceCode" id="cb420"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb420-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-1" tabindex="-1"></a><span class="co"># estimate J-divergence with each sample</span></span>
+<span id="cb420-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-2" tabindex="-1"></a>jdiv.estimate.list <span class="ot">&lt;-</span></span>
+<span id="cb420-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-3" tabindex="-1"></a>  <span class="fu">lapply</span>(survey.list ,</span>
+<span id="cb420-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-4" tabindex="-1"></a>         <span class="cf">function</span>(this.sample) {</span>
+<span id="cb420-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-5" tabindex="-1"></a>           <span class="fu">svyjdiv</span>( <span class="sc">~</span> x ,</span>
+<span id="cb420-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-6" tabindex="-1"></a>                    <span class="fu">subset</span>(this.sample , x <span class="sc">&gt;</span> <span class="dv">0</span>) ,</span>
+<span id="cb420-7"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-7" tabindex="-1"></a>                    <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb420-8"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-8" tabindex="-1"></a>         })</span>
+<span id="cb420-9"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-9" tabindex="-1"></a></span>
+<span id="cb420-10"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-10" tabindex="-1"></a><span class="co"># compute the (finite population overall) J-divergence</span></span>
+<span id="cb420-11"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-11" tabindex="-1"></a>(theta.pop <span class="ot">&lt;-</span></span>
+<span id="cb420-12"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb420-12" tabindex="-1"></a>    convey<span class="sc">:::</span><span class="fu">CalcJDiv</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>)))</span></code></pre></div>
 <pre><code>## [1] 0.4332649</code></pre>
-<div class="sourceCode" id="cb423"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb423-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb423-1" tabindex="-1"></a><span class="co"># estimate the expected value of the J-divergence estimator</span></span>
-<span id="cb423-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb423-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
-<span id="cb423-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb423-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(jdiv.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb422"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb422-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb422-1" tabindex="-1"></a><span class="co"># estimate the expected value of the J-divergence estimator</span></span>
+<span id="cb422-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb422-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
+<span id="cb422-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb422-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(jdiv.estimate.list , coef)))</span></code></pre></div>
 <pre><code>## [1] 0.4327823</code></pre>
-<div class="sourceCode" id="cb425"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb425-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb425-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
-<span id="cb425-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb425-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb424"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb424-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb424-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
+<span id="cb424-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb424-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
 <pre><code>## [1] -0.1113765</code></pre>
-<div class="sourceCode" id="cb427"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb427-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb427-1" tabindex="-1"></a><span class="co"># estimate the variance of the J-divergence estimator</span></span>
-<span id="cb427-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb427-2" tabindex="-1"></a><span class="co"># using the variance of the estimates</span></span>
-<span id="cb427-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb427-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span> <span class="fu">var</span>(<span class="fu">sapply</span>(jdiv.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb426"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb426-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb426-1" tabindex="-1"></a><span class="co"># estimate the variance of the J-divergence estimator</span></span>
+<span id="cb426-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb426-2" tabindex="-1"></a><span class="co"># using the variance of the estimates</span></span>
+<span id="cb426-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb426-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span> <span class="fu">var</span>(<span class="fu">sapply</span>(jdiv.estimate.list , coef)))</span></code></pre></div>
 <pre><code>## [1] 0.0005434848</code></pre>
-<div class="sourceCode" id="cb429"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb429-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb429-1" tabindex="-1"></a><span class="co"># estimate the expected value of the J-divergence index variance estimator</span></span>
-<span id="cb429-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb429-2" tabindex="-1"></a><span class="co"># using the expected of the variance estimates</span></span>
-<span id="cb429-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb429-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(jdiv.estimate.list , vcov)))</span></code></pre></div>
+<div class="sourceCode" id="cb428"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb428-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb428-1" tabindex="-1"></a><span class="co"># estimate the expected value of the J-divergence index variance estimator</span></span>
+<span id="cb428-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb428-2" tabindex="-1"></a><span class="co"># using the expected of the variance estimates</span></span>
+<span id="cb428-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb428-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(jdiv.estimate.list , vcov)))</span></code></pre></div>
 <pre><code>## [1] 0.0005342947</code></pre>
-<div class="sourceCode" id="cb431"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb431-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb431-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimator</span></span>
-<span id="cb431-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb431-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb430"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb430-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb430-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimator</span></span>
+<span id="cb430-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb430-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
 <pre><code>## [1] -1.690964</code></pre>
 <p>For the decomposition, we repeat the same procedure:</p>
-<div class="sourceCode" id="cb433"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb433-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-1" tabindex="-1"></a><span class="co"># estimate J-divergence decomposition with each sample</span></span>
-<span id="cb433-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-2" tabindex="-1"></a>jdivdec.estimate.list <span class="ot">&lt;-</span></span>
-<span id="cb433-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-3" tabindex="-1"></a>  <span class="fu">lapply</span>(survey.list ,</span>
-<span id="cb433-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-4" tabindex="-1"></a>         <span class="cf">function</span>(this.sample) {</span>
-<span id="cb433-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-5" tabindex="-1"></a>           <span class="fu">svyjdivdec</span>( <span class="sc">~</span> x ,</span>
-<span id="cb433-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-6" tabindex="-1"></a>                       <span class="sc">~</span> SEX ,</span>
-<span id="cb433-7"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-7" tabindex="-1"></a>                       <span class="fu">subset</span>(this.sample , x <span class="sc">&gt;</span> <span class="dv">0</span>) ,</span>
-<span id="cb433-8"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-8" tabindex="-1"></a>                       <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb433-9"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-9" tabindex="-1"></a>         })</span>
-<span id="cb433-10"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-10" tabindex="-1"></a></span>
-<span id="cb433-11"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-11" tabindex="-1"></a><span class="co"># compute the (finite population) J-divergence decomposition per sex</span></span>
-<span id="cb433-12"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-12" tabindex="-1"></a>jdivt.pop <span class="ot">&lt;-</span></span>
-<span id="cb433-13"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-13" tabindex="-1"></a>  convey<span class="sc">:::</span><span class="fu">CalcJDiv</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>))</span>
-<span id="cb433-14"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-14" tabindex="-1"></a></span>
-<span id="cb433-15"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-15" tabindex="-1"></a>overall.mean <span class="ot">&lt;-</span> <span class="fu">mean</span>(pop.df<span class="sc">$</span>x[pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span>])</span>
-<span id="cb433-16"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-16" tabindex="-1"></a></span>
-<span id="cb433-17"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-17" tabindex="-1"></a>group.mean <span class="ot">&lt;-</span></span>
-<span id="cb433-18"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-18" tabindex="-1"></a>  <span class="fu">c</span>(<span class="fu">by</span>(pop.df<span class="sc">$</span>x[pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span>] , <span class="fu">list</span>(<span class="st">&quot;SEX&quot;</span> <span class="ot">=</span> <span class="fu">factor</span>(pop.df<span class="sc">$</span>SEX[pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span>])) , <span class="at">FUN =</span> mean))</span>
-<span id="cb433-19"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-19" tabindex="-1"></a></span>
-<span id="cb433-20"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-20" tabindex="-1"></a>group.pshare <span class="ot">&lt;-</span></span>
-<span id="cb433-21"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-21" tabindex="-1"></a>  <span class="fu">c</span>(<span class="fu">prop.table</span>(<span class="fu">by</span>(<span class="fu">rep</span>(<span class="dv">1</span> , <span class="fu">sum</span>(</span>
-<span id="cb433-22"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-22" tabindex="-1"></a>    pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span></span>
-<span id="cb433-23"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-23" tabindex="-1"></a>  )) , <span class="fu">list</span>(</span>
-<span id="cb433-24"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-24" tabindex="-1"></a>    <span class="st">&quot;SEX&quot;</span> <span class="ot">=</span> <span class="fu">factor</span>(pop.df<span class="sc">$</span>SEX[pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span>])</span>
-<span id="cb433-25"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-25" tabindex="-1"></a>  ) , <span class="at">FUN =</span> sum)))</span>
-<span id="cb433-26"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-26" tabindex="-1"></a></span>
-<span id="cb433-27"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-27" tabindex="-1"></a>jdivb.pop <span class="ot">&lt;-</span></span>
-<span id="cb433-28"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-28" tabindex="-1"></a>  <span class="fu">sum</span>(group.pshare <span class="sc">*</span> (group.mean <span class="sc">/</span> overall.mean <span class="sc">-</span> <span class="dv">1</span>) <span class="sc">*</span> <span class="fu">log</span>(group.mean <span class="sc">/</span> overall.mean))</span>
-<span id="cb433-29"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-29" tabindex="-1"></a></span>
-<span id="cb433-30"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-30" tabindex="-1"></a>jdivw.pop <span class="ot">&lt;-</span> jdivt.pop <span class="sc">-</span> jdivb.pop</span>
-<span id="cb433-31"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-31" tabindex="-1"></a></span>
-<span id="cb433-32"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb433-32" tabindex="-1"></a>(theta.pop <span class="ot">&lt;-</span> <span class="fu">c</span>(jdivt.pop , jdivw.pop , jdivb.pop))</span></code></pre></div>
+<div class="sourceCode" id="cb432"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb432-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-1" tabindex="-1"></a><span class="co"># estimate J-divergence decomposition with each sample</span></span>
+<span id="cb432-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-2" tabindex="-1"></a>jdivdec.estimate.list <span class="ot">&lt;-</span></span>
+<span id="cb432-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-3" tabindex="-1"></a>  <span class="fu">lapply</span>(survey.list ,</span>
+<span id="cb432-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-4" tabindex="-1"></a>         <span class="cf">function</span>(this.sample) {</span>
+<span id="cb432-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-5" tabindex="-1"></a>           <span class="fu">svyjdivdec</span>( <span class="sc">~</span> x ,</span>
+<span id="cb432-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-6" tabindex="-1"></a>                       <span class="sc">~</span> SEX ,</span>
+<span id="cb432-7"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-7" tabindex="-1"></a>                       <span class="fu">subset</span>(this.sample , x <span class="sc">&gt;</span> <span class="dv">0</span>) ,</span>
+<span id="cb432-8"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-8" tabindex="-1"></a>                       <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb432-9"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-9" tabindex="-1"></a>         })</span>
+<span id="cb432-10"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-10" tabindex="-1"></a></span>
+<span id="cb432-11"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-11" tabindex="-1"></a><span class="co"># compute the (finite population) J-divergence decomposition per sex</span></span>
+<span id="cb432-12"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-12" tabindex="-1"></a>jdivt.pop <span class="ot">&lt;-</span></span>
+<span id="cb432-13"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-13" tabindex="-1"></a>  convey<span class="sc">:::</span><span class="fu">CalcJDiv</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>))</span>
+<span id="cb432-14"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-14" tabindex="-1"></a></span>
+<span id="cb432-15"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-15" tabindex="-1"></a>overall.mean <span class="ot">&lt;-</span> <span class="fu">mean</span>(pop.df<span class="sc">$</span>x[pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span>])</span>
+<span id="cb432-16"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-16" tabindex="-1"></a></span>
+<span id="cb432-17"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-17" tabindex="-1"></a>group.mean <span class="ot">&lt;-</span></span>
+<span id="cb432-18"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-18" tabindex="-1"></a>  <span class="fu">c</span>(<span class="fu">by</span>(pop.df<span class="sc">$</span>x[pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span>] , <span class="fu">list</span>(<span class="st">&quot;SEX&quot;</span> <span class="ot">=</span> <span class="fu">factor</span>(pop.df<span class="sc">$</span>SEX[pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span>])) , <span class="at">FUN =</span> mean))</span>
+<span id="cb432-19"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-19" tabindex="-1"></a></span>
+<span id="cb432-20"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-20" tabindex="-1"></a>group.pshare <span class="ot">&lt;-</span></span>
+<span id="cb432-21"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-21" tabindex="-1"></a>  <span class="fu">c</span>(<span class="fu">prop.table</span>(<span class="fu">by</span>(<span class="fu">rep</span>(<span class="dv">1</span> , <span class="fu">sum</span>(</span>
+<span id="cb432-22"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-22" tabindex="-1"></a>    pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span></span>
+<span id="cb432-23"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-23" tabindex="-1"></a>  )) , <span class="fu">list</span>(</span>
+<span id="cb432-24"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-24" tabindex="-1"></a>    <span class="st">&quot;SEX&quot;</span> <span class="ot">=</span> <span class="fu">factor</span>(pop.df<span class="sc">$</span>SEX[pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span>])</span>
+<span id="cb432-25"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-25" tabindex="-1"></a>  ) , <span class="at">FUN =</span> sum)))</span>
+<span id="cb432-26"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-26" tabindex="-1"></a></span>
+<span id="cb432-27"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-27" tabindex="-1"></a>jdivb.pop <span class="ot">&lt;-</span></span>
+<span id="cb432-28"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-28" tabindex="-1"></a>  <span class="fu">sum</span>(group.pshare <span class="sc">*</span> (group.mean <span class="sc">/</span> overall.mean <span class="sc">-</span> <span class="dv">1</span>) <span class="sc">*</span> <span class="fu">log</span>(group.mean <span class="sc">/</span> overall.mean))</span>
+<span id="cb432-29"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-29" tabindex="-1"></a></span>
+<span id="cb432-30"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-30" tabindex="-1"></a>jdivw.pop <span class="ot">&lt;-</span> jdivt.pop <span class="sc">-</span> jdivb.pop</span>
+<span id="cb432-31"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-31" tabindex="-1"></a></span>
+<span id="cb432-32"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb432-32" tabindex="-1"></a>(theta.pop <span class="ot">&lt;-</span> <span class="fu">c</span>(jdivt.pop , jdivw.pop , jdivb.pop))</span></code></pre></div>
 <pre><code>## [1] 0.433264877 0.428398928 0.004865949</code></pre>
-<div class="sourceCode" id="cb435"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb435-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb435-1" tabindex="-1"></a><span class="co"># estimate the expected value of the J-divergence decomposition estimator</span></span>
-<span id="cb435-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb435-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
-<span id="cb435-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb435-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(jdivdec.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb434"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb434-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb434-1" tabindex="-1"></a><span class="co"># estimate the expected value of the J-divergence decomposition estimator</span></span>
+<span id="cb434-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb434-2" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
+<span id="cb434-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb434-3" tabindex="-1"></a>(theta.exp <span class="ot">&lt;-</span> <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(jdivdec.estimate.list , coef)))</span></code></pre></div>
 <pre><code>##       total      within     between 
 ## 0.432782322 0.427480257 0.005302065</code></pre>
-<div class="sourceCode" id="cb437"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb437-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb437-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
-<span id="cb437-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb437-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb436"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb436-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb436-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
+<span id="cb436-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb436-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
 <pre><code>##      total     within    between 
 ## -0.1113765 -0.2144430  8.9626164</code></pre>
 <p>The estimated PRB for the total is the same as before, so we will focus on the within and between components. While the within component has a small relative bias (-0.21%), the between component PRB is significant, amounting to 8.96%.</p>
 <p>For the variance estimator, we do:</p>
-<div class="sourceCode" id="cb439"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb439-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb439-1" tabindex="-1"></a><span class="co"># estimate the variance of the J-divergence estimator</span></span>
-<span id="cb439-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb439-2" tabindex="-1"></a><span class="co"># using the variance of the estimates</span></span>
-<span id="cb439-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb439-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span></span>
-<span id="cb439-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb439-4" tabindex="-1"></a>   <span class="fu">diag</span>(<span class="fu">var</span>(<span class="fu">t</span>(</span>
-<span id="cb439-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb439-5" tabindex="-1"></a>     <span class="fu">sapply</span>(jdivdec.estimate.list , coef)</span>
-<span id="cb439-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb439-6" tabindex="-1"></a>   ))))</span></code></pre></div>
+<div class="sourceCode" id="cb438"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb438-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb438-1" tabindex="-1"></a><span class="co"># estimate the variance of the J-divergence estimator</span></span>
+<span id="cb438-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb438-2" tabindex="-1"></a><span class="co"># using the variance of the estimates</span></span>
+<span id="cb438-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb438-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span></span>
+<span id="cb438-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb438-4" tabindex="-1"></a>   <span class="fu">diag</span>(<span class="fu">var</span>(<span class="fu">t</span>(</span>
+<span id="cb438-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb438-5" tabindex="-1"></a>     <span class="fu">sapply</span>(jdivdec.estimate.list , coef)</span>
+<span id="cb438-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb438-6" tabindex="-1"></a>   ))))</span></code></pre></div>
 <pre><code>##        total       within      between 
 ## 5.434848e-04 5.391901e-04 8.750879e-06</code></pre>
-<div class="sourceCode" id="cb441"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb441-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb441-1" tabindex="-1"></a><span class="co"># estimate the expected value of the J-divergence index variance estimator</span></span>
-<span id="cb441-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb441-2" tabindex="-1"></a><span class="co"># using the expected of the variance estimates</span></span>
-<span id="cb441-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb441-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span></span>
-<span id="cb441-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb441-4" tabindex="-1"></a>    <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(jdivdec.estimate.list , <span class="cf">function</span>(z)</span>
-<span id="cb441-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb441-5" tabindex="-1"></a>      <span class="fu">diag</span>(<span class="fu">vcov</span>(</span>
-<span id="cb441-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb441-6" tabindex="-1"></a>        z</span>
-<span id="cb441-7"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb441-7" tabindex="-1"></a>      )))))</span></code></pre></div>
+<div class="sourceCode" id="cb440"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb440-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb440-1" tabindex="-1"></a><span class="co"># estimate the expected value of the J-divergence index variance estimator</span></span>
+<span id="cb440-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb440-2" tabindex="-1"></a><span class="co"># using the expected of the variance estimates</span></span>
+<span id="cb440-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb440-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span></span>
+<span id="cb440-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb440-4" tabindex="-1"></a>    <span class="fu">rowMeans</span>(<span class="fu">sapply</span>(jdivdec.estimate.list , <span class="cf">function</span>(z)</span>
+<span id="cb440-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb440-5" tabindex="-1"></a>      <span class="fu">diag</span>(<span class="fu">vcov</span>(</span>
+<span id="cb440-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb440-6" tabindex="-1"></a>        z</span>
+<span id="cb440-7"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb440-7" tabindex="-1"></a>      )))))</span></code></pre></div>
 <pre><code>##        total       within      between 
 ## 5.342947e-04 5.286750e-04 8.891772e-06</code></pre>
-<div class="sourceCode" id="cb443"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb443-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb443-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimator</span></span>
-<span id="cb443-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb443-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb442"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb442-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb442-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias of the variance estimator</span></span>
+<span id="cb442-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb442-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
 <pre><code>##     total    within   between 
 ## -1.690964 -1.950177  1.610034</code></pre>
 <p>The PRB of the variance estimators for both components are small: -1.95% for the within component and 1.61% for the between component.</p>
 <p>Now, how much should we care about the between component bias? Our simulations show that the Squared Bias of this estimator accounts for less than 2% of its Mean Squared Error:</p>
-<div class="sourceCode" id="cb445"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb445-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb445-1" tabindex="-1"></a>theta.bias2 <span class="ot">&lt;-</span> (theta.exp <span class="sc">-</span> theta.pop) <span class="sc">^</span> <span class="dv">2</span></span>
-<span id="cb445-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb445-2" tabindex="-1"></a>theta.mse <span class="ot">&lt;-</span> theta.bias2 <span class="sc">+</span> vartheta.popest</span>
-<span id="cb445-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb445-3" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (theta.bias2 <span class="sc">/</span> theta.mse)</span></code></pre></div>
+<div class="sourceCode" id="cb444"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb444-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb444-1" tabindex="-1"></a>theta.bias2 <span class="ot">&lt;-</span> (theta.exp <span class="sc">-</span> theta.pop) <span class="sc">^</span> <span class="dv">2</span></span>
+<span id="cb444-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb444-2" tabindex="-1"></a>theta.mse <span class="ot">&lt;-</span> theta.bias2 <span class="sc">+</span> vartheta.popest</span>
+<span id="cb444-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb444-3" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (theta.bias2 <span class="sc">/</span> theta.mse)</span></code></pre></div>
 <pre><code>##      total     within    between 
 ## 0.04282728 0.15627854 2.12723212</code></pre>
 <p>Next, we evaluate the Percentage Coverage Rate (PCR). In theory, under repeated sampling, the estimated 95% CIs should cover the population parameter 95% of the time. We can evaluate that using:</p>
-<div class="sourceCode" id="cb447"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb447-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb447-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Zenga index</span></span>
-<span id="cb447-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb447-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
-<span id="cb447-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb447-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
-<span id="cb447-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb447-4" tabindex="-1"></a>  <span class="fu">t</span>(<span class="fu">sapply</span>(jdivdec.estimate.list, <span class="cf">function</span>(this.stat)</span>
-<span id="cb447-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb447-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
-<span id="cb447-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb447-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop))</span>
-<span id="cb447-7"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb447-7" tabindex="-1"></a></span>
-<span id="cb447-8"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb447-8" tabindex="-1"></a><span class="co"># evaluate</span></span>
-<span id="cb447-9"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb447-9" tabindex="-1"></a><span class="fu">colMeans</span>(est.coverage)</span></code></pre></div>
+<div class="sourceCode" id="cb446"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb446-1"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb446-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Zenga index</span></span>
+<span id="cb446-2"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb446-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
+<span id="cb446-3"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb446-3" tabindex="-1"></a>est.coverage <span class="ot">&lt;-</span></span>
+<span id="cb446-4"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb446-4" tabindex="-1"></a>  <span class="fu">t</span>(<span class="fu">sapply</span>(jdivdec.estimate.list, <span class="cf">function</span>(this.stat)</span>
+<span id="cb446-5"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb446-5" tabindex="-1"></a>    <span class="fu">confint</span>(this.stat)[, <span class="dv">1</span>] <span class="sc">&lt;=</span> theta.pop <span class="sc">&amp;</span></span>
+<span id="cb446-6"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb446-6" tabindex="-1"></a>      <span class="fu">confint</span>(this.stat)[, <span class="dv">2</span>] <span class="sc">&gt;=</span> theta.pop))</span>
+<span id="cb446-7"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb446-7" tabindex="-1"></a></span>
+<span id="cb446-8"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb446-8" tabindex="-1"></a><span class="co"># evaluate</span></span>
+<span id="cb446-9"><a href="4.12-j-divergence-and-decomposition-svyjdiv-svyjdivdec.html#cb446-9" tabindex="-1"></a><span class="fu">colMeans</span>(est.coverage)</span></code></pre></div>
 <pre><code>##   total  within between 
 ##  0.9390  0.9376  0.9108</code></pre>
 <p>Our coverages are not too far from the nominal coverage level of 95%, however the bias of the between component estimator can affect its coverage rate.</p>
diff --git a/docs/4.2-the-gender-pay-gap-svygpg.html b/docs/4.2-the-gender-pay-gap-svygpg.html
index 5a1f3b9..46d250b 100644
--- a/docs/4.2-the-gender-pay-gap-svygpg.html
+++ b/docs/4.2-the-gender-pay-gap-svygpg.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,12 +253,12 @@
 <div class="col-sm-12">
 <div id="the-gender-pay-gap-svygpg" class="section level2" number="4.2">
 <h2><span class="header-section-number">4.2</span> The Gender Pay Gap (svygpg)</h2>
-<div class="sourceCode" id="cb252"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb252-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-1" tabindex="-1"></a>✔️ easy to understand</span>
-<span id="cb252-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-2" tabindex="-1"></a>✔️ the difference of men and women average wages expressed as a fraction of average men wages</span>
-<span id="cb252-3"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-3" tabindex="-1"></a>✔️ alternatively<span class="sc">:</span> the average women wage is <span class="st">`</span><span class="at">( 1 - GPG ) x average men wage</span><span class="st">`</span></span>
-<span id="cb252-4"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-4" tabindex="-1"></a>❌ not an inequality measure <span class="cf">in</span> the Pigou<span class="sc">-</span>Dalton Principle sense</span>
-<span id="cb252-5"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-5" tabindex="-1"></a>❌ ignores within<span class="sc">-</span>inequality among men and among women</span>
-<span id="cb252-6"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-6" tabindex="-1"></a>❌ binary gender only</span></code></pre></div>
+<div class="sourceCode" id="cb251"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb251-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb251-1" tabindex="-1"></a>✔️ easy to understand</span>
+<span id="cb251-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb251-2" tabindex="-1"></a>✔️ the difference of men and women average wages expressed as a fraction of average men wages</span>
+<span id="cb251-3"><a href="4.2-the-gender-pay-gap-svygpg.html#cb251-3" tabindex="-1"></a>✔️ alternatively<span class="sc">:</span> the average women wage is <span class="st">`</span><span class="at">( 1 - GPG ) x average men wage</span><span class="st">`</span></span>
+<span id="cb251-4"><a href="4.2-the-gender-pay-gap-svygpg.html#cb251-4" tabindex="-1"></a>❌ not an inequality measure <span class="cf">in</span> the Pigou<span class="sc">-</span>Dalton Principle sense</span>
+<span id="cb251-5"><a href="4.2-the-gender-pay-gap-svygpg.html#cb251-5" tabindex="-1"></a>❌ ignores within<span class="sc">-</span>inequality among men and among women</span>
+<span id="cb251-6"><a href="4.2-the-gender-pay-gap-svygpg.html#cb251-6" tabindex="-1"></a>❌ binary gender only</span></code></pre></div>
 <p>Although the Gender Pay Gap (GPG) is not an inequality measure in the usual sense, it can still be a useful instrument to evaluate the effects of gender discrimination. Put simply, it expresses the relative difference between the average hourly earnings of men and women, presenting this difference as a percentage of the average of hourly earnings of men. Like some other functions described in this text, the GPG can also be calculated using wealth or assets in place of earnings.</p>
 <p>In mathematical terms, this index can be described as,</p>
 <p><span class="math display">\[ GPG = \frac{ \bar{y}_{male} - \bar{y}_{female} }{ \bar{y}_{male} } \]</span></p>
@@ -270,148 +270,148 @@ <h2><span class="header-section-number">4.2</span> The Gender Pay Gap (svygpg)</
 <h3><span class="header-section-number">4.2.1</span> Replication Example</h3>
 <p>The R <code>vardpoor</code> package <span class="citation">(<label for="tufte-mn-64" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-64" class="margin-toggle">Breidaks, Liberts, and Ivanova 2016<span class="marginnote">Breidaks, Juris, Martins Liberts, and Santa Ivanova. 2016. <span>“Vardpoor: Estimation of Indicators on Social Exclusion and Poverty and Its Linearization, Variance Estimation.”</span> Riga, Latvia: CSB.</span>)</span>, created by researchers at the Central Statistical Bureau of Latvia, includes a GPG coefficient calculation using the ultimate cluster method. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb253"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb253-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb253-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb253-3"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-3" tabindex="-1"></a></span>
-<span id="cb253-4"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb253-5"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb253-6"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-6" tabindex="-1"></a></span>
-<span id="cb253-7"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb253-8"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
-<span id="cb253-9"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-9" tabindex="-1"></a></span>
-<span id="cb253-10"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-10" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
-<span id="cb253-11"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
-<span id="cb253-12"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-12" tabindex="-1"></a></span>
-<span id="cb253-13"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
-<span id="cb253-14"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
-<span id="cb253-15"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-15" tabindex="-1"></a></span>
-<span id="cb253-16"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
-<span id="cb253-17"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
-<span id="cb253-18"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-18" tabindex="-1"></a></span>
-<span id="cb253-19"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-19" tabindex="-1"></a><span class="co"># coerce the gender variable to numeric 1 or 2</span></span>
-<span id="cb253-20"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-20" tabindex="-1"></a>eusilc<span class="sc">$</span>one_two <span class="ot">&lt;-</span> <span class="fu">as.numeric</span>(eusilc<span class="sc">$</span>rb090 <span class="sc">==</span> <span class="st">&quot;female&quot;</span>) <span class="sc">+</span> <span class="dv">1</span></span>
-<span id="cb253-21"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-21" tabindex="-1"></a></span>
-<span id="cb253-22"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-22" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
-<span id="cb253-23"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-23" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
-<span id="cb253-24"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-24" tabindex="-1"></a></span>
-<span id="cb253-25"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-25" tabindex="-1"></a><span class="co"># calculate the gpg coefficient</span></span>
-<span id="cb253-26"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-26" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
-<span id="cb253-27"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-27" tabindex="-1"></a>varpoord_gpg_calculation <span class="ot">&lt;-</span></span>
-<span id="cb253-28"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-28" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
-<span id="cb253-29"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-29" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
-<span id="cb253-30"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-30" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
-<span id="cb253-31"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-31" tabindex="-1"></a>    </span>
-<span id="cb253-32"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-32" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
-<span id="cb253-33"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-33" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
-<span id="cb253-34"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-34" tabindex="-1"></a>    </span>
-<span id="cb253-35"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb253-36"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-36" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb253-37"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-37" tabindex="-1"></a>    </span>
-<span id="cb253-38"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-38" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb253-39"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-39" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb253-40"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-40" tabindex="-1"></a>    </span>
-<span id="cb253-41"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-41" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
-<span id="cb253-42"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-42" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
-<span id="cb253-43"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-43" tabindex="-1"></a>    </span>
-<span id="cb253-44"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-44" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
-<span id="cb253-45"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-45" tabindex="-1"></a>    </span>
-<span id="cb253-46"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-46" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
-<span id="cb253-47"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-47" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
-<span id="cb253-48"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-48" tabindex="-1"></a>    </span>
-<span id="cb253-49"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-49" tabindex="-1"></a>    <span class="co"># data.table</span></span>
-<span id="cb253-50"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-50" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
-<span id="cb253-51"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-51" tabindex="-1"></a>    </span>
-<span id="cb253-52"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-52" tabindex="-1"></a>    <span class="co"># gpg coefficient function</span></span>
-<span id="cb253-53"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-53" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;lingpg&quot;</span> ,</span>
-<span id="cb253-54"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-54" tabindex="-1"></a>    </span>
-<span id="cb253-55"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-55" tabindex="-1"></a>    <span class="co"># gender variable</span></span>
-<span id="cb253-56"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-56" tabindex="-1"></a>    <span class="at">gender =</span> <span class="st">&quot;one_two&quot;</span>,</span>
-<span id="cb253-57"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-57" tabindex="-1"></a>    </span>
-<span id="cb253-58"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-58" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
-<span id="cb253-59"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-59" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
-<span id="cb253-60"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-60" tabindex="-1"></a>  )</span>
-<span id="cb253-61"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-61" tabindex="-1"></a></span>
-<span id="cb253-62"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-62" tabindex="-1"></a></span>
-<span id="cb253-63"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-63" tabindex="-1"></a></span>
-<span id="cb253-64"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-64" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb253-65"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-65" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
-<span id="cb253-66"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-66" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
-<span id="cb253-67"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-67" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb253-68"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-68" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb253-69"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-69" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb253-70"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-70" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb253-71"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-71" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
-<span id="cb253-72"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-72" tabindex="-1"></a>  )</span>
-<span id="cb253-73"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-73" tabindex="-1"></a></span>
-<span id="cb253-74"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-74" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
-<span id="cb253-75"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-75" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
-<span id="cb253-76"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-76" tabindex="-1"></a></span>
-<span id="cb253-77"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-77" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
-<span id="cb253-78"><a href="4.2-the-gender-pay-gap-svygpg.html#cb253-78" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
+<div class="sourceCode" id="cb252"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb252-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb252-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb252-3"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-3" tabindex="-1"></a></span>
+<span id="cb252-4"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb252-5"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb252-6"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-6" tabindex="-1"></a></span>
+<span id="cb252-7"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb252-8"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
+<span id="cb252-9"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-9" tabindex="-1"></a></span>
+<span id="cb252-10"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-10" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
+<span id="cb252-11"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
+<span id="cb252-12"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-12" tabindex="-1"></a></span>
+<span id="cb252-13"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
+<span id="cb252-14"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
+<span id="cb252-15"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-15" tabindex="-1"></a></span>
+<span id="cb252-16"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
+<span id="cb252-17"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
+<span id="cb252-18"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-18" tabindex="-1"></a></span>
+<span id="cb252-19"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-19" tabindex="-1"></a><span class="co"># coerce the gender variable to numeric 1 or 2</span></span>
+<span id="cb252-20"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-20" tabindex="-1"></a>eusilc<span class="sc">$</span>one_two <span class="ot">&lt;-</span> <span class="fu">as.numeric</span>(eusilc<span class="sc">$</span>rb090 <span class="sc">==</span> <span class="st">&quot;female&quot;</span>) <span class="sc">+</span> <span class="dv">1</span></span>
+<span id="cb252-21"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-21" tabindex="-1"></a></span>
+<span id="cb252-22"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-22" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
+<span id="cb252-23"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-23" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
+<span id="cb252-24"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-24" tabindex="-1"></a></span>
+<span id="cb252-25"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-25" tabindex="-1"></a><span class="co"># calculate the gpg coefficient</span></span>
+<span id="cb252-26"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-26" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
+<span id="cb252-27"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-27" tabindex="-1"></a>varpoord_gpg_calculation <span class="ot">&lt;-</span></span>
+<span id="cb252-28"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-28" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
+<span id="cb252-29"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-29" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
+<span id="cb252-30"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-30" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
+<span id="cb252-31"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-31" tabindex="-1"></a>    </span>
+<span id="cb252-32"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-32" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
+<span id="cb252-33"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-33" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
+<span id="cb252-34"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-34" tabindex="-1"></a>    </span>
+<span id="cb252-35"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb252-36"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-36" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb252-37"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-37" tabindex="-1"></a>    </span>
+<span id="cb252-38"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-38" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb252-39"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-39" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb252-40"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-40" tabindex="-1"></a>    </span>
+<span id="cb252-41"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-41" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
+<span id="cb252-42"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-42" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
+<span id="cb252-43"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-43" tabindex="-1"></a>    </span>
+<span id="cb252-44"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-44" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
+<span id="cb252-45"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-45" tabindex="-1"></a>    </span>
+<span id="cb252-46"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-46" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
+<span id="cb252-47"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-47" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
+<span id="cb252-48"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-48" tabindex="-1"></a>    </span>
+<span id="cb252-49"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-49" tabindex="-1"></a>    <span class="co"># data.table</span></span>
+<span id="cb252-50"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-50" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
+<span id="cb252-51"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-51" tabindex="-1"></a>    </span>
+<span id="cb252-52"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-52" tabindex="-1"></a>    <span class="co"># gpg coefficient function</span></span>
+<span id="cb252-53"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-53" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;lingpg&quot;</span> ,</span>
+<span id="cb252-54"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-54" tabindex="-1"></a>    </span>
+<span id="cb252-55"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-55" tabindex="-1"></a>    <span class="co"># gender variable</span></span>
+<span id="cb252-56"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-56" tabindex="-1"></a>    <span class="at">gender =</span> <span class="st">&quot;one_two&quot;</span>,</span>
+<span id="cb252-57"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-57" tabindex="-1"></a>    </span>
+<span id="cb252-58"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-58" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
+<span id="cb252-59"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-59" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
+<span id="cb252-60"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-60" tabindex="-1"></a>  )</span>
+<span id="cb252-61"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-61" tabindex="-1"></a></span>
+<span id="cb252-62"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-62" tabindex="-1"></a></span>
+<span id="cb252-63"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-63" tabindex="-1"></a></span>
+<span id="cb252-64"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-64" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb252-65"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-65" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
+<span id="cb252-66"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-66" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
+<span id="cb252-67"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-67" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb252-68"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-68" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb252-69"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-69" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb252-70"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-70" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb252-71"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-71" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
+<span id="cb252-72"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-72" tabindex="-1"></a>  )</span>
+<span id="cb252-73"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-73" tabindex="-1"></a></span>
+<span id="cb252-74"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-74" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
+<span id="cb252-75"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-75" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
+<span id="cb252-76"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-76" tabindex="-1"></a></span>
+<span id="cb252-77"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-77" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
+<span id="cb252-78"><a href="4.2-the-gender-pay-gap-svygpg.html#cb252-78" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
 <pre><code>## [1] 7.645389</code></pre>
-<div class="sourceCode" id="cb255"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb255-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb255-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">sex =</span> <span class="sc">~</span> rb090)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb254"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb254-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb254-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">sex =</span> <span class="sc">~</span> rb090)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>##  eqincome 
 ## -8.278297</code></pre>
-<div class="sourceCode" id="cb257"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb257-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb257-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
-<span id="cb257-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb257-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
-<span id="cb257-3"><a href="4.2-the-gender-pay-gap-svygpg.html#cb257-3" tabindex="-1"></a>lin_gpg_varpoord <span class="ot">&lt;-</span> varpoord_gpg_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_gpg</span>
-<span id="cb257-4"><a href="4.2-the-gender-pay-gap-svygpg.html#cb257-4" tabindex="-1"></a><span class="co"># convey</span></span>
-<span id="cb257-5"><a href="4.2-the-gender-pay-gap-svygpg.html#cb257-5" tabindex="-1"></a>lin_gpg_convey <span class="ot">&lt;-</span></span>
-<span id="cb257-6"><a href="4.2-the-gender-pay-gap-svygpg.html#cb257-6" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc, <span class="at">sex =</span> <span class="sc">~</span> rb090), <span class="st">&quot;lin&quot;</span>)</span>
-<span id="cb257-7"><a href="4.2-the-gender-pay-gap-svygpg.html#cb257-7" tabindex="-1"></a></span>
-<span id="cb257-8"><a href="4.2-the-gender-pay-gap-svygpg.html#cb257-8" tabindex="-1"></a><span class="co"># check equality</span></span>
-<span id="cb257-9"><a href="4.2-the-gender-pay-gap-svygpg.html#cb257-9" tabindex="-1"></a><span class="fu">all.equal</span>(lin_gpg_varpoord, <span class="dv">100</span> <span class="sc">*</span> lin_gpg_convey[, <span class="dv">1</span>])</span></code></pre></div>
+<div class="sourceCode" id="cb256"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb256-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb256-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
+<span id="cb256-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb256-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
+<span id="cb256-3"><a href="4.2-the-gender-pay-gap-svygpg.html#cb256-3" tabindex="-1"></a>lin_gpg_varpoord <span class="ot">&lt;-</span> varpoord_gpg_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_gpg</span>
+<span id="cb256-4"><a href="4.2-the-gender-pay-gap-svygpg.html#cb256-4" tabindex="-1"></a><span class="co"># convey</span></span>
+<span id="cb256-5"><a href="4.2-the-gender-pay-gap-svygpg.html#cb256-5" tabindex="-1"></a>lin_gpg_convey <span class="ot">&lt;-</span></span>
+<span id="cb256-6"><a href="4.2-the-gender-pay-gap-svygpg.html#cb256-6" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc, <span class="at">sex =</span> <span class="sc">~</span> rb090), <span class="st">&quot;lin&quot;</span>)</span>
+<span id="cb256-7"><a href="4.2-the-gender-pay-gap-svygpg.html#cb256-7" tabindex="-1"></a></span>
+<span id="cb256-8"><a href="4.2-the-gender-pay-gap-svygpg.html#cb256-8" tabindex="-1"></a><span class="co"># check equality</span></span>
+<span id="cb256-9"><a href="4.2-the-gender-pay-gap-svygpg.html#cb256-9" tabindex="-1"></a><span class="fu">all.equal</span>(lin_gpg_varpoord, <span class="dv">100</span> <span class="sc">*</span> lin_gpg_convey[, <span class="dv">1</span>])</span></code></pre></div>
 <pre><code>## [1] &quot;Mean relative difference: 2.172419&quot;</code></pre>
-<div class="sourceCode" id="cb259"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb259-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb259-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
-<span id="cb259-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb259-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">sex =</span> <span class="sc">~</span> rb090) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
+<div class="sourceCode" id="cb258"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb258-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb258-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
+<span id="cb258-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb258-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">sex =</span> <span class="sc">~</span> rb090) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
 <pre><code>##           eqincome
 ## eqincome 0.8926311</code></pre>
-<div class="sourceCode" id="cb261"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb261-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb261-1" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb260"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb260-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb260-1" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.6482346</code></pre>
-<div class="sourceCode" id="cb263"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb263-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb263-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
-<span id="cb263-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb263-2" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb262"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb262-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb262-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
+<span id="cb262-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb262-2" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.8051301</code></pre>
-<div class="sourceCode" id="cb265"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb265-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb265-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">sex =</span> <span class="sc">~</span> rb090)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb264"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb264-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb264-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">sex =</span> <span class="sc">~</span> rb090)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>##           eqincome
 ## eqincome 0.9447916</code></pre>
 <p>The variance estimate is computed by using the approximation defined in <a href="2-var.html#var">2</a>, while the linearized variable <span class="math inline">\(z\)</span> is defined by <a href="2.1-lin.html#lin">2.1</a>. The functions <code>convey::svygpg</code> and <code>vardpoor::lingpg</code> produce the same linearized variable <span class="math inline">\(z\)</span>.</p>
 <p>However, the measures of uncertainty do not line up, because <code>library(vardpoor)</code> defaults to an ultimate cluster method that can be replicated with an alternative setup of the <code>survey.design</code> object.</p>
-<div class="sourceCode" id="cb267"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb267-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
-<span id="cb267-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
-<span id="cb267-3"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
-<span id="cb267-4"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-4" tabindex="-1"></a></span>
-<span id="cb267-5"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
-<span id="cb267-6"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
-<span id="cb267-7"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-7" tabindex="-1"></a></span>
-<span id="cb267-8"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
-<span id="cb267-9"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
-<span id="cb267-10"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-10" tabindex="-1"></a></span>
-<span id="cb267-11"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb267-12"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
-<span id="cb267-13"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb267-14"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb267-15"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb267-16"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb267-17"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb267-18"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
-<span id="cb267-19"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
-<span id="cb267-20"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-20" tabindex="-1"></a>  )</span>
-<span id="cb267-21"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-21" tabindex="-1"></a></span>
-<span id="cb267-22"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
-<span id="cb267-23"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb267-24"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
-<span id="cb267-25"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-25" tabindex="-1"></a></span>
-<span id="cb267-26"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-26" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb267-27"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-27" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster , <span class="at">sex =</span> <span class="sc">~</span> rb090) ,</span>
-<span id="cb267-28"><a href="4.2-the-gender-pay-gap-svygpg.html#cb267-28" tabindex="-1"></a>     <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
+<div class="sourceCode" id="cb266"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb266-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
+<span id="cb266-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
+<span id="cb266-3"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
+<span id="cb266-4"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-4" tabindex="-1"></a></span>
+<span id="cb266-5"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
+<span id="cb266-6"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
+<span id="cb266-7"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-7" tabindex="-1"></a></span>
+<span id="cb266-8"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
+<span id="cb266-9"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
+<span id="cb266-10"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-10" tabindex="-1"></a></span>
+<span id="cb266-11"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb266-12"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
+<span id="cb266-13"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb266-14"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb266-15"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb266-16"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb266-17"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb266-18"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
+<span id="cb266-19"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
+<span id="cb266-20"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-20" tabindex="-1"></a>  )</span>
+<span id="cb266-21"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-21" tabindex="-1"></a></span>
+<span id="cb266-22"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
+<span id="cb266-23"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb266-24"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
+<span id="cb266-25"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-25" tabindex="-1"></a></span>
+<span id="cb266-26"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-26" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb266-27"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-27" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster , <span class="at">sex =</span> <span class="sc">~</span> rb090) ,</span>
+<span id="cb266-28"><a href="4.2-the-gender-pay-gap-svygpg.html#cb266-28" tabindex="-1"></a>     <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
 <pre><code>##           eqincome
 ## eqincome 0.8910413</code></pre>
-<div class="sourceCode" id="cb269"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb269-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb269-1" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb268"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb268-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb268-1" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.6482346</code></pre>
-<div class="sourceCode" id="cb271"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb271-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb271-1" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb271-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb271-2" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb270"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb270-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb270-1" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb270-2"><a href="4.2-the-gender-pay-gap-svygpg.html#cb270-2" tabindex="-1"></a>varpoord_gpg_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.8051301</code></pre>
-<div class="sourceCode" id="cb273"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb273-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb273-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster , <span class="at">sex =</span> <span class="sc">~</span> rb090)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb272"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb272-1"><a href="4.2-the-gender-pay-gap-svygpg.html#cb272-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svygpg</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster , <span class="at">sex =</span> <span class="sc">~</span> rb090)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>##           eqincome
 ## eqincome 0.9439499</code></pre>
 <p>For additional usage examples of <code>svygpg</code>, type <code>?convey::svygpg</code> in the R console.</p>
diff --git a/docs/4.3-quintile-share-ratio-svyqsr.html b/docs/4.3-quintile-share-ratio-svyqsr.html
index 6208476..fa31d5f 100644
--- a/docs/4.3-quintile-share-ratio-svyqsr.html
+++ b/docs/4.3-quintile-share-ratio-svyqsr.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,11 +253,11 @@
 <div class="col-sm-12">
 <div id="quintile-share-ratio-svyqsr" class="section level2" number="4.3">
 <h2><span class="header-section-number">4.3</span> Quintile Share Ratio (svyqsr)</h2>
-<div class="sourceCode" id="cb275"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb275-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-1" tabindex="-1"></a>✔️ Easy to understand</span>
-<span id="cb275-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-2" tabindex="-1"></a>✔️ Can be adapted into other more commonly used variants, like the Palma ratio</span>
-<span id="cb275-3"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-3" tabindex="-1"></a>✔️ Can be interpreted using a Lorenz curve</span>
-<span id="cb275-4"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-4" tabindex="-1"></a>❌ Fails the Pigou<span class="sc">-</span>Dalton <span class="fu">Principle</span> (depending on the donor and recipient position <span class="cf">in</span> the income distribution)</span>
-<span id="cb275-5"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-5" tabindex="-1"></a>❌ Focuses on specific parts of the income  distribution, not the entire distribution</span></code></pre></div>
+<div class="sourceCode" id="cb274"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb274-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb274-1" tabindex="-1"></a>✔️ Easy to understand</span>
+<span id="cb274-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb274-2" tabindex="-1"></a>✔️ Can be adapted into other more commonly used variants, like the Palma ratio</span>
+<span id="cb274-3"><a href="4.3-quintile-share-ratio-svyqsr.html#cb274-3" tabindex="-1"></a>✔️ Can be interpreted using a Lorenz curve</span>
+<span id="cb274-4"><a href="4.3-quintile-share-ratio-svyqsr.html#cb274-4" tabindex="-1"></a>❌ Fails the Pigou<span class="sc">-</span>Dalton <span class="fu">Principle</span> (depending on the donor and recipient position <span class="cf">in</span> the income distribution)</span>
+<span id="cb274-5"><a href="4.3-quintile-share-ratio-svyqsr.html#cb274-5" tabindex="-1"></a>❌ Focuses on specific parts of the income  distribution, not the entire distribution</span></code></pre></div>
 <p>Unlike the previous measure, the Quintile Share Ratio (QSR) is an inequality measure in itself, depending only on the income distribution to evaluate the degree of inequality. By definition, it can be described as the ratio between the income share held by the richest 20% and the poorest 20% of the population.</p>
 <p>In plain terms, it expresses how many times the wealthier part of the population are richer than the poorest part. For instance, a <span class="math inline">\(QSR = 4\)</span> implies that the upper class takes home 4 times as much of the total income as the poor.</p>
 <p>The QSR can be modified to a more general function of percentile share ratios. For instance, <span class="citation">Cobham, Schlogl, and Sumner (<label for="tufte-mn-65" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-65" class="margin-toggle">2015<span class="marginnote">Cobham, Alex, Luke Schlogl, and Andy Sumner. 2015. <span>“<span class="nocase">Inequality and the Tails: The Palma Proposition and Ratio Revisited</span>.”</span> Working Papers 143. United Nations, Department of Economics; Social Affairs. <a href="http://www.un.org/esa/desa/papers/2015/wp143_2015.pdf">http://www.un.org/esa/desa/papers/2015/wp143_2015.pdf</a>.</span>)</span> argues for using the Palma index, defined as the ratio between the share of the 10% richest over the share held by the poorest 40%. There are actually two ways to compute the Palma ratio with the <code>convey</code> package. One is using <code>convey::svyqsr</code> and the other is using <code>convey::svylorenz</code> - they won’t match exactly because of different estimators, but are asymptotically equal. Since the Palma ratio is the top 10% divided by the bottom 40%, in <code>convey::svyqsr</code> this could be achieved using <code>alpha1 = .40</code> and <code>alpha2 = .90</code>. Note that the <code>vardpoor::linqsr</code> function only accepts a single <code>alpha</code> parameter (defaulting to <code>0.2</code> and <code>1 - 0.2</code>), meaning the Palma index cannot presently be computed using that function.</p>
@@ -267,148 +267,148 @@ <h2><span class="header-section-number">4.3</span> Quintile Share Ratio (svyqsr)
 <h3><span class="header-section-number">4.3.1</span> Replication Example</h3>
 <p>The R <code>vardpoor</code> package <span class="citation">(<label for="tufte-mn-68" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-68" class="margin-toggle">Breidaks, Liberts, and Ivanova 2016<span class="marginnote">Breidaks, Juris, Martins Liberts, and Santa Ivanova. 2016. <span>“Vardpoor: Estimation of Indicators on Social Exclusion and Poverty and Its Linearization, Variance Estimation.”</span> Riga, Latvia: CSB.</span>)</span>, created by researchers at the Central Statistical Bureau of Latvia, includes a QSR coefficient calculation using the ultimate cluster method. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb276"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb276-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb276-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb276-3"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-3" tabindex="-1"></a></span>
-<span id="cb276-4"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb276-5"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb276-6"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-6" tabindex="-1"></a></span>
-<span id="cb276-7"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb276-8"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
-<span id="cb276-9"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-9" tabindex="-1"></a></span>
-<span id="cb276-10"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-10" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
-<span id="cb276-11"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
-<span id="cb276-12"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-12" tabindex="-1"></a></span>
-<span id="cb276-13"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
-<span id="cb276-14"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
-<span id="cb276-15"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-15" tabindex="-1"></a></span>
-<span id="cb276-16"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
-<span id="cb276-17"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
-<span id="cb276-18"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-18" tabindex="-1"></a></span>
-<span id="cb276-19"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
-<span id="cb276-20"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
-<span id="cb276-21"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-21" tabindex="-1"></a></span>
-<span id="cb276-22"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-22" tabindex="-1"></a><span class="co"># calculate the qsr coefficient</span></span>
-<span id="cb276-23"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
-<span id="cb276-24"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-24" tabindex="-1"></a>varpoord_qsr_calculation <span class="ot">&lt;-</span></span>
-<span id="cb276-25"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
-<span id="cb276-26"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
-<span id="cb276-27"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
-<span id="cb276-28"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-28" tabindex="-1"></a>    </span>
-<span id="cb276-29"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
-<span id="cb276-30"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
-<span id="cb276-31"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-31" tabindex="-1"></a>    </span>
-<span id="cb276-32"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb276-33"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb276-34"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-34" tabindex="-1"></a>    </span>
-<span id="cb276-35"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb276-36"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb276-37"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-37" tabindex="-1"></a>    </span>
-<span id="cb276-38"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
-<span id="cb276-39"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
-<span id="cb276-40"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-40" tabindex="-1"></a>    </span>
-<span id="cb276-41"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
-<span id="cb276-42"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-42" tabindex="-1"></a>    </span>
-<span id="cb276-43"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
-<span id="cb276-44"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
-<span id="cb276-45"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-45" tabindex="-1"></a>    </span>
-<span id="cb276-46"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
-<span id="cb276-47"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
-<span id="cb276-48"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-48" tabindex="-1"></a>    </span>
-<span id="cb276-49"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-49" tabindex="-1"></a>    <span class="co"># qsr coefficient function</span></span>
-<span id="cb276-50"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linqsr&quot;</span>,</span>
-<span id="cb276-51"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-51" tabindex="-1"></a>    </span>
-<span id="cb276-52"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-52" tabindex="-1"></a>    <span class="co"># poverty threshold range</span></span>
-<span id="cb276-53"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-53" tabindex="-1"></a>    <span class="at">alpha =</span> <span class="dv">20</span> ,</span>
-<span id="cb276-54"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-54" tabindex="-1"></a>    </span>
-<span id="cb276-55"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-55" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
-<span id="cb276-56"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-56" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
-<span id="cb276-57"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-57" tabindex="-1"></a>    </span>
-<span id="cb276-58"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-58" tabindex="-1"></a>  )</span>
-<span id="cb276-59"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-59" tabindex="-1"></a></span>
-<span id="cb276-60"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-60" tabindex="-1"></a></span>
-<span id="cb276-61"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-61" tabindex="-1"></a></span>
-<span id="cb276-62"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-62" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb276-63"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-63" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
-<span id="cb276-64"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-64" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
-<span id="cb276-65"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-65" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb276-66"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-66" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb276-67"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-67" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb276-68"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-68" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb276-69"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-69" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
-<span id="cb276-70"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-70" tabindex="-1"></a>  )</span>
-<span id="cb276-71"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-71" tabindex="-1"></a></span>
-<span id="cb276-72"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-72" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
-<span id="cb276-73"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-73" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
-<span id="cb276-74"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-74" tabindex="-1"></a></span>
-<span id="cb276-75"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-75" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
-<span id="cb276-76"><a href="4.3-quintile-share-ratio-svyqsr.html#cb276-76" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
+<div class="sourceCode" id="cb275"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb275-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb275-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb275-3"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-3" tabindex="-1"></a></span>
+<span id="cb275-4"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb275-5"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb275-6"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-6" tabindex="-1"></a></span>
+<span id="cb275-7"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb275-8"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
+<span id="cb275-9"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-9" tabindex="-1"></a></span>
+<span id="cb275-10"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-10" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
+<span id="cb275-11"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
+<span id="cb275-12"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-12" tabindex="-1"></a></span>
+<span id="cb275-13"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
+<span id="cb275-14"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
+<span id="cb275-15"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-15" tabindex="-1"></a></span>
+<span id="cb275-16"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
+<span id="cb275-17"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
+<span id="cb275-18"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-18" tabindex="-1"></a></span>
+<span id="cb275-19"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
+<span id="cb275-20"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
+<span id="cb275-21"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-21" tabindex="-1"></a></span>
+<span id="cb275-22"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-22" tabindex="-1"></a><span class="co"># calculate the qsr coefficient</span></span>
+<span id="cb275-23"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
+<span id="cb275-24"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-24" tabindex="-1"></a>varpoord_qsr_calculation <span class="ot">&lt;-</span></span>
+<span id="cb275-25"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
+<span id="cb275-26"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
+<span id="cb275-27"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
+<span id="cb275-28"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-28" tabindex="-1"></a>    </span>
+<span id="cb275-29"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
+<span id="cb275-30"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
+<span id="cb275-31"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-31" tabindex="-1"></a>    </span>
+<span id="cb275-32"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb275-33"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb275-34"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-34" tabindex="-1"></a>    </span>
+<span id="cb275-35"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb275-36"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb275-37"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-37" tabindex="-1"></a>    </span>
+<span id="cb275-38"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
+<span id="cb275-39"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
+<span id="cb275-40"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-40" tabindex="-1"></a>    </span>
+<span id="cb275-41"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
+<span id="cb275-42"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-42" tabindex="-1"></a>    </span>
+<span id="cb275-43"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
+<span id="cb275-44"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
+<span id="cb275-45"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-45" tabindex="-1"></a>    </span>
+<span id="cb275-46"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
+<span id="cb275-47"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
+<span id="cb275-48"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-48" tabindex="-1"></a>    </span>
+<span id="cb275-49"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-49" tabindex="-1"></a>    <span class="co"># qsr coefficient function</span></span>
+<span id="cb275-50"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;linqsr&quot;</span>,</span>
+<span id="cb275-51"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-51" tabindex="-1"></a>    </span>
+<span id="cb275-52"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-52" tabindex="-1"></a>    <span class="co"># poverty threshold range</span></span>
+<span id="cb275-53"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-53" tabindex="-1"></a>    <span class="at">alpha =</span> <span class="dv">20</span> ,</span>
+<span id="cb275-54"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-54" tabindex="-1"></a>    </span>
+<span id="cb275-55"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-55" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
+<span id="cb275-56"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-56" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
+<span id="cb275-57"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-57" tabindex="-1"></a>    </span>
+<span id="cb275-58"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-58" tabindex="-1"></a>  )</span>
+<span id="cb275-59"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-59" tabindex="-1"></a></span>
+<span id="cb275-60"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-60" tabindex="-1"></a></span>
+<span id="cb275-61"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-61" tabindex="-1"></a></span>
+<span id="cb275-62"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-62" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb275-63"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-63" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
+<span id="cb275-64"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-64" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
+<span id="cb275-65"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-65" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb275-66"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-66" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb275-67"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-67" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb275-68"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-68" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb275-69"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-69" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
+<span id="cb275-70"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-70" tabindex="-1"></a>  )</span>
+<span id="cb275-71"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-71" tabindex="-1"></a></span>
+<span id="cb275-72"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-72" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
+<span id="cb275-73"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-73" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
+<span id="cb275-74"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-74" tabindex="-1"></a></span>
+<span id="cb275-75"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-75" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
+<span id="cb275-76"><a href="4.3-quintile-share-ratio-svyqsr.html#cb275-76" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
 <pre><code>## [1] 3.970004</code></pre>
-<div class="sourceCode" id="cb278"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb278-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb278-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
+<div class="sourceCode" id="cb277"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb277-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb277-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
 <pre><code>## eqincome 
 ## 3.970004</code></pre>
-<div class="sourceCode" id="cb280"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb280-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
-<span id="cb280-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
-<span id="cb280-3"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-3" tabindex="-1"></a>lin_qsr_varpoord <span class="ot">&lt;-</span> varpoord_qsr_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_qsr</span>
-<span id="cb280-4"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-4" tabindex="-1"></a><span class="co"># convey</span></span>
-<span id="cb280-5"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-5" tabindex="-1"></a>lin_qsr_convey <span class="ot">&lt;-</span></span>
-<span id="cb280-6"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-6" tabindex="-1"></a>  <span class="fu">as.numeric</span>(<span class="fu">attr</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome ,</span>
-<span id="cb280-7"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-7" tabindex="-1"></a>                          des_eusilc ,</span>
-<span id="cb280-8"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-8" tabindex="-1"></a>                          <span class="at">linearized =</span> <span class="cn">TRUE</span>) ,</span>
-<span id="cb280-9"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-9" tabindex="-1"></a>                  <span class="st">&quot;linearized&quot;</span>))</span>
-<span id="cb280-10"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-10" tabindex="-1"></a></span>
-<span id="cb280-11"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-11" tabindex="-1"></a><span class="co"># check equality</span></span>
-<span id="cb280-12"><a href="4.3-quintile-share-ratio-svyqsr.html#cb280-12" tabindex="-1"></a><span class="fu">all.equal</span>(lin_qsr_varpoord, lin_qsr_convey)</span></code></pre></div>
+<div class="sourceCode" id="cb279"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb279-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
+<span id="cb279-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-2" tabindex="-1"></a><span class="co"># vardpoor</span></span>
+<span id="cb279-3"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-3" tabindex="-1"></a>lin_qsr_varpoord <span class="ot">&lt;-</span> varpoord_qsr_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_qsr</span>
+<span id="cb279-4"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-4" tabindex="-1"></a><span class="co"># convey</span></span>
+<span id="cb279-5"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-5" tabindex="-1"></a>lin_qsr_convey <span class="ot">&lt;-</span></span>
+<span id="cb279-6"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-6" tabindex="-1"></a>  <span class="fu">as.numeric</span>(<span class="fu">attr</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome ,</span>
+<span id="cb279-7"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-7" tabindex="-1"></a>                          des_eusilc ,</span>
+<span id="cb279-8"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-8" tabindex="-1"></a>                          <span class="at">linearized =</span> <span class="cn">TRUE</span>) ,</span>
+<span id="cb279-9"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-9" tabindex="-1"></a>                  <span class="st">&quot;linearized&quot;</span>))</span>
+<span id="cb279-10"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-10" tabindex="-1"></a></span>
+<span id="cb279-11"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-11" tabindex="-1"></a><span class="co"># check equality</span></span>
+<span id="cb279-12"><a href="4.3-quintile-share-ratio-svyqsr.html#cb279-12" tabindex="-1"></a><span class="fu">all.equal</span>(lin_qsr_varpoord, lin_qsr_convey)</span></code></pre></div>
 <pre><code>## [1] TRUE</code></pre>
-<div class="sourceCode" id="cb282"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb282-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb282-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
-<span id="cb282-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb282-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb281"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb281-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb281-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
+<span id="cb281-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb281-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
 <pre><code>##             eqincome
 ## eqincome 0.001810537</code></pre>
-<div class="sourceCode" id="cb284"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb284-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb284-1" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb283"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb283-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb283-1" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.001807323</code></pre>
-<div class="sourceCode" id="cb286"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb286-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb286-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
-<span id="cb286-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb286-2" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb285"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb285-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb285-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
+<span id="cb285-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb285-2" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.04251263</code></pre>
-<div class="sourceCode" id="cb288"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb288-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb288-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
+<div class="sourceCode" id="cb287"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb287-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb287-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc))</span></code></pre></div>
 <pre><code>##            eqincome
 ## eqincome 0.04255041</code></pre>
 <p>The variance estimate is computed by using the approximation defined in <a href="2-var.html#var">2</a>, while the linearized variable <span class="math inline">\(z\)</span> is defined by <a href="2.1-lin.html#lin">2.1</a>. The functions <code>convey::svyqsr</code> and <code>vardpoor::linqsr</code> produce the same linearized variable <span class="math inline">\(z\)</span>.</p>
 <p>However, the measures of uncertainty do not line up, because <code>library(vardpoor)</code> defaults to an ultimate cluster method that can be replicated with an alternative setup of the <code>survey.design</code> object.</p>
-<div class="sourceCode" id="cb290"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb290-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
-<span id="cb290-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
-<span id="cb290-3"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
-<span id="cb290-4"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-4" tabindex="-1"></a></span>
-<span id="cb290-5"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
-<span id="cb290-6"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
-<span id="cb290-7"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-7" tabindex="-1"></a></span>
-<span id="cb290-8"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
-<span id="cb290-9"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
-<span id="cb290-10"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-10" tabindex="-1"></a></span>
-<span id="cb290-11"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb290-12"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
-<span id="cb290-13"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb290-14"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb290-15"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb290-16"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb290-17"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb290-18"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
-<span id="cb290-19"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
-<span id="cb290-20"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-20" tabindex="-1"></a>  )</span>
-<span id="cb290-21"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-21" tabindex="-1"></a></span>
-<span id="cb290-22"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
-<span id="cb290-23"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb290-24"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
-<span id="cb290-25"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-25" tabindex="-1"></a></span>
-<span id="cb290-26"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-26" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb290-27"><a href="4.3-quintile-share-ratio-svyqsr.html#cb290-27" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb289"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb289-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
+<span id="cb289-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
+<span id="cb289-3"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
+<span id="cb289-4"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-4" tabindex="-1"></a></span>
+<span id="cb289-5"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
+<span id="cb289-6"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
+<span id="cb289-7"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-7" tabindex="-1"></a></span>
+<span id="cb289-8"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
+<span id="cb289-9"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
+<span id="cb289-10"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-10" tabindex="-1"></a></span>
+<span id="cb289-11"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb289-12"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
+<span id="cb289-13"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb289-14"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb289-15"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb289-16"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb289-17"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb289-18"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
+<span id="cb289-19"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
+<span id="cb289-20"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-20" tabindex="-1"></a>  )</span>
+<span id="cb289-21"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-21" tabindex="-1"></a></span>
+<span id="cb289-22"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
+<span id="cb289-23"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb289-24"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
+<span id="cb289-25"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-25" tabindex="-1"></a></span>
+<span id="cb289-26"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-26" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb289-27"><a href="4.3-quintile-share-ratio-svyqsr.html#cb289-27" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>)</span></code></pre></div>
 <pre><code>##             eqincome
 ## eqincome 0.001807323</code></pre>
-<div class="sourceCode" id="cb292"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb292-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb292-1" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb291"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb291-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb291-1" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.001807323</code></pre>
-<div class="sourceCode" id="cb294"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb294-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb294-1" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb294-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb294-2" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb293"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb293-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb293-1" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb293-2"><a href="4.3-quintile-share-ratio-svyqsr.html#cb293-2" tabindex="-1"></a>varpoord_qsr_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.04251263</code></pre>
-<div class="sourceCode" id="cb296"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb296-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb296-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster))</span></code></pre></div>
+<div class="sourceCode" id="cb295"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb295-1"><a href="4.3-quintile-share-ratio-svyqsr.html#cb295-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svyqsr</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster))</span></code></pre></div>
 <pre><code>##            eqincome
 ## eqincome 0.04251263</code></pre>
 <p>For additional usage examples of <code>svyqsr</code>, type <code>?convey::svyqsr</code> in the R console.</p>
diff --git a/docs/4.4-lorenz-curve-based-measures.html b/docs/4.4-lorenz-curve-based-measures.html
index feaecd1..9cf3791 100644
--- a/docs/4.4-lorenz-curve-based-measures.html
+++ b/docs/4.4-lorenz-curve-based-measures.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
diff --git a/docs/4.5-lorenz-curve-svylorenz.html b/docs/4.5-lorenz-curve-svylorenz.html
index 38c9af0..5a33e0d 100644
--- a/docs/4.5-lorenz-curve-svylorenz.html
+++ b/docs/4.5-lorenz-curve-svylorenz.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,13 +253,13 @@
 <div class="col-sm-12">
 <div id="lorenz-curve-svylorenz" class="section level2" number="4.5">
 <h2><span class="header-section-number">4.5</span> Lorenz Curve (svylorenz)</h2>
-<div class="sourceCode" id="cb298"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb298-1"><a href="4.5-lorenz-curve-svylorenz.html#cb298-1" tabindex="-1"></a>✔️ graphical device <span class="cf">for</span> understanding inequality measurement</span>
-<span id="cb298-2"><a href="4.5-lorenz-curve-svylorenz.html#cb298-2" tabindex="-1"></a>✔️ simple to understand</span>
-<span id="cb298-3"><a href="4.5-lorenz-curve-svylorenz.html#cb298-3" tabindex="-1"></a>✔️ conveys information about inequality across the entire income distribution</span>
-<span id="cb298-4"><a href="4.5-lorenz-curve-svylorenz.html#cb298-4" tabindex="-1"></a>✔️ Lorenz dominance and inequality measure ordering</span>
-<span id="cb298-5"><a href="4.5-lorenz-curve-svylorenz.html#cb298-5" tabindex="-1"></a>❌ testing Lorenz dominance is difficult</span>
-<span id="cb298-6"><a href="4.5-lorenz-curve-svylorenz.html#cb298-6" tabindex="-1"></a>❌ can hide inequality <span class="cf">in</span> the top or bottom</span>
-<span id="cb298-7"><a href="4.5-lorenz-curve-svylorenz.html#cb298-7" tabindex="-1"></a>❌ cannot be summarised into a single number</span></code></pre></div>
+<div class="sourceCode" id="cb297"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb297-1"><a href="4.5-lorenz-curve-svylorenz.html#cb297-1" tabindex="-1"></a>✔️ graphical device <span class="cf">for</span> understanding inequality measurement</span>
+<span id="cb297-2"><a href="4.5-lorenz-curve-svylorenz.html#cb297-2" tabindex="-1"></a>✔️ simple to understand</span>
+<span id="cb297-3"><a href="4.5-lorenz-curve-svylorenz.html#cb297-3" tabindex="-1"></a>✔️ conveys information about inequality across the entire income distribution</span>
+<span id="cb297-4"><a href="4.5-lorenz-curve-svylorenz.html#cb297-4" tabindex="-1"></a>✔️ Lorenz dominance and inequality measure ordering</span>
+<span id="cb297-5"><a href="4.5-lorenz-curve-svylorenz.html#cb297-5" tabindex="-1"></a>❌ testing Lorenz dominance is difficult</span>
+<span id="cb297-6"><a href="4.5-lorenz-curve-svylorenz.html#cb297-6" tabindex="-1"></a>❌ can hide inequality <span class="cf">in</span> the top or bottom</span>
+<span id="cb297-7"><a href="4.5-lorenz-curve-svylorenz.html#cb297-7" tabindex="-1"></a>❌ cannot be summarised into a single number</span></code></pre></div>
 <p>Though not an inequality measure in itself, the Lorenz curve is a classic instrument of distribution analysis. This function associates a cumulative share of the population to the share of the total income earned. In mathematical terms,</p>
 <p><span class="math display">\[
 L(p) = \frac{\int_{-\infty}^{Q_p}yf(y)dy}{\int_{-\infty}^{+\infty}yf(y)dy}
@@ -296,57 +296,57 @@ <h2><span class="header-section-number">4.5</span> Lorenz Curve (svylorenz)</h2>
 <div id="replication-example-8" class="section level3" number="4.5.1">
 <h3><span class="header-section-number">4.5.1</span> Replication Example</h3>
 <p>In October 2016, <span class="citation">(<label for="tufte-mn-71" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-71" class="margin-toggle">Jann 2016<span class="marginnote">Jann, Ben. 2016. <span>“<span class="nocase">Estimating Lorenz and concentration curves in Stata</span>.”</span> University of Bern Social Sciences Working Papers 15. University of Bern, Department of Social Sciences. <a href="https://ideas.repec.org/p/bss/wpaper/15.html">https://ideas.repec.org/p/bss/wpaper/15.html</a>.</span>)</span> released a pre-publication working paper to estimate Lorenz and concentration curves using stata. The example below reproduces the statistics presented in his section 4.1.</p>
-<div class="sourceCode" id="cb299"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb299-1"><a href="4.5-lorenz-curve-svylorenz.html#cb299-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb299-2"><a href="4.5-lorenz-curve-svylorenz.html#cb299-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb299-3"><a href="4.5-lorenz-curve-svylorenz.html#cb299-3" tabindex="-1"></a></span>
-<span id="cb299-4"><a href="4.5-lorenz-curve-svylorenz.html#cb299-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb299-5"><a href="4.5-lorenz-curve-svylorenz.html#cb299-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb299-6"><a href="4.5-lorenz-curve-svylorenz.html#cb299-6" tabindex="-1"></a></span>
-<span id="cb299-7"><a href="4.5-lorenz-curve-svylorenz.html#cb299-7" tabindex="-1"></a><span class="co"># load the stata-style webuse library</span></span>
-<span id="cb299-8"><a href="4.5-lorenz-curve-svylorenz.html#cb299-8" tabindex="-1"></a><span class="fu">library</span>(webuse)</span>
-<span id="cb299-9"><a href="4.5-lorenz-curve-svylorenz.html#cb299-9" tabindex="-1"></a></span>
-<span id="cb299-10"><a href="4.5-lorenz-curve-svylorenz.html#cb299-10" tabindex="-1"></a><span class="co"># load the NLSW 1988 data</span></span>
-<span id="cb299-11"><a href="4.5-lorenz-curve-svylorenz.html#cb299-11" tabindex="-1"></a><span class="fu">webuse</span>(<span class="st">&quot;nlsw88&quot;</span>)</span>
-<span id="cb299-12"><a href="4.5-lorenz-curve-svylorenz.html#cb299-12" tabindex="-1"></a></span>
-<span id="cb299-13"><a href="4.5-lorenz-curve-svylorenz.html#cb299-13" tabindex="-1"></a><span class="co"># coerce that `tbl_df` to a standard R `data.frame`</span></span>
-<span id="cb299-14"><a href="4.5-lorenz-curve-svylorenz.html#cb299-14" tabindex="-1"></a>nlsw88 <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(nlsw88)</span>
-<span id="cb299-15"><a href="4.5-lorenz-curve-svylorenz.html#cb299-15" tabindex="-1"></a></span>
-<span id="cb299-16"><a href="4.5-lorenz-curve-svylorenz.html#cb299-16" tabindex="-1"></a><span class="co"># initiate a linearized survey design object</span></span>
-<span id="cb299-17"><a href="4.5-lorenz-curve-svylorenz.html#cb299-17" tabindex="-1"></a>des_nlsw88 <span class="ot">&lt;-</span> <span class="fu">svydesign</span>(<span class="at">ids =</span> <span class="sc">~</span> <span class="dv">1</span> , <span class="at">data =</span> nlsw88)</span></code></pre></div>
+<div class="sourceCode" id="cb298"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb298-1"><a href="4.5-lorenz-curve-svylorenz.html#cb298-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb298-2"><a href="4.5-lorenz-curve-svylorenz.html#cb298-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb298-3"><a href="4.5-lorenz-curve-svylorenz.html#cb298-3" tabindex="-1"></a></span>
+<span id="cb298-4"><a href="4.5-lorenz-curve-svylorenz.html#cb298-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb298-5"><a href="4.5-lorenz-curve-svylorenz.html#cb298-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb298-6"><a href="4.5-lorenz-curve-svylorenz.html#cb298-6" tabindex="-1"></a></span>
+<span id="cb298-7"><a href="4.5-lorenz-curve-svylorenz.html#cb298-7" tabindex="-1"></a><span class="co"># load the stata-style webuse library</span></span>
+<span id="cb298-8"><a href="4.5-lorenz-curve-svylorenz.html#cb298-8" tabindex="-1"></a><span class="fu">library</span>(webuse)</span>
+<span id="cb298-9"><a href="4.5-lorenz-curve-svylorenz.html#cb298-9" tabindex="-1"></a></span>
+<span id="cb298-10"><a href="4.5-lorenz-curve-svylorenz.html#cb298-10" tabindex="-1"></a><span class="co"># load the NLSW 1988 data</span></span>
+<span id="cb298-11"><a href="4.5-lorenz-curve-svylorenz.html#cb298-11" tabindex="-1"></a><span class="fu">webuse</span>(<span class="st">&quot;nlsw88&quot;</span>)</span>
+<span id="cb298-12"><a href="4.5-lorenz-curve-svylorenz.html#cb298-12" tabindex="-1"></a></span>
+<span id="cb298-13"><a href="4.5-lorenz-curve-svylorenz.html#cb298-13" tabindex="-1"></a><span class="co"># coerce that `tbl_df` to a standard R `data.frame`</span></span>
+<span id="cb298-14"><a href="4.5-lorenz-curve-svylorenz.html#cb298-14" tabindex="-1"></a>nlsw88 <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(nlsw88)</span>
+<span id="cb298-15"><a href="4.5-lorenz-curve-svylorenz.html#cb298-15" tabindex="-1"></a></span>
+<span id="cb298-16"><a href="4.5-lorenz-curve-svylorenz.html#cb298-16" tabindex="-1"></a><span class="co"># initiate a linearized survey design object</span></span>
+<span id="cb298-17"><a href="4.5-lorenz-curve-svylorenz.html#cb298-17" tabindex="-1"></a>des_nlsw88 <span class="ot">&lt;-</span> <span class="fu">svydesign</span>(<span class="at">ids =</span> <span class="sc">~</span> <span class="dv">1</span> , <span class="at">data =</span> nlsw88)</span></code></pre></div>
 <pre><code>## Warning in svydesign.default(ids = ~1, data = nlsw88): No weights or
 ## probabilities supplied, assuming equal probability</code></pre>
-<div class="sourceCode" id="cb301"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb301-1"><a href="4.5-lorenz-curve-svylorenz.html#cb301-1" tabindex="-1"></a><span class="co"># immediately run the `convey_prep` function on the survey design</span></span>
-<span id="cb301-2"><a href="4.5-lorenz-curve-svylorenz.html#cb301-2" tabindex="-1"></a>des_nlsw88 <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_nlsw88)</span>
-<span id="cb301-3"><a href="4.5-lorenz-curve-svylorenz.html#cb301-3" tabindex="-1"></a></span>
-<span id="cb301-4"><a href="4.5-lorenz-curve-svylorenz.html#cb301-4" tabindex="-1"></a><span class="co"># estimates lorenz curve</span></span>
-<span id="cb301-5"><a href="4.5-lorenz-curve-svylorenz.html#cb301-5" tabindex="-1"></a>result.lin <span class="ot">&lt;-</span></span>
-<span id="cb301-6"><a href="4.5-lorenz-curve-svylorenz.html#cb301-6" tabindex="-1"></a>  <span class="fu">svylorenz</span>( <span class="sc">~</span> wage,</span>
-<span id="cb301-7"><a href="4.5-lorenz-curve-svylorenz.html#cb301-7" tabindex="-1"></a>             des_nlsw88,</span>
-<span id="cb301-8"><a href="4.5-lorenz-curve-svylorenz.html#cb301-8" tabindex="-1"></a>             <span class="at">quantiles =</span> <span class="fu">seq</span>(<span class="dv">0</span>, <span class="dv">1</span>, .<span class="dv">05</span>),</span>
-<span id="cb301-9"><a href="4.5-lorenz-curve-svylorenz.html#cb301-9" tabindex="-1"></a>             <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb300"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb300-1"><a href="4.5-lorenz-curve-svylorenz.html#cb300-1" tabindex="-1"></a><span class="co"># immediately run the `convey_prep` function on the survey design</span></span>
+<span id="cb300-2"><a href="4.5-lorenz-curve-svylorenz.html#cb300-2" tabindex="-1"></a>des_nlsw88 <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_nlsw88)</span>
+<span id="cb300-3"><a href="4.5-lorenz-curve-svylorenz.html#cb300-3" tabindex="-1"></a></span>
+<span id="cb300-4"><a href="4.5-lorenz-curve-svylorenz.html#cb300-4" tabindex="-1"></a><span class="co"># estimates lorenz curve</span></span>
+<span id="cb300-5"><a href="4.5-lorenz-curve-svylorenz.html#cb300-5" tabindex="-1"></a>result.lin <span class="ot">&lt;-</span></span>
+<span id="cb300-6"><a href="4.5-lorenz-curve-svylorenz.html#cb300-6" tabindex="-1"></a>  <span class="fu">svylorenz</span>( <span class="sc">~</span> wage,</span>
+<span id="cb300-7"><a href="4.5-lorenz-curve-svylorenz.html#cb300-7" tabindex="-1"></a>             des_nlsw88,</span>
+<span id="cb300-8"><a href="4.5-lorenz-curve-svylorenz.html#cb300-8" tabindex="-1"></a>             <span class="at">quantiles =</span> <span class="fu">seq</span>(<span class="dv">0</span>, <span class="dv">1</span>, .<span class="dv">05</span>),</span>
+<span id="cb300-9"><a href="4.5-lorenz-curve-svylorenz.html#cb300-9" tabindex="-1"></a>             <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span></code></pre></div>
 <p><img src="context_files/figure-html/unnamed-chunk-82-1.png" width="672"  /></p>
-<div class="sourceCode" id="cb302"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb302-1"><a href="4.5-lorenz-curve-svylorenz.html#cb302-1" tabindex="-1"></a><span class="co"># note: most survey commands in R use Inf degrees of freedom by default</span></span>
-<span id="cb302-2"><a href="4.5-lorenz-curve-svylorenz.html#cb302-2" tabindex="-1"></a><span class="co"># stata generally uses the degrees of freedom of the survey design.</span></span>
-<span id="cb302-3"><a href="4.5-lorenz-curve-svylorenz.html#cb302-3" tabindex="-1"></a><span class="co"># therefore, while the degf() parameters passed to qt()</span></span>
-<span id="cb302-4"><a href="4.5-lorenz-curve-svylorenz.html#cb302-4" tabindex="-1"></a><span class="co"># serve to prove a precise replication of stata,</span></span>
-<span id="cb302-5"><a href="4.5-lorenz-curve-svylorenz.html#cb302-5" tabindex="-1"></a><span class="co"># it is generally not necessary</span></span>
-<span id="cb302-6"><a href="4.5-lorenz-curve-svylorenz.html#cb302-6" tabindex="-1"></a>section_four_one <span class="ot">&lt;-</span></span>
-<span id="cb302-7"><a href="4.5-lorenz-curve-svylorenz.html#cb302-7" tabindex="-1"></a>  <span class="fu">data.frame</span>(</span>
-<span id="cb302-8"><a href="4.5-lorenz-curve-svylorenz.html#cb302-8" tabindex="-1"></a>    <span class="at">estimate =</span> <span class="fu">coef</span>(result.lin) ,</span>
-<span id="cb302-9"><a href="4.5-lorenz-curve-svylorenz.html#cb302-9" tabindex="-1"></a>    <span class="at">standard_error =</span> <span class="fu">SE</span>(result.lin) ,</span>
-<span id="cb302-10"><a href="4.5-lorenz-curve-svylorenz.html#cb302-10" tabindex="-1"></a>    <span class="at">ci_lower_bound =</span></span>
-<span id="cb302-11"><a href="4.5-lorenz-curve-svylorenz.html#cb302-11" tabindex="-1"></a>      <span class="fu">coef</span>(result.lin) <span class="sc">+</span></span>
-<span id="cb302-12"><a href="4.5-lorenz-curve-svylorenz.html#cb302-12" tabindex="-1"></a>      <span class="fu">SE</span>(result.lin) <span class="sc">*</span></span>
-<span id="cb302-13"><a href="4.5-lorenz-curve-svylorenz.html#cb302-13" tabindex="-1"></a>      <span class="fu">qt</span>(<span class="fl">0.025</span> , <span class="fu">degf</span>(<span class="fu">subset</span>(</span>
-<span id="cb302-14"><a href="4.5-lorenz-curve-svylorenz.html#cb302-14" tabindex="-1"></a>        des_nlsw88 , <span class="sc">!</span><span class="fu">is.na</span>(wage)</span>
-<span id="cb302-15"><a href="4.5-lorenz-curve-svylorenz.html#cb302-15" tabindex="-1"></a>      ))) ,</span>
-<span id="cb302-16"><a href="4.5-lorenz-curve-svylorenz.html#cb302-16" tabindex="-1"></a>    <span class="at">ci_upper_bound =</span></span>
-<span id="cb302-17"><a href="4.5-lorenz-curve-svylorenz.html#cb302-17" tabindex="-1"></a>      <span class="fu">coef</span>(result.lin) <span class="sc">+</span></span>
-<span id="cb302-18"><a href="4.5-lorenz-curve-svylorenz.html#cb302-18" tabindex="-1"></a>      <span class="fu">SE</span>(result.lin) <span class="sc">*</span></span>
-<span id="cb302-19"><a href="4.5-lorenz-curve-svylorenz.html#cb302-19" tabindex="-1"></a>      <span class="fu">qt</span>(<span class="fl">0.975</span> , <span class="fu">degf</span>(<span class="fu">subset</span>(</span>
-<span id="cb302-20"><a href="4.5-lorenz-curve-svylorenz.html#cb302-20" tabindex="-1"></a>        des_nlsw88 , <span class="sc">!</span><span class="fu">is.na</span>(wage)</span>
-<span id="cb302-21"><a href="4.5-lorenz-curve-svylorenz.html#cb302-21" tabindex="-1"></a>      )))</span>
-<span id="cb302-22"><a href="4.5-lorenz-curve-svylorenz.html#cb302-22" tabindex="-1"></a>  )</span></code></pre></div>
+<div class="sourceCode" id="cb301"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb301-1"><a href="4.5-lorenz-curve-svylorenz.html#cb301-1" tabindex="-1"></a><span class="co"># note: most survey commands in R use Inf degrees of freedom by default</span></span>
+<span id="cb301-2"><a href="4.5-lorenz-curve-svylorenz.html#cb301-2" tabindex="-1"></a><span class="co"># stata generally uses the degrees of freedom of the survey design.</span></span>
+<span id="cb301-3"><a href="4.5-lorenz-curve-svylorenz.html#cb301-3" tabindex="-1"></a><span class="co"># therefore, while the degf() parameters passed to qt()</span></span>
+<span id="cb301-4"><a href="4.5-lorenz-curve-svylorenz.html#cb301-4" tabindex="-1"></a><span class="co"># serve to prove a precise replication of stata,</span></span>
+<span id="cb301-5"><a href="4.5-lorenz-curve-svylorenz.html#cb301-5" tabindex="-1"></a><span class="co"># it is generally not necessary</span></span>
+<span id="cb301-6"><a href="4.5-lorenz-curve-svylorenz.html#cb301-6" tabindex="-1"></a>section_four_one <span class="ot">&lt;-</span></span>
+<span id="cb301-7"><a href="4.5-lorenz-curve-svylorenz.html#cb301-7" tabindex="-1"></a>  <span class="fu">data.frame</span>(</span>
+<span id="cb301-8"><a href="4.5-lorenz-curve-svylorenz.html#cb301-8" tabindex="-1"></a>    <span class="at">estimate =</span> <span class="fu">coef</span>(result.lin) ,</span>
+<span id="cb301-9"><a href="4.5-lorenz-curve-svylorenz.html#cb301-9" tabindex="-1"></a>    <span class="at">standard_error =</span> <span class="fu">SE</span>(result.lin) ,</span>
+<span id="cb301-10"><a href="4.5-lorenz-curve-svylorenz.html#cb301-10" tabindex="-1"></a>    <span class="at">ci_lower_bound =</span></span>
+<span id="cb301-11"><a href="4.5-lorenz-curve-svylorenz.html#cb301-11" tabindex="-1"></a>      <span class="fu">coef</span>(result.lin) <span class="sc">+</span></span>
+<span id="cb301-12"><a href="4.5-lorenz-curve-svylorenz.html#cb301-12" tabindex="-1"></a>      <span class="fu">SE</span>(result.lin) <span class="sc">*</span></span>
+<span id="cb301-13"><a href="4.5-lorenz-curve-svylorenz.html#cb301-13" tabindex="-1"></a>      <span class="fu">qt</span>(<span class="fl">0.025</span> , <span class="fu">degf</span>(<span class="fu">subset</span>(</span>
+<span id="cb301-14"><a href="4.5-lorenz-curve-svylorenz.html#cb301-14" tabindex="-1"></a>        des_nlsw88 , <span class="sc">!</span><span class="fu">is.na</span>(wage)</span>
+<span id="cb301-15"><a href="4.5-lorenz-curve-svylorenz.html#cb301-15" tabindex="-1"></a>      ))) ,</span>
+<span id="cb301-16"><a href="4.5-lorenz-curve-svylorenz.html#cb301-16" tabindex="-1"></a>    <span class="at">ci_upper_bound =</span></span>
+<span id="cb301-17"><a href="4.5-lorenz-curve-svylorenz.html#cb301-17" tabindex="-1"></a>      <span class="fu">coef</span>(result.lin) <span class="sc">+</span></span>
+<span id="cb301-18"><a href="4.5-lorenz-curve-svylorenz.html#cb301-18" tabindex="-1"></a>      <span class="fu">SE</span>(result.lin) <span class="sc">*</span></span>
+<span id="cb301-19"><a href="4.5-lorenz-curve-svylorenz.html#cb301-19" tabindex="-1"></a>      <span class="fu">qt</span>(<span class="fl">0.975</span> , <span class="fu">degf</span>(<span class="fu">subset</span>(</span>
+<span id="cb301-20"><a href="4.5-lorenz-curve-svylorenz.html#cb301-20" tabindex="-1"></a>        des_nlsw88 , <span class="sc">!</span><span class="fu">is.na</span>(wage)</span>
+<span id="cb301-21"><a href="4.5-lorenz-curve-svylorenz.html#cb301-21" tabindex="-1"></a>      )))</span>
+<span id="cb301-22"><a href="4.5-lorenz-curve-svylorenz.html#cb301-22" tabindex="-1"></a>  )</span></code></pre></div>
 <table>
 <thead>
 <tr class="header">
diff --git a/docs/4.6-gini-index-svygini.html b/docs/4.6-gini-index-svygini.html
index bfb3d6b..7212fd9 100644
--- a/docs/4.6-gini-index-svygini.html
+++ b/docs/4.6-gini-index-svygini.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,13 +253,13 @@
 <div class="col-sm-12">
 <div id="gini-index-svygini" class="section level2" number="4.6">
 <h2><span class="header-section-number">4.6</span> Gini index (svygini)</h2>
-<div class="sourceCode" id="cb303"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb303-1"><a href="4.6-gini-index-svygini.html#cb303-1" tabindex="-1"></a>✔️ direct relationship with the Lorenz curve</span>
-<span id="cb303-2"><a href="4.6-gini-index-svygini.html#cb303-2" tabindex="-1"></a>✔️ most used inequality measure</span>
-<span id="cb303-3"><a href="4.6-gini-index-svygini.html#cb303-3" tabindex="-1"></a>✔️ [<span class="dv">0</span>,<span class="dv">1</span>]<span class="sc">-</span>bounded, easy to compare</span>
-<span id="cb303-4"><a href="4.6-gini-index-svygini.html#cb303-4" tabindex="-1"></a>✔️ allows <span class="cf">for</span> zero incomes</span>
-<span id="cb303-5"><a href="4.6-gini-index-svygini.html#cb303-5" tabindex="-1"></a>❌ hard to interpret without a graphical device</span>
-<span id="cb303-6"><a href="4.6-gini-index-svygini.html#cb303-6" tabindex="-1"></a>❌ more sensitive to <span class="fu">outliers</span> (when compared to <span class="st">`</span><span class="at">svyzenga</span><span class="st">`</span>)</span>
-<span id="cb303-7"><a href="4.6-gini-index-svygini.html#cb303-7" tabindex="-1"></a>❌ https<span class="sc">:</span><span class="er">//</span>pubmed.ncbi.nlm.nih.gov<span class="sc">/</span><span class="dv">26292521</span><span class="sc">/</span> and https<span class="sc">:</span><span class="er">//</span>www.jstor.org<span class="sc">/</span>stable<span class="sc">/</span><span class="dv">2142862</span></span></code></pre></div>
+<div class="sourceCode" id="cb302"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb302-1"><a href="4.6-gini-index-svygini.html#cb302-1" tabindex="-1"></a>✔️ direct relationship with the Lorenz curve</span>
+<span id="cb302-2"><a href="4.6-gini-index-svygini.html#cb302-2" tabindex="-1"></a>✔️ most used inequality measure</span>
+<span id="cb302-3"><a href="4.6-gini-index-svygini.html#cb302-3" tabindex="-1"></a>✔️ [<span class="dv">0</span>,<span class="dv">1</span>]<span class="sc">-</span>bounded, easy to compare</span>
+<span id="cb302-4"><a href="4.6-gini-index-svygini.html#cb302-4" tabindex="-1"></a>✔️ allows <span class="cf">for</span> zero incomes</span>
+<span id="cb302-5"><a href="4.6-gini-index-svygini.html#cb302-5" tabindex="-1"></a>❌ hard to interpret without a graphical device</span>
+<span id="cb302-6"><a href="4.6-gini-index-svygini.html#cb302-6" tabindex="-1"></a>❌ more sensitive to <span class="fu">outliers</span> (when compared to <span class="st">`</span><span class="at">svyzenga</span><span class="st">`</span>)</span>
+<span id="cb302-7"><a href="4.6-gini-index-svygini.html#cb302-7" tabindex="-1"></a>❌ https<span class="sc">:</span><span class="er">//</span>pubmed.ncbi.nlm.nih.gov<span class="sc">/</span><span class="dv">26292521</span><span class="sc">/</span> and https<span class="sc">:</span><span class="er">//</span>www.jstor.org<span class="sc">/</span>stable<span class="sc">/</span><span class="dv">2142862</span></span></code></pre></div>
 <p>The Gini index (or Gini coefficient) is an attempt to express the inequality presented in the Lorenz curve as a single number. In essence, it is twice the area between the equality curve and the real Lorenz curve. Put simply:</p>
 <p><span class="math display">\[
 \begin{aligned}
@@ -278,142 +278,142 @@ <h2><span class="header-section-number">4.6</span> Gini index (svygini)</h2>
 <h3><span class="header-section-number">4.6.1</span> Replication Example</h3>
 <p>The R <code>vardpoor</code> package <span class="citation">(<label for="tufte-mn-73" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-73" class="margin-toggle">Breidaks, Liberts, and Ivanova 2016<span class="marginnote">Breidaks, Juris, Martins Liberts, and Santa Ivanova. 2016. <span>“Vardpoor: Estimation of Indicators on Social Exclusion and Poverty and Its Linearization, Variance Estimation.”</span> Riga, Latvia: CSB.</span>)</span>, created by researchers at the Central Statistical Bureau of Latvia, includes a Gini coefficient calculation using the ultimate cluster method. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb304"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb304-1"><a href="4.6-gini-index-svygini.html#cb304-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb304-2"><a href="4.6-gini-index-svygini.html#cb304-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb304-3"><a href="4.6-gini-index-svygini.html#cb304-3" tabindex="-1"></a></span>
-<span id="cb304-4"><a href="4.6-gini-index-svygini.html#cb304-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb304-5"><a href="4.6-gini-index-svygini.html#cb304-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb304-6"><a href="4.6-gini-index-svygini.html#cb304-6" tabindex="-1"></a></span>
-<span id="cb304-7"><a href="4.6-gini-index-svygini.html#cb304-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
-<span id="cb304-8"><a href="4.6-gini-index-svygini.html#cb304-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
-<span id="cb304-9"><a href="4.6-gini-index-svygini.html#cb304-9" tabindex="-1"></a></span>
-<span id="cb304-10"><a href="4.6-gini-index-svygini.html#cb304-10" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
-<span id="cb304-11"><a href="4.6-gini-index-svygini.html#cb304-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
-<span id="cb304-12"><a href="4.6-gini-index-svygini.html#cb304-12" tabindex="-1"></a></span>
-<span id="cb304-13"><a href="4.6-gini-index-svygini.html#cb304-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
-<span id="cb304-14"><a href="4.6-gini-index-svygini.html#cb304-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
-<span id="cb304-15"><a href="4.6-gini-index-svygini.html#cb304-15" tabindex="-1"></a></span>
-<span id="cb304-16"><a href="4.6-gini-index-svygini.html#cb304-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
-<span id="cb304-17"><a href="4.6-gini-index-svygini.html#cb304-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
-<span id="cb304-18"><a href="4.6-gini-index-svygini.html#cb304-18" tabindex="-1"></a></span>
-<span id="cb304-19"><a href="4.6-gini-index-svygini.html#cb304-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
-<span id="cb304-20"><a href="4.6-gini-index-svygini.html#cb304-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
-<span id="cb304-21"><a href="4.6-gini-index-svygini.html#cb304-21" tabindex="-1"></a></span>
-<span id="cb304-22"><a href="4.6-gini-index-svygini.html#cb304-22" tabindex="-1"></a><span class="co"># calculate the gini coefficient</span></span>
-<span id="cb304-23"><a href="4.6-gini-index-svygini.html#cb304-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
-<span id="cb304-24"><a href="4.6-gini-index-svygini.html#cb304-24" tabindex="-1"></a>varpoord_gini_calculation <span class="ot">&lt;-</span></span>
-<span id="cb304-25"><a href="4.6-gini-index-svygini.html#cb304-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
-<span id="cb304-26"><a href="4.6-gini-index-svygini.html#cb304-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
-<span id="cb304-27"><a href="4.6-gini-index-svygini.html#cb304-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
-<span id="cb304-28"><a href="4.6-gini-index-svygini.html#cb304-28" tabindex="-1"></a>    </span>
-<span id="cb304-29"><a href="4.6-gini-index-svygini.html#cb304-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
-<span id="cb304-30"><a href="4.6-gini-index-svygini.html#cb304-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
-<span id="cb304-31"><a href="4.6-gini-index-svygini.html#cb304-31" tabindex="-1"></a>    </span>
-<span id="cb304-32"><a href="4.6-gini-index-svygini.html#cb304-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb304-33"><a href="4.6-gini-index-svygini.html#cb304-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb304-34"><a href="4.6-gini-index-svygini.html#cb304-34" tabindex="-1"></a>    </span>
-<span id="cb304-35"><a href="4.6-gini-index-svygini.html#cb304-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
-<span id="cb304-36"><a href="4.6-gini-index-svygini.html#cb304-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
-<span id="cb304-37"><a href="4.6-gini-index-svygini.html#cb304-37" tabindex="-1"></a>    </span>
-<span id="cb304-38"><a href="4.6-gini-index-svygini.html#cb304-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
-<span id="cb304-39"><a href="4.6-gini-index-svygini.html#cb304-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
-<span id="cb304-40"><a href="4.6-gini-index-svygini.html#cb304-40" tabindex="-1"></a>    </span>
-<span id="cb304-41"><a href="4.6-gini-index-svygini.html#cb304-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
-<span id="cb304-42"><a href="4.6-gini-index-svygini.html#cb304-42" tabindex="-1"></a>    </span>
-<span id="cb304-43"><a href="4.6-gini-index-svygini.html#cb304-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
-<span id="cb304-44"><a href="4.6-gini-index-svygini.html#cb304-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
-<span id="cb304-45"><a href="4.6-gini-index-svygini.html#cb304-45" tabindex="-1"></a>    </span>
-<span id="cb304-46"><a href="4.6-gini-index-svygini.html#cb304-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
-<span id="cb304-47"><a href="4.6-gini-index-svygini.html#cb304-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
-<span id="cb304-48"><a href="4.6-gini-index-svygini.html#cb304-48" tabindex="-1"></a>    </span>
-<span id="cb304-49"><a href="4.6-gini-index-svygini.html#cb304-49" tabindex="-1"></a>    <span class="co"># gini coefficient function</span></span>
-<span id="cb304-50"><a href="4.6-gini-index-svygini.html#cb304-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;lingini&quot;</span>,</span>
-<span id="cb304-51"><a href="4.6-gini-index-svygini.html#cb304-51" tabindex="-1"></a>    </span>
-<span id="cb304-52"><a href="4.6-gini-index-svygini.html#cb304-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
-<span id="cb304-53"><a href="4.6-gini-index-svygini.html#cb304-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
-<span id="cb304-54"><a href="4.6-gini-index-svygini.html#cb304-54" tabindex="-1"></a>    </span>
-<span id="cb304-55"><a href="4.6-gini-index-svygini.html#cb304-55" tabindex="-1"></a>  )</span>
-<span id="cb304-56"><a href="4.6-gini-index-svygini.html#cb304-56" tabindex="-1"></a></span>
-<span id="cb304-57"><a href="4.6-gini-index-svygini.html#cb304-57" tabindex="-1"></a></span>
-<span id="cb304-58"><a href="4.6-gini-index-svygini.html#cb304-58" tabindex="-1"></a></span>
-<span id="cb304-59"><a href="4.6-gini-index-svygini.html#cb304-59" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb304-60"><a href="4.6-gini-index-svygini.html#cb304-60" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
-<span id="cb304-61"><a href="4.6-gini-index-svygini.html#cb304-61" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
-<span id="cb304-62"><a href="4.6-gini-index-svygini.html#cb304-62" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb304-63"><a href="4.6-gini-index-svygini.html#cb304-63" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb304-64"><a href="4.6-gini-index-svygini.html#cb304-64" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb304-65"><a href="4.6-gini-index-svygini.html#cb304-65" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb304-66"><a href="4.6-gini-index-svygini.html#cb304-66" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
-<span id="cb304-67"><a href="4.6-gini-index-svygini.html#cb304-67" tabindex="-1"></a>  )</span>
-<span id="cb304-68"><a href="4.6-gini-index-svygini.html#cb304-68" tabindex="-1"></a></span>
-<span id="cb304-69"><a href="4.6-gini-index-svygini.html#cb304-69" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
-<span id="cb304-70"><a href="4.6-gini-index-svygini.html#cb304-70" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
-<span id="cb304-71"><a href="4.6-gini-index-svygini.html#cb304-71" tabindex="-1"></a></span>
-<span id="cb304-72"><a href="4.6-gini-index-svygini.html#cb304-72" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
-<span id="cb304-73"><a href="4.6-gini-index-svygini.html#cb304-73" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
+<div class="sourceCode" id="cb303"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb303-1"><a href="4.6-gini-index-svygini.html#cb303-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb303-2"><a href="4.6-gini-index-svygini.html#cb303-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb303-3"><a href="4.6-gini-index-svygini.html#cb303-3" tabindex="-1"></a></span>
+<span id="cb303-4"><a href="4.6-gini-index-svygini.html#cb303-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb303-5"><a href="4.6-gini-index-svygini.html#cb303-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb303-6"><a href="4.6-gini-index-svygini.html#cb303-6" tabindex="-1"></a></span>
+<span id="cb303-7"><a href="4.6-gini-index-svygini.html#cb303-7" tabindex="-1"></a><span class="co"># load the vardpoor library</span></span>
+<span id="cb303-8"><a href="4.6-gini-index-svygini.html#cb303-8" tabindex="-1"></a><span class="fu">library</span>(vardpoor)</span>
+<span id="cb303-9"><a href="4.6-gini-index-svygini.html#cb303-9" tabindex="-1"></a></span>
+<span id="cb303-10"><a href="4.6-gini-index-svygini.html#cb303-10" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
+<span id="cb303-11"><a href="4.6-gini-index-svygini.html#cb303-11" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
+<span id="cb303-12"><a href="4.6-gini-index-svygini.html#cb303-12" tabindex="-1"></a></span>
+<span id="cb303-13"><a href="4.6-gini-index-svygini.html#cb303-13" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
+<span id="cb303-14"><a href="4.6-gini-index-svygini.html#cb303-14" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
+<span id="cb303-15"><a href="4.6-gini-index-svygini.html#cb303-15" tabindex="-1"></a></span>
+<span id="cb303-16"><a href="4.6-gini-index-svygini.html#cb303-16" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
+<span id="cb303-17"><a href="4.6-gini-index-svygini.html#cb303-17" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
+<span id="cb303-18"><a href="4.6-gini-index-svygini.html#cb303-18" tabindex="-1"></a></span>
+<span id="cb303-19"><a href="4.6-gini-index-svygini.html#cb303-19" tabindex="-1"></a><span class="co"># add a column with the row number</span></span>
+<span id="cb303-20"><a href="4.6-gini-index-svygini.html#cb303-20" tabindex="-1"></a>dati <span class="ot">&lt;-</span> data.table<span class="sc">::</span><span class="fu">data.table</span>(<span class="at">IDd =</span> <span class="dv">1</span><span class="sc">:</span><span class="fu">nrow</span>(eusilc), eusilc)</span>
+<span id="cb303-21"><a href="4.6-gini-index-svygini.html#cb303-21" tabindex="-1"></a></span>
+<span id="cb303-22"><a href="4.6-gini-index-svygini.html#cb303-22" tabindex="-1"></a><span class="co"># calculate the gini coefficient</span></span>
+<span id="cb303-23"><a href="4.6-gini-index-svygini.html#cb303-23" tabindex="-1"></a><span class="co"># using the R vardpoor library</span></span>
+<span id="cb303-24"><a href="4.6-gini-index-svygini.html#cb303-24" tabindex="-1"></a>varpoord_gini_calculation <span class="ot">&lt;-</span></span>
+<span id="cb303-25"><a href="4.6-gini-index-svygini.html#cb303-25" tabindex="-1"></a>  <span class="fu">varpoord</span>(</span>
+<span id="cb303-26"><a href="4.6-gini-index-svygini.html#cb303-26" tabindex="-1"></a>    <span class="co"># analysis variable</span></span>
+<span id="cb303-27"><a href="4.6-gini-index-svygini.html#cb303-27" tabindex="-1"></a>    <span class="at">Y =</span> <span class="st">&quot;eqincome&quot;</span>,</span>
+<span id="cb303-28"><a href="4.6-gini-index-svygini.html#cb303-28" tabindex="-1"></a>    </span>
+<span id="cb303-29"><a href="4.6-gini-index-svygini.html#cb303-29" tabindex="-1"></a>    <span class="co"># weights variable</span></span>
+<span id="cb303-30"><a href="4.6-gini-index-svygini.html#cb303-30" tabindex="-1"></a>    <span class="at">w_final =</span> <span class="st">&quot;rb050&quot;</span>,</span>
+<span id="cb303-31"><a href="4.6-gini-index-svygini.html#cb303-31" tabindex="-1"></a>    </span>
+<span id="cb303-32"><a href="4.6-gini-index-svygini.html#cb303-32" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb303-33"><a href="4.6-gini-index-svygini.html#cb303-33" tabindex="-1"></a>    <span class="at">ID_level1 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb303-34"><a href="4.6-gini-index-svygini.html#cb303-34" tabindex="-1"></a>    </span>
+<span id="cb303-35"><a href="4.6-gini-index-svygini.html#cb303-35" tabindex="-1"></a>    <span class="co"># row number variable</span></span>
+<span id="cb303-36"><a href="4.6-gini-index-svygini.html#cb303-36" tabindex="-1"></a>    <span class="at">ID_level2 =</span> <span class="st">&quot;IDd&quot;</span>,</span>
+<span id="cb303-37"><a href="4.6-gini-index-svygini.html#cb303-37" tabindex="-1"></a>    </span>
+<span id="cb303-38"><a href="4.6-gini-index-svygini.html#cb303-38" tabindex="-1"></a>    <span class="co"># strata variable</span></span>
+<span id="cb303-39"><a href="4.6-gini-index-svygini.html#cb303-39" tabindex="-1"></a>    <span class="at">H =</span> <span class="st">&quot;db040&quot;</span>,</span>
+<span id="cb303-40"><a href="4.6-gini-index-svygini.html#cb303-40" tabindex="-1"></a>    </span>
+<span id="cb303-41"><a href="4.6-gini-index-svygini.html#cb303-41" tabindex="-1"></a>    <span class="at">N_h =</span> <span class="cn">NULL</span> ,</span>
+<span id="cb303-42"><a href="4.6-gini-index-svygini.html#cb303-42" tabindex="-1"></a>    </span>
+<span id="cb303-43"><a href="4.6-gini-index-svygini.html#cb303-43" tabindex="-1"></a>    <span class="co"># clustering variable</span></span>
+<span id="cb303-44"><a href="4.6-gini-index-svygini.html#cb303-44" tabindex="-1"></a>    <span class="at">PSU =</span> <span class="st">&quot;rb030&quot;</span>,</span>
+<span id="cb303-45"><a href="4.6-gini-index-svygini.html#cb303-45" tabindex="-1"></a>    </span>
+<span id="cb303-46"><a href="4.6-gini-index-svygini.html#cb303-46" tabindex="-1"></a>    <span class="co"># data.table</span></span>
+<span id="cb303-47"><a href="4.6-gini-index-svygini.html#cb303-47" tabindex="-1"></a>    <span class="at">dataset =</span> dati,</span>
+<span id="cb303-48"><a href="4.6-gini-index-svygini.html#cb303-48" tabindex="-1"></a>    </span>
+<span id="cb303-49"><a href="4.6-gini-index-svygini.html#cb303-49" tabindex="-1"></a>    <span class="co"># gini coefficient function</span></span>
+<span id="cb303-50"><a href="4.6-gini-index-svygini.html#cb303-50" tabindex="-1"></a>    <span class="at">type =</span> <span class="st">&quot;lingini&quot;</span>,</span>
+<span id="cb303-51"><a href="4.6-gini-index-svygini.html#cb303-51" tabindex="-1"></a>    </span>
+<span id="cb303-52"><a href="4.6-gini-index-svygini.html#cb303-52" tabindex="-1"></a>    <span class="co"># get linearized variable</span></span>
+<span id="cb303-53"><a href="4.6-gini-index-svygini.html#cb303-53" tabindex="-1"></a>    <span class="at">outp_lin =</span> <span class="cn">TRUE</span></span>
+<span id="cb303-54"><a href="4.6-gini-index-svygini.html#cb303-54" tabindex="-1"></a>    </span>
+<span id="cb303-55"><a href="4.6-gini-index-svygini.html#cb303-55" tabindex="-1"></a>  )</span>
+<span id="cb303-56"><a href="4.6-gini-index-svygini.html#cb303-56" tabindex="-1"></a></span>
+<span id="cb303-57"><a href="4.6-gini-index-svygini.html#cb303-57" tabindex="-1"></a></span>
+<span id="cb303-58"><a href="4.6-gini-index-svygini.html#cb303-58" tabindex="-1"></a></span>
+<span id="cb303-59"><a href="4.6-gini-index-svygini.html#cb303-59" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb303-60"><a href="4.6-gini-index-svygini.html#cb303-60" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
+<span id="cb303-61"><a href="4.6-gini-index-svygini.html#cb303-61" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
+<span id="cb303-62"><a href="4.6-gini-index-svygini.html#cb303-62" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb303-63"><a href="4.6-gini-index-svygini.html#cb303-63" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb303-64"><a href="4.6-gini-index-svygini.html#cb303-64" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb303-65"><a href="4.6-gini-index-svygini.html#cb303-65" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb303-66"><a href="4.6-gini-index-svygini.html#cb303-66" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
+<span id="cb303-67"><a href="4.6-gini-index-svygini.html#cb303-67" tabindex="-1"></a>  )</span>
+<span id="cb303-68"><a href="4.6-gini-index-svygini.html#cb303-68" tabindex="-1"></a></span>
+<span id="cb303-69"><a href="4.6-gini-index-svygini.html#cb303-69" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
+<span id="cb303-70"><a href="4.6-gini-index-svygini.html#cb303-70" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc)</span>
+<span id="cb303-71"><a href="4.6-gini-index-svygini.html#cb303-71" tabindex="-1"></a></span>
+<span id="cb303-72"><a href="4.6-gini-index-svygini.html#cb303-72" tabindex="-1"></a><span class="co"># coefficients do match</span></span>
+<span id="cb303-73"><a href="4.6-gini-index-svygini.html#cb303-73" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>value</span></code></pre></div>
 <pre><code>## [1] 26.49652</code></pre>
-<div class="sourceCode" id="cb306"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb306-1"><a href="4.6-gini-index-svygini.html#cb306-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb305"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb305-1"><a href="4.6-gini-index-svygini.html#cb305-1" tabindex="-1"></a><span class="fu">coef</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>## eqincome 
 ## 26.49652</code></pre>
-<div class="sourceCode" id="cb308"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb308-1"><a href="4.6-gini-index-svygini.html#cb308-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
-<span id="cb308-2"><a href="4.6-gini-index-svygini.html#cb308-2" tabindex="-1"></a><span class="co"># varpoord</span></span>
-<span id="cb308-3"><a href="4.6-gini-index-svygini.html#cb308-3" tabindex="-1"></a>lin_gini_varpoord <span class="ot">&lt;-</span> varpoord_gini_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_gini</span>
-<span id="cb308-4"><a href="4.6-gini-index-svygini.html#cb308-4" tabindex="-1"></a><span class="co"># convey</span></span>
-<span id="cb308-5"><a href="4.6-gini-index-svygini.html#cb308-5" tabindex="-1"></a>lin_gini_convey <span class="ot">&lt;-</span></span>
-<span id="cb308-6"><a href="4.6-gini-index-svygini.html#cb308-6" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">linearized =</span> <span class="cn">TRUE</span>) , <span class="st">&quot;linearized&quot;</span>)</span>
-<span id="cb308-7"><a href="4.6-gini-index-svygini.html#cb308-7" tabindex="-1"></a></span>
-<span id="cb308-8"><a href="4.6-gini-index-svygini.html#cb308-8" tabindex="-1"></a><span class="co"># check equality</span></span>
-<span id="cb308-9"><a href="4.6-gini-index-svygini.html#cb308-9" tabindex="-1"></a><span class="fu">all.equal</span>(lin_gini_varpoord , (<span class="dv">100</span> <span class="sc">*</span> <span class="fu">as.numeric</span>(lin_gini_convey)))</span></code></pre></div>
+<div class="sourceCode" id="cb307"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb307-1"><a href="4.6-gini-index-svygini.html#cb307-1" tabindex="-1"></a><span class="co"># linearized variables do match</span></span>
+<span id="cb307-2"><a href="4.6-gini-index-svygini.html#cb307-2" tabindex="-1"></a><span class="co"># varpoord</span></span>
+<span id="cb307-3"><a href="4.6-gini-index-svygini.html#cb307-3" tabindex="-1"></a>lin_gini_varpoord <span class="ot">&lt;-</span> varpoord_gini_calculation<span class="sc">$</span>lin_out<span class="sc">$</span>lin_gini</span>
+<span id="cb307-4"><a href="4.6-gini-index-svygini.html#cb307-4" tabindex="-1"></a><span class="co"># convey</span></span>
+<span id="cb307-5"><a href="4.6-gini-index-svygini.html#cb307-5" tabindex="-1"></a>lin_gini_convey <span class="ot">&lt;-</span></span>
+<span id="cb307-6"><a href="4.6-gini-index-svygini.html#cb307-6" tabindex="-1"></a>  <span class="fu">attr</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc , <span class="at">linearized =</span> <span class="cn">TRUE</span>) , <span class="st">&quot;linearized&quot;</span>)</span>
+<span id="cb307-7"><a href="4.6-gini-index-svygini.html#cb307-7" tabindex="-1"></a></span>
+<span id="cb307-8"><a href="4.6-gini-index-svygini.html#cb307-8" tabindex="-1"></a><span class="co"># check equality</span></span>
+<span id="cb307-9"><a href="4.6-gini-index-svygini.html#cb307-9" tabindex="-1"></a><span class="fu">all.equal</span>(lin_gini_varpoord , (<span class="dv">100</span> <span class="sc">*</span> <span class="fu">as.numeric</span>(lin_gini_convey)))</span></code></pre></div>
 <pre><code>## [1] TRUE</code></pre>
-<div class="sourceCode" id="cb310"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb310-1"><a href="4.6-gini-index-svygini.html#cb310-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
-<span id="cb310-2"><a href="4.6-gini-index-svygini.html#cb310-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
+<div class="sourceCode" id="cb309"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb309-1"><a href="4.6-gini-index-svygini.html#cb309-1" tabindex="-1"></a><span class="co"># variances do not match exactly</span></span>
+<span id="cb309-2"><a href="4.6-gini-index-svygini.html#cb309-2" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
 <pre><code>##            eqincome
 ## eqincome 0.03790739</code></pre>
-<div class="sourceCode" id="cb312"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb312-1"><a href="4.6-gini-index-svygini.html#cb312-1" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb311"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb311-1"><a href="4.6-gini-index-svygini.html#cb311-1" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.03783931</code></pre>
-<div class="sourceCode" id="cb314"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb314-1"><a href="4.6-gini-index-svygini.html#cb314-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
-<span id="cb314-2"><a href="4.6-gini-index-svygini.html#cb314-2" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb313"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb313-1"><a href="4.6-gini-index-svygini.html#cb313-1" tabindex="-1"></a><span class="co"># standard errors do not match exactly</span></span>
+<span id="cb313-2"><a href="4.6-gini-index-svygini.html#cb313-2" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.1945233</code></pre>
-<div class="sourceCode" id="cb316"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb316-1"><a href="4.6-gini-index-svygini.html#cb316-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb315"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb315-1"><a href="4.6-gini-index-svygini.html#cb315-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>##           eqincome
 ## eqincome 0.1946982</code></pre>
 <p>The variance estimate is computed by using the approximation defined in <a href="2-var.html#var">2</a>, while the linearized variable <span class="math inline">\(z\)</span> is defined by <a href="2.1-lin.html#lin">2.1</a>. The functions <code>convey::svygini</code> and <code>vardpoor::lingini</code> produce the same linearized variable <span class="math inline">\(z\)</span>.</p>
 <p>However, the measures of uncertainty do not line up, because <code>library(vardpoor)</code> defaults to an ultimate cluster method that can be replicated with an alternative setup of the <code>survey.design</code> object.</p>
-<div class="sourceCode" id="cb318"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb318-1"><a href="4.6-gini-index-svygini.html#cb318-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
-<span id="cb318-2"><a href="4.6-gini-index-svygini.html#cb318-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
-<span id="cb318-3"><a href="4.6-gini-index-svygini.html#cb318-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
-<span id="cb318-4"><a href="4.6-gini-index-svygini.html#cb318-4" tabindex="-1"></a></span>
-<span id="cb318-5"><a href="4.6-gini-index-svygini.html#cb318-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
-<span id="cb318-6"><a href="4.6-gini-index-svygini.html#cb318-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
-<span id="cb318-7"><a href="4.6-gini-index-svygini.html#cb318-7" tabindex="-1"></a></span>
-<span id="cb318-8"><a href="4.6-gini-index-svygini.html#cb318-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
-<span id="cb318-9"><a href="4.6-gini-index-svygini.html#cb318-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
-<span id="cb318-10"><a href="4.6-gini-index-svygini.html#cb318-10" tabindex="-1"></a></span>
-<span id="cb318-11"><a href="4.6-gini-index-svygini.html#cb318-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb318-12"><a href="4.6-gini-index-svygini.html#cb318-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
-<span id="cb318-13"><a href="4.6-gini-index-svygini.html#cb318-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb318-14"><a href="4.6-gini-index-svygini.html#cb318-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb318-15"><a href="4.6-gini-index-svygini.html#cb318-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb318-16"><a href="4.6-gini-index-svygini.html#cb318-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb318-17"><a href="4.6-gini-index-svygini.html#cb318-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb318-18"><a href="4.6-gini-index-svygini.html#cb318-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
-<span id="cb318-19"><a href="4.6-gini-index-svygini.html#cb318-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
-<span id="cb318-20"><a href="4.6-gini-index-svygini.html#cb318-20" tabindex="-1"></a>  )</span>
-<span id="cb318-21"><a href="4.6-gini-index-svygini.html#cb318-21" tabindex="-1"></a></span>
-<span id="cb318-22"><a href="4.6-gini-index-svygini.html#cb318-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
-<span id="cb318-23"><a href="4.6-gini-index-svygini.html#cb318-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
-<span id="cb318-24"><a href="4.6-gini-index-svygini.html#cb318-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
-<span id="cb318-25"><a href="4.6-gini-index-svygini.html#cb318-25" tabindex="-1"></a></span>
-<span id="cb318-26"><a href="4.6-gini-index-svygini.html#cb318-26" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb318-27"><a href="4.6-gini-index-svygini.html#cb318-27" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
+<div class="sourceCode" id="cb317"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb317-1"><a href="4.6-gini-index-svygini.html#cb317-1" tabindex="-1"></a><span class="co"># within each strata, sum up the weights</span></span>
+<span id="cb317-2"><a href="4.6-gini-index-svygini.html#cb317-2" tabindex="-1"></a>cluster_sums <span class="ot">&lt;-</span></span>
+<span id="cb317-3"><a href="4.6-gini-index-svygini.html#cb317-3" tabindex="-1"></a>  <span class="fu">aggregate</span>(eusilc<span class="sc">$</span>rb050 , <span class="fu">list</span>(eusilc<span class="sc">$</span>db040) , sum)</span>
+<span id="cb317-4"><a href="4.6-gini-index-svygini.html#cb317-4" tabindex="-1"></a></span>
+<span id="cb317-5"><a href="4.6-gini-index-svygini.html#cb317-5" tabindex="-1"></a><span class="co"># name the within-strata sums of weights the `cluster_sum`</span></span>
+<span id="cb317-6"><a href="4.6-gini-index-svygini.html#cb317-6" tabindex="-1"></a><span class="fu">names</span>(cluster_sums) <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="st">&quot;db040&quot;</span> , <span class="st">&quot;cluster_sum&quot;</span>)</span>
+<span id="cb317-7"><a href="4.6-gini-index-svygini.html#cb317-7" tabindex="-1"></a></span>
+<span id="cb317-8"><a href="4.6-gini-index-svygini.html#cb317-8" tabindex="-1"></a><span class="co"># merge this column back onto the data.frame</span></span>
+<span id="cb317-9"><a href="4.6-gini-index-svygini.html#cb317-9" tabindex="-1"></a>eusilc <span class="ot">&lt;-</span> <span class="fu">merge</span>(eusilc , cluster_sums)</span>
+<span id="cb317-10"><a href="4.6-gini-index-svygini.html#cb317-10" tabindex="-1"></a></span>
+<span id="cb317-11"><a href="4.6-gini-index-svygini.html#cb317-11" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb317-12"><a href="4.6-gini-index-svygini.html#cb317-12" tabindex="-1"></a><span class="co"># with the fpc using the cluster sum</span></span>
+<span id="cb317-13"><a href="4.6-gini-index-svygini.html#cb317-13" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb317-14"><a href="4.6-gini-index-svygini.html#cb317-14" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb317-15"><a href="4.6-gini-index-svygini.html#cb317-15" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb317-16"><a href="4.6-gini-index-svygini.html#cb317-16" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb317-17"><a href="4.6-gini-index-svygini.html#cb317-17" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb317-18"><a href="4.6-gini-index-svygini.html#cb317-18" tabindex="-1"></a>    <span class="at">data =</span> eusilc ,</span>
+<span id="cb317-19"><a href="4.6-gini-index-svygini.html#cb317-19" tabindex="-1"></a>    <span class="at">fpc =</span> <span class="sc">~</span> cluster_sum</span>
+<span id="cb317-20"><a href="4.6-gini-index-svygini.html#cb317-20" tabindex="-1"></a>  )</span>
+<span id="cb317-21"><a href="4.6-gini-index-svygini.html#cb317-21" tabindex="-1"></a></span>
+<span id="cb317-22"><a href="4.6-gini-index-svygini.html#cb317-22" tabindex="-1"></a><span class="co"># again, immediately run the convey_prep function on the `survey.design`</span></span>
+<span id="cb317-23"><a href="4.6-gini-index-svygini.html#cb317-23" tabindex="-1"></a>des_eusilc_ultimate_cluster <span class="ot">&lt;-</span></span>
+<span id="cb317-24"><a href="4.6-gini-index-svygini.html#cb317-24" tabindex="-1"></a>  <span class="fu">convey_prep</span>(des_eusilc_ultimate_cluster)</span>
+<span id="cb317-25"><a href="4.6-gini-index-svygini.html#cb317-25" tabindex="-1"></a></span>
+<span id="cb317-26"><a href="4.6-gini-index-svygini.html#cb317-26" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb317-27"><a href="4.6-gini-index-svygini.html#cb317-27" tabindex="-1"></a><span class="fu">attr</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster) , <span class="st">&#39;var&#39;</span>) <span class="sc">*</span> <span class="dv">10000</span></span></code></pre></div>
 <pre><code>##            eqincome
 ## eqincome 0.03783931</code></pre>
-<div class="sourceCode" id="cb320"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb320-1"><a href="4.6-gini-index-svygini.html#cb320-1" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
+<div class="sourceCode" id="cb319"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb319-1"><a href="4.6-gini-index-svygini.html#cb319-1" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>var</span></code></pre></div>
 <pre><code>## [1] 0.03783931</code></pre>
-<div class="sourceCode" id="cb322"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb322-1"><a href="4.6-gini-index-svygini.html#cb322-1" tabindex="-1"></a><span class="co"># matches</span></span>
-<span id="cb322-2"><a href="4.6-gini-index-svygini.html#cb322-2" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
+<div class="sourceCode" id="cb321"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb321-1"><a href="4.6-gini-index-svygini.html#cb321-1" tabindex="-1"></a><span class="co"># matches</span></span>
+<span id="cb321-2"><a href="4.6-gini-index-svygini.html#cb321-2" tabindex="-1"></a>varpoord_gini_calculation<span class="sc">$</span>all_result<span class="sc">$</span>se</span></code></pre></div>
 <pre><code>## [1] 0.1945233</code></pre>
-<div class="sourceCode" id="cb324"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb324-1"><a href="4.6-gini-index-svygini.html#cb324-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
+<div class="sourceCode" id="cb323"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb323-1"><a href="4.6-gini-index-svygini.html#cb323-1" tabindex="-1"></a><span class="fu">SE</span>(<span class="fu">svygini</span>( <span class="sc">~</span> eqincome , des_eusilc_ultimate_cluster)) <span class="sc">*</span> <span class="dv">100</span></span></code></pre></div>
 <pre><code>##           eqincome
 ## eqincome 0.1945233</code></pre>
 </div>
diff --git a/docs/4.7-zenga-index-svyzenga.html b/docs/4.7-zenga-index-svyzenga.html
index 851f3ee..31548b3 100644
--- a/docs/4.7-zenga-index-svyzenga.html
+++ b/docs/4.7-zenga-index-svyzenga.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -253,13 +253,13 @@
 <div class="col-sm-12">
 <div id="zenga-index-svyzenga" class="section level2" number="4.7">
 <h2><span class="header-section-number">4.7</span> Zenga index (svyzenga)</h2>
-<div class="sourceCode" id="cb326"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb326-1"><a href="4.7-zenga-index-svyzenga.html#cb326-1" tabindex="-1"></a>✔️ [<span class="dv">0</span>,<span class="dv">1</span>]<span class="sc">-</span>bounded</span>
-<span id="cb326-2"><a href="4.7-zenga-index-svyzenga.html#cb326-2" tabindex="-1"></a>✔️ can account <span class="cf">for</span> zero incomes</span>
-<span id="cb326-3"><a href="4.7-zenga-index-svyzenga.html#cb326-3" tabindex="-1"></a>✔️ not extremely sensitive to top incomes</span>
-<span id="cb326-4"><a href="4.7-zenga-index-svyzenga.html#cb326-4" tabindex="-1"></a>✔️ can be interpreted <span class="fu">using</span> (a transformation of) the Lorenz curve</span>
-<span id="cb326-5"><a href="4.7-zenga-index-svyzenga.html#cb326-5" tabindex="-1"></a>❌ very uncommon</span>
-<span id="cb326-6"><a href="4.7-zenga-index-svyzenga.html#cb326-6" tabindex="-1"></a>❌ difficult to find applications to compare</span>
-<span id="cb326-7"><a href="4.7-zenga-index-svyzenga.html#cb326-7" tabindex="-1"></a>❌ difficult to explain</span></code></pre></div>
+<div class="sourceCode" id="cb325"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb325-1"><a href="4.7-zenga-index-svyzenga.html#cb325-1" tabindex="-1"></a>✔️ [<span class="dv">0</span>,<span class="dv">1</span>]<span class="sc">-</span>bounded</span>
+<span id="cb325-2"><a href="4.7-zenga-index-svyzenga.html#cb325-2" tabindex="-1"></a>✔️ can account <span class="cf">for</span> zero incomes</span>
+<span id="cb325-3"><a href="4.7-zenga-index-svyzenga.html#cb325-3" tabindex="-1"></a>✔️ not extremely sensitive to top incomes</span>
+<span id="cb325-4"><a href="4.7-zenga-index-svyzenga.html#cb325-4" tabindex="-1"></a>✔️ can be interpreted <span class="fu">using</span> (a transformation of) the Lorenz curve</span>
+<span id="cb325-5"><a href="4.7-zenga-index-svyzenga.html#cb325-5" tabindex="-1"></a>❌ very uncommon</span>
+<span id="cb325-6"><a href="4.7-zenga-index-svyzenga.html#cb325-6" tabindex="-1"></a>❌ difficult to find applications to compare</span>
+<span id="cb325-7"><a href="4.7-zenga-index-svyzenga.html#cb325-7" tabindex="-1"></a>❌ difficult to explain</span></code></pre></div>
 <p>Proposed by <span class="citation">Zenga (<label for="tufte-mn-74" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-74" class="margin-toggle">2007<span class="marginnote">Zenga, Michele. 2007. <span>“Inequality Curve and Inequality Index Based on the Ratios Between Lower and Upper Arithmetic Means.”</span> <em>Statistica e Applicazioni</em> 1 (4): 3–27.</span>)</span>, the Zenga index is another inequality measure related to the Lorenz curve with interesting properties. For continuous populations, it is defined as:</p>
 <p><span class="math display">\[
 Z = 1 - \int_{0}^{1} \frac{L(p)}{p} \cdot \frac{ 1 - p }{ 1 - L(p) } dp
@@ -278,159 +278,159 @@ <h2><span class="header-section-number">4.7</span> Zenga index (svyzenga)</h2>
 <h3><span class="header-section-number">4.7.1</span> Replication Example</h3>
 <p>While it is not possible to reproduce the exact results because their simulation includes random sampling, we can replicate a Monte Carlo experiment similar to the one presented by <span class="citation">Barabesi, Diana, and Perri (<label for="tufte-mn-82" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-82" class="margin-toggle">2016<span class="marginnote">Barabesi, Lucio, Giancarlo Diana, and Pier Francesco Perri. 2016. <span>“Linearization of Inequality Indices in the Design-Based Framework.”</span> <em>Statistics</em> 50 (5): 1161–72. <a href="https://doi.org/10.1080/02331888.2015.1135924">https://doi.org/10.1080/02331888.2015.1135924</a>.</span>)</span> in Table 2.</p>
 <p>Load and prepare the data set:</p>
-<div class="sourceCode" id="cb327"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb327-1"><a href="4.7-zenga-index-svyzenga.html#cb327-1" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb327-2"><a href="4.7-zenga-index-svyzenga.html#cb327-2" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb327-3"><a href="4.7-zenga-index-svyzenga.html#cb327-3" tabindex="-1"></a><span class="fu">library</span>(parallel)</span>
-<span id="cb327-4"><a href="4.7-zenga-index-svyzenga.html#cb327-4" tabindex="-1"></a></span>
-<span id="cb327-5"><a href="4.7-zenga-index-svyzenga.html#cb327-5" tabindex="-1"></a><span class="co"># create a temporary file on the local disk</span></span>
-<span id="cb327-6"><a href="4.7-zenga-index-svyzenga.html#cb327-6" tabindex="-1"></a>tf <span class="ot">&lt;-</span> <span class="fu">tempfile</span>()</span>
-<span id="cb327-7"><a href="4.7-zenga-index-svyzenga.html#cb327-7" tabindex="-1"></a></span>
-<span id="cb327-8"><a href="4.7-zenga-index-svyzenga.html#cb327-8" tabindex="-1"></a><span class="co"># store the location of the zip file</span></span>
-<span id="cb327-9"><a href="4.7-zenga-index-svyzenga.html#cb327-9" tabindex="-1"></a>data_zip <span class="ot">&lt;-</span></span>
-<span id="cb327-10"><a href="4.7-zenga-index-svyzenga.html#cb327-10" tabindex="-1"></a>  <span class="st">&quot;https://www.bancaditalia.it/statistiche/tematiche/indagini-famiglie-imprese/bilanci-famiglie/distribuzione-microdati/documenti/ind12_ascii.zip&quot;</span></span>
-<span id="cb327-11"><a href="4.7-zenga-index-svyzenga.html#cb327-11" tabindex="-1"></a></span>
-<span id="cb327-12"><a href="4.7-zenga-index-svyzenga.html#cb327-12" tabindex="-1"></a><span class="co"># download to the temporary file</span></span>
-<span id="cb327-13"><a href="4.7-zenga-index-svyzenga.html#cb327-13" tabindex="-1"></a><span class="fu">download.file</span>(data_zip , tf , <span class="at">mode =</span> <span class="st">&#39;wb&#39;</span>)</span>
-<span id="cb327-14"><a href="4.7-zenga-index-svyzenga.html#cb327-14" tabindex="-1"></a></span>
-<span id="cb327-15"><a href="4.7-zenga-index-svyzenga.html#cb327-15" tabindex="-1"></a><span class="co"># unzip the contents of the archive to a temporary directory</span></span>
-<span id="cb327-16"><a href="4.7-zenga-index-svyzenga.html#cb327-16" tabindex="-1"></a>td <span class="ot">&lt;-</span> <span class="fu">file.path</span>(<span class="fu">tempdir</span>() , <span class="st">&quot;shiw2012&quot;</span>)</span>
-<span id="cb327-17"><a href="4.7-zenga-index-svyzenga.html#cb327-17" tabindex="-1"></a>data_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> td)</span>
-<span id="cb327-18"><a href="4.7-zenga-index-svyzenga.html#cb327-18" tabindex="-1"></a></span>
-<span id="cb327-19"><a href="4.7-zenga-index-svyzenga.html#cb327-19" tabindex="-1"></a><span class="co"># load the household, consumption and income from SHIW (2012) survey data</span></span>
-<span id="cb327-20"><a href="4.7-zenga-index-svyzenga.html#cb327-20" tabindex="-1"></a>hhr.df <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="fu">grep</span>(<span class="st">&quot;carcom12&quot;</span> , data_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb327-21"><a href="4.7-zenga-index-svyzenga.html#cb327-21" tabindex="-1"></a>cns.df <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="fu">grep</span>(<span class="st">&quot;risfam12&quot;</span> , data_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb327-22"><a href="4.7-zenga-index-svyzenga.html#cb327-22" tabindex="-1"></a>inc.df <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="fu">grep</span>(<span class="st">&quot;rper12&quot;</span> , data_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb327-23"><a href="4.7-zenga-index-svyzenga.html#cb327-23" tabindex="-1"></a></span>
-<span id="cb327-24"><a href="4.7-zenga-index-svyzenga.html#cb327-24" tabindex="-1"></a><span class="co"># fixes names</span></span>
-<span id="cb327-25"><a href="4.7-zenga-index-svyzenga.html#cb327-25" tabindex="-1"></a><span class="fu">colnames</span>(cns.df)[<span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">colnames</span>(cns.df))[<span class="dv">1</span>]</span>
-<span id="cb327-26"><a href="4.7-zenga-index-svyzenga.html#cb327-26" tabindex="-1"></a></span>
-<span id="cb327-27"><a href="4.7-zenga-index-svyzenga.html#cb327-27" tabindex="-1"></a><span class="co"># household count should be 8151</span></span>
-<span id="cb327-28"><a href="4.7-zenga-index-svyzenga.html#cb327-28" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">sum</span>(<span class="sc">!</span><span class="fu">duplicated</span>(hhr.df<span class="sc">$</span>nquest)) <span class="sc">==</span> <span class="dv">8151</span>)</span>
-<span id="cb327-29"><a href="4.7-zenga-index-svyzenga.html#cb327-29" tabindex="-1"></a></span>
-<span id="cb327-30"><a href="4.7-zenga-index-svyzenga.html#cb327-30" tabindex="-1"></a><span class="co"># person count should be 20022</span></span>
-<span id="cb327-31"><a href="4.7-zenga-index-svyzenga.html#cb327-31" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">sum</span>(<span class="sc">!</span><span class="fu">duplicated</span>(<span class="fu">paste0</span>(</span>
-<span id="cb327-32"><a href="4.7-zenga-index-svyzenga.html#cb327-32" tabindex="-1"></a>  hhr.df<span class="sc">$</span>nquest , <span class="st">&quot;-&quot;</span> , hhr.df<span class="sc">$</span>nord</span>
-<span id="cb327-33"><a href="4.7-zenga-index-svyzenga.html#cb327-33" tabindex="-1"></a>))) <span class="sc">==</span> <span class="dv">20022</span>)</span>
-<span id="cb327-34"><a href="4.7-zenga-index-svyzenga.html#cb327-34" tabindex="-1"></a></span>
-<span id="cb327-35"><a href="4.7-zenga-index-svyzenga.html#cb327-35" tabindex="-1"></a><span class="co"># income recipients: should be 12986</span></span>
-<span id="cb327-36"><a href="4.7-zenga-index-svyzenga.html#cb327-36" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">sum</span>(hhr.df<span class="sc">$</span>PERC) <span class="sc">==</span> <span class="dv">12986</span>)</span>
-<span id="cb327-37"><a href="4.7-zenga-index-svyzenga.html#cb327-37" tabindex="-1"></a></span>
-<span id="cb327-38"><a href="4.7-zenga-index-svyzenga.html#cb327-38" tabindex="-1"></a><span class="co"># combine household roster and income datasets</span></span>
-<span id="cb327-39"><a href="4.7-zenga-index-svyzenga.html#cb327-39" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
-<span id="cb327-40"><a href="4.7-zenga-index-svyzenga.html#cb327-40" tabindex="-1"></a>  <span class="fu">merge</span>(</span>
-<span id="cb327-41"><a href="4.7-zenga-index-svyzenga.html#cb327-41" tabindex="-1"></a>    hhr.df ,</span>
-<span id="cb327-42"><a href="4.7-zenga-index-svyzenga.html#cb327-42" tabindex="-1"></a>    inc.df ,</span>
-<span id="cb327-43"><a href="4.7-zenga-index-svyzenga.html#cb327-43" tabindex="-1"></a>    <span class="at">by =</span> <span class="fu">c</span>(<span class="st">&quot;nquest&quot;</span> , <span class="st">&quot;nord&quot;</span>) ,</span>
-<span id="cb327-44"><a href="4.7-zenga-index-svyzenga.html#cb327-44" tabindex="-1"></a>    <span class="at">all.x =</span> <span class="cn">TRUE</span> ,</span>
-<span id="cb327-45"><a href="4.7-zenga-index-svyzenga.html#cb327-45" tabindex="-1"></a>    <span class="at">sort =</span> <span class="cn">FALSE</span></span>
-<span id="cb327-46"><a href="4.7-zenga-index-svyzenga.html#cb327-46" tabindex="-1"></a>  )</span>
-<span id="cb327-47"><a href="4.7-zenga-index-svyzenga.html#cb327-47" tabindex="-1"></a></span>
-<span id="cb327-48"><a href="4.7-zenga-index-svyzenga.html#cb327-48" tabindex="-1"></a><span class="co"># compute household-level income</span></span>
-<span id="cb327-49"><a href="4.7-zenga-index-svyzenga.html#cb327-49" tabindex="-1"></a>hinc.df <span class="ot">&lt;-</span></span>
-<span id="cb327-50"><a href="4.7-zenga-index-svyzenga.html#cb327-50" tabindex="-1"></a>  pop.df[pop.df<span class="sc">$</span>PERC <span class="sc">==</span> <span class="dv">1</span> ,</span>
-<span id="cb327-51"><a href="4.7-zenga-index-svyzenga.html#cb327-51" tabindex="-1"></a>         <span class="fu">c</span>(<span class="st">&quot;nquest&quot;</span> , <span class="st">&quot;nord&quot;</span> , <span class="st">&quot;PERC&quot;</span> , <span class="st">&quot;Y&quot;</span> , <span class="st">&quot;YL&quot;</span> , <span class="st">&quot;YM&quot;</span> , <span class="st">&quot;YT&quot;</span> , <span class="st">&quot;YC&quot;</span>) ,</span>
-<span id="cb327-52"><a href="4.7-zenga-index-svyzenga.html#cb327-52" tabindex="-1"></a>         drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
-<span id="cb327-53"><a href="4.7-zenga-index-svyzenga.html#cb327-53" tabindex="-1"></a></span>
-<span id="cb327-54"><a href="4.7-zenga-index-svyzenga.html#cb327-54" tabindex="-1"></a>hinc.df <span class="ot">&lt;-</span></span>
-<span id="cb327-55"><a href="4.7-zenga-index-svyzenga.html#cb327-55" tabindex="-1"></a>  <span class="fu">aggregate</span>(<span class="fu">rowSums</span>(hinc.df[, <span class="fu">c</span>(<span class="st">&quot;YL&quot;</span>  , <span class="st">&quot;YM&quot;</span> , <span class="st">&quot;YT&quot;</span>) , <span class="at">drop =</span> <span class="cn">FALSE</span>]) ,</span>
-<span id="cb327-56"><a href="4.7-zenga-index-svyzenga.html#cb327-56" tabindex="-1"></a>            <span class="fu">list</span>(<span class="st">&quot;nquest&quot;</span> <span class="ot">=</span> hinc.df<span class="sc">$</span>nquest) ,</span>
-<span id="cb327-57"><a href="4.7-zenga-index-svyzenga.html#cb327-57" tabindex="-1"></a>            sum ,</span>
-<span id="cb327-58"><a href="4.7-zenga-index-svyzenga.html#cb327-58" tabindex="-1"></a>            <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb327-59"><a href="4.7-zenga-index-svyzenga.html#cb327-59" tabindex="-1"></a></span>
-<span id="cb327-60"><a href="4.7-zenga-index-svyzenga.html#cb327-60" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
-<span id="cb327-61"><a href="4.7-zenga-index-svyzenga.html#cb327-61" tabindex="-1"></a>  <span class="fu">merge</span>(pop.df ,</span>
-<span id="cb327-62"><a href="4.7-zenga-index-svyzenga.html#cb327-62" tabindex="-1"></a>        hinc.df ,</span>
-<span id="cb327-63"><a href="4.7-zenga-index-svyzenga.html#cb327-63" tabindex="-1"></a>        <span class="at">by =</span> <span class="st">&quot;nquest&quot;</span> ,</span>
-<span id="cb327-64"><a href="4.7-zenga-index-svyzenga.html#cb327-64" tabindex="-1"></a>        <span class="at">all.x =</span> <span class="cn">TRUE</span> ,</span>
-<span id="cb327-65"><a href="4.7-zenga-index-svyzenga.html#cb327-65" tabindex="-1"></a>        <span class="at">sort =</span> <span class="cn">FALSE</span>)</span>
-<span id="cb327-66"><a href="4.7-zenga-index-svyzenga.html#cb327-66" tabindex="-1"></a></span>
-<span id="cb327-67"><a href="4.7-zenga-index-svyzenga.html#cb327-67" tabindex="-1"></a><span class="co"># combine with consumption data</span></span>
-<span id="cb327-68"><a href="4.7-zenga-index-svyzenga.html#cb327-68" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
-<span id="cb327-69"><a href="4.7-zenga-index-svyzenga.html#cb327-69" tabindex="-1"></a>  <span class="fu">merge</span>(pop.df ,</span>
-<span id="cb327-70"><a href="4.7-zenga-index-svyzenga.html#cb327-70" tabindex="-1"></a>        cns.df ,</span>
-<span id="cb327-71"><a href="4.7-zenga-index-svyzenga.html#cb327-71" tabindex="-1"></a>        <span class="at">by =</span> <span class="st">&quot;nquest&quot;</span> ,</span>
-<span id="cb327-72"><a href="4.7-zenga-index-svyzenga.html#cb327-72" tabindex="-1"></a>        <span class="at">all.x =</span> <span class="cn">TRUE</span> ,</span>
-<span id="cb327-73"><a href="4.7-zenga-index-svyzenga.html#cb327-73" tabindex="-1"></a>        <span class="at">sort =</span> <span class="cn">FALSE</span>)</span>
-<span id="cb327-74"><a href="4.7-zenga-index-svyzenga.html#cb327-74" tabindex="-1"></a></span>
-<span id="cb327-75"><a href="4.7-zenga-index-svyzenga.html#cb327-75" tabindex="-1"></a><span class="co"># treat household-level sample as the finite population</span></span>
-<span id="cb327-76"><a href="4.7-zenga-index-svyzenga.html#cb327-76" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
-<span id="cb327-77"><a href="4.7-zenga-index-svyzenga.html#cb327-77" tabindex="-1"></a>  pop.df[<span class="sc">!</span><span class="fu">duplicated</span>(pop.df<span class="sc">$</span>nquest) , , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span></code></pre></div>
+<div class="sourceCode" id="cb326"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb326-1"><a href="4.7-zenga-index-svyzenga.html#cb326-1" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb326-2"><a href="4.7-zenga-index-svyzenga.html#cb326-2" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb326-3"><a href="4.7-zenga-index-svyzenga.html#cb326-3" tabindex="-1"></a><span class="fu">library</span>(parallel)</span>
+<span id="cb326-4"><a href="4.7-zenga-index-svyzenga.html#cb326-4" tabindex="-1"></a></span>
+<span id="cb326-5"><a href="4.7-zenga-index-svyzenga.html#cb326-5" tabindex="-1"></a><span class="co"># create a temporary file on the local disk</span></span>
+<span id="cb326-6"><a href="4.7-zenga-index-svyzenga.html#cb326-6" tabindex="-1"></a>tf <span class="ot">&lt;-</span> <span class="fu">tempfile</span>()</span>
+<span id="cb326-7"><a href="4.7-zenga-index-svyzenga.html#cb326-7" tabindex="-1"></a></span>
+<span id="cb326-8"><a href="4.7-zenga-index-svyzenga.html#cb326-8" tabindex="-1"></a><span class="co"># store the location of the zip file</span></span>
+<span id="cb326-9"><a href="4.7-zenga-index-svyzenga.html#cb326-9" tabindex="-1"></a>data_zip <span class="ot">&lt;-</span></span>
+<span id="cb326-10"><a href="4.7-zenga-index-svyzenga.html#cb326-10" tabindex="-1"></a>  <span class="st">&quot;https://www.bancaditalia.it/statistiche/tematiche/indagini-famiglie-imprese/bilanci-famiglie/distribuzione-microdati/documenti/ind12_ascii.zip&quot;</span></span>
+<span id="cb326-11"><a href="4.7-zenga-index-svyzenga.html#cb326-11" tabindex="-1"></a></span>
+<span id="cb326-12"><a href="4.7-zenga-index-svyzenga.html#cb326-12" tabindex="-1"></a><span class="co"># download to the temporary file</span></span>
+<span id="cb326-13"><a href="4.7-zenga-index-svyzenga.html#cb326-13" tabindex="-1"></a><span class="fu">download.file</span>(data_zip , tf , <span class="at">mode =</span> <span class="st">&#39;wb&#39;</span>)</span>
+<span id="cb326-14"><a href="4.7-zenga-index-svyzenga.html#cb326-14" tabindex="-1"></a></span>
+<span id="cb326-15"><a href="4.7-zenga-index-svyzenga.html#cb326-15" tabindex="-1"></a><span class="co"># unzip the contents of the archive to a temporary directory</span></span>
+<span id="cb326-16"><a href="4.7-zenga-index-svyzenga.html#cb326-16" tabindex="-1"></a>td <span class="ot">&lt;-</span> <span class="fu">file.path</span>(<span class="fu">tempdir</span>() , <span class="st">&quot;shiw2012&quot;</span>)</span>
+<span id="cb326-17"><a href="4.7-zenga-index-svyzenga.html#cb326-17" tabindex="-1"></a>data_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> td)</span>
+<span id="cb326-18"><a href="4.7-zenga-index-svyzenga.html#cb326-18" tabindex="-1"></a></span>
+<span id="cb326-19"><a href="4.7-zenga-index-svyzenga.html#cb326-19" tabindex="-1"></a><span class="co"># load the household, consumption and income from SHIW (2012) survey data</span></span>
+<span id="cb326-20"><a href="4.7-zenga-index-svyzenga.html#cb326-20" tabindex="-1"></a>hhr.df <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="fu">grep</span>(<span class="st">&quot;carcom12&quot;</span> , data_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb326-21"><a href="4.7-zenga-index-svyzenga.html#cb326-21" tabindex="-1"></a>cns.df <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="fu">grep</span>(<span class="st">&quot;risfam12&quot;</span> , data_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb326-22"><a href="4.7-zenga-index-svyzenga.html#cb326-22" tabindex="-1"></a>inc.df <span class="ot">&lt;-</span> <span class="fu">read.csv</span>(<span class="fu">grep</span>(<span class="st">&quot;rper12&quot;</span> , data_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb326-23"><a href="4.7-zenga-index-svyzenga.html#cb326-23" tabindex="-1"></a></span>
+<span id="cb326-24"><a href="4.7-zenga-index-svyzenga.html#cb326-24" tabindex="-1"></a><span class="co"># fixes names</span></span>
+<span id="cb326-25"><a href="4.7-zenga-index-svyzenga.html#cb326-25" tabindex="-1"></a><span class="fu">colnames</span>(cns.df)[<span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">colnames</span>(cns.df))[<span class="dv">1</span>]</span>
+<span id="cb326-26"><a href="4.7-zenga-index-svyzenga.html#cb326-26" tabindex="-1"></a></span>
+<span id="cb326-27"><a href="4.7-zenga-index-svyzenga.html#cb326-27" tabindex="-1"></a><span class="co"># household count should be 8151</span></span>
+<span id="cb326-28"><a href="4.7-zenga-index-svyzenga.html#cb326-28" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">sum</span>(<span class="sc">!</span><span class="fu">duplicated</span>(hhr.df<span class="sc">$</span>nquest)) <span class="sc">==</span> <span class="dv">8151</span>)</span>
+<span id="cb326-29"><a href="4.7-zenga-index-svyzenga.html#cb326-29" tabindex="-1"></a></span>
+<span id="cb326-30"><a href="4.7-zenga-index-svyzenga.html#cb326-30" tabindex="-1"></a><span class="co"># person count should be 20022</span></span>
+<span id="cb326-31"><a href="4.7-zenga-index-svyzenga.html#cb326-31" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">sum</span>(<span class="sc">!</span><span class="fu">duplicated</span>(<span class="fu">paste0</span>(</span>
+<span id="cb326-32"><a href="4.7-zenga-index-svyzenga.html#cb326-32" tabindex="-1"></a>  hhr.df<span class="sc">$</span>nquest , <span class="st">&quot;-&quot;</span> , hhr.df<span class="sc">$</span>nord</span>
+<span id="cb326-33"><a href="4.7-zenga-index-svyzenga.html#cb326-33" tabindex="-1"></a>))) <span class="sc">==</span> <span class="dv">20022</span>)</span>
+<span id="cb326-34"><a href="4.7-zenga-index-svyzenga.html#cb326-34" tabindex="-1"></a></span>
+<span id="cb326-35"><a href="4.7-zenga-index-svyzenga.html#cb326-35" tabindex="-1"></a><span class="co"># income recipients: should be 12986</span></span>
+<span id="cb326-36"><a href="4.7-zenga-index-svyzenga.html#cb326-36" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">sum</span>(hhr.df<span class="sc">$</span>PERC) <span class="sc">==</span> <span class="dv">12986</span>)</span>
+<span id="cb326-37"><a href="4.7-zenga-index-svyzenga.html#cb326-37" tabindex="-1"></a></span>
+<span id="cb326-38"><a href="4.7-zenga-index-svyzenga.html#cb326-38" tabindex="-1"></a><span class="co"># combine household roster and income datasets</span></span>
+<span id="cb326-39"><a href="4.7-zenga-index-svyzenga.html#cb326-39" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
+<span id="cb326-40"><a href="4.7-zenga-index-svyzenga.html#cb326-40" tabindex="-1"></a>  <span class="fu">merge</span>(</span>
+<span id="cb326-41"><a href="4.7-zenga-index-svyzenga.html#cb326-41" tabindex="-1"></a>    hhr.df ,</span>
+<span id="cb326-42"><a href="4.7-zenga-index-svyzenga.html#cb326-42" tabindex="-1"></a>    inc.df ,</span>
+<span id="cb326-43"><a href="4.7-zenga-index-svyzenga.html#cb326-43" tabindex="-1"></a>    <span class="at">by =</span> <span class="fu">c</span>(<span class="st">&quot;nquest&quot;</span> , <span class="st">&quot;nord&quot;</span>) ,</span>
+<span id="cb326-44"><a href="4.7-zenga-index-svyzenga.html#cb326-44" tabindex="-1"></a>    <span class="at">all.x =</span> <span class="cn">TRUE</span> ,</span>
+<span id="cb326-45"><a href="4.7-zenga-index-svyzenga.html#cb326-45" tabindex="-1"></a>    <span class="at">sort =</span> <span class="cn">FALSE</span></span>
+<span id="cb326-46"><a href="4.7-zenga-index-svyzenga.html#cb326-46" tabindex="-1"></a>  )</span>
+<span id="cb326-47"><a href="4.7-zenga-index-svyzenga.html#cb326-47" tabindex="-1"></a></span>
+<span id="cb326-48"><a href="4.7-zenga-index-svyzenga.html#cb326-48" tabindex="-1"></a><span class="co"># compute household-level income</span></span>
+<span id="cb326-49"><a href="4.7-zenga-index-svyzenga.html#cb326-49" tabindex="-1"></a>hinc.df <span class="ot">&lt;-</span></span>
+<span id="cb326-50"><a href="4.7-zenga-index-svyzenga.html#cb326-50" tabindex="-1"></a>  pop.df[pop.df<span class="sc">$</span>PERC <span class="sc">==</span> <span class="dv">1</span> ,</span>
+<span id="cb326-51"><a href="4.7-zenga-index-svyzenga.html#cb326-51" tabindex="-1"></a>         <span class="fu">c</span>(<span class="st">&quot;nquest&quot;</span> , <span class="st">&quot;nord&quot;</span> , <span class="st">&quot;PERC&quot;</span> , <span class="st">&quot;Y&quot;</span> , <span class="st">&quot;YL&quot;</span> , <span class="st">&quot;YM&quot;</span> , <span class="st">&quot;YT&quot;</span> , <span class="st">&quot;YC&quot;</span>) ,</span>
+<span id="cb326-52"><a href="4.7-zenga-index-svyzenga.html#cb326-52" tabindex="-1"></a>         drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
+<span id="cb326-53"><a href="4.7-zenga-index-svyzenga.html#cb326-53" tabindex="-1"></a></span>
+<span id="cb326-54"><a href="4.7-zenga-index-svyzenga.html#cb326-54" tabindex="-1"></a>hinc.df <span class="ot">&lt;-</span></span>
+<span id="cb326-55"><a href="4.7-zenga-index-svyzenga.html#cb326-55" tabindex="-1"></a>  <span class="fu">aggregate</span>(<span class="fu">rowSums</span>(hinc.df[, <span class="fu">c</span>(<span class="st">&quot;YL&quot;</span>  , <span class="st">&quot;YM&quot;</span> , <span class="st">&quot;YT&quot;</span>) , <span class="at">drop =</span> <span class="cn">FALSE</span>]) ,</span>
+<span id="cb326-56"><a href="4.7-zenga-index-svyzenga.html#cb326-56" tabindex="-1"></a>            <span class="fu">list</span>(<span class="st">&quot;nquest&quot;</span> <span class="ot">=</span> hinc.df<span class="sc">$</span>nquest) ,</span>
+<span id="cb326-57"><a href="4.7-zenga-index-svyzenga.html#cb326-57" tabindex="-1"></a>            sum ,</span>
+<span id="cb326-58"><a href="4.7-zenga-index-svyzenga.html#cb326-58" tabindex="-1"></a>            <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb326-59"><a href="4.7-zenga-index-svyzenga.html#cb326-59" tabindex="-1"></a></span>
+<span id="cb326-60"><a href="4.7-zenga-index-svyzenga.html#cb326-60" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
+<span id="cb326-61"><a href="4.7-zenga-index-svyzenga.html#cb326-61" tabindex="-1"></a>  <span class="fu">merge</span>(pop.df ,</span>
+<span id="cb326-62"><a href="4.7-zenga-index-svyzenga.html#cb326-62" tabindex="-1"></a>        hinc.df ,</span>
+<span id="cb326-63"><a href="4.7-zenga-index-svyzenga.html#cb326-63" tabindex="-1"></a>        <span class="at">by =</span> <span class="st">&quot;nquest&quot;</span> ,</span>
+<span id="cb326-64"><a href="4.7-zenga-index-svyzenga.html#cb326-64" tabindex="-1"></a>        <span class="at">all.x =</span> <span class="cn">TRUE</span> ,</span>
+<span id="cb326-65"><a href="4.7-zenga-index-svyzenga.html#cb326-65" tabindex="-1"></a>        <span class="at">sort =</span> <span class="cn">FALSE</span>)</span>
+<span id="cb326-66"><a href="4.7-zenga-index-svyzenga.html#cb326-66" tabindex="-1"></a></span>
+<span id="cb326-67"><a href="4.7-zenga-index-svyzenga.html#cb326-67" tabindex="-1"></a><span class="co"># combine with consumption data</span></span>
+<span id="cb326-68"><a href="4.7-zenga-index-svyzenga.html#cb326-68" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
+<span id="cb326-69"><a href="4.7-zenga-index-svyzenga.html#cb326-69" tabindex="-1"></a>  <span class="fu">merge</span>(pop.df ,</span>
+<span id="cb326-70"><a href="4.7-zenga-index-svyzenga.html#cb326-70" tabindex="-1"></a>        cns.df ,</span>
+<span id="cb326-71"><a href="4.7-zenga-index-svyzenga.html#cb326-71" tabindex="-1"></a>        <span class="at">by =</span> <span class="st">&quot;nquest&quot;</span> ,</span>
+<span id="cb326-72"><a href="4.7-zenga-index-svyzenga.html#cb326-72" tabindex="-1"></a>        <span class="at">all.x =</span> <span class="cn">TRUE</span> ,</span>
+<span id="cb326-73"><a href="4.7-zenga-index-svyzenga.html#cb326-73" tabindex="-1"></a>        <span class="at">sort =</span> <span class="cn">FALSE</span>)</span>
+<span id="cb326-74"><a href="4.7-zenga-index-svyzenga.html#cb326-74" tabindex="-1"></a></span>
+<span id="cb326-75"><a href="4.7-zenga-index-svyzenga.html#cb326-75" tabindex="-1"></a><span class="co"># treat household-level sample as the finite population</span></span>
+<span id="cb326-76"><a href="4.7-zenga-index-svyzenga.html#cb326-76" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
+<span id="cb326-77"><a href="4.7-zenga-index-svyzenga.html#cb326-77" tabindex="-1"></a>  pop.df[<span class="sc">!</span><span class="fu">duplicated</span>(pop.df<span class="sc">$</span>nquest) , , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span></code></pre></div>
 <p>For the Monte Carlo experiment, we take <code>5000</code> samples of (expected) size <code>1000</code> using Poisson sampling<label for="tufte-sn-5" class="margin-toggle sidenote-number">5</label><input type="checkbox" id="tufte-sn-5" class="margin-toggle"><span class="sidenote"><span class="sidenote-number">5</span> but not Conditional Poisson Sampling.</span>:</p>
-<div class="sourceCode" id="cb328"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb328-1"><a href="4.7-zenga-index-svyzenga.html#cb328-1" tabindex="-1"></a><span class="co"># set up monte carlo attributes</span></span>
-<span id="cb328-2"><a href="4.7-zenga-index-svyzenga.html#cb328-2" tabindex="-1"></a>mc.rep <span class="ot">&lt;-</span> 5000L</span>
-<span id="cb328-3"><a href="4.7-zenga-index-svyzenga.html#cb328-3" tabindex="-1"></a>n.size <span class="ot">=</span> 1000L</span>
-<span id="cb328-4"><a href="4.7-zenga-index-svyzenga.html#cb328-4" tabindex="-1"></a>N.size <span class="ot">=</span> <span class="fu">nrow</span>(pop.df)</span>
-<span id="cb328-5"><a href="4.7-zenga-index-svyzenga.html#cb328-5" tabindex="-1"></a></span>
-<span id="cb328-6"><a href="4.7-zenga-index-svyzenga.html#cb328-6" tabindex="-1"></a><span class="co"># calculate first order probabilities</span></span>
-<span id="cb328-7"><a href="4.7-zenga-index-svyzenga.html#cb328-7" tabindex="-1"></a>pop.df<span class="sc">$</span>pik <span class="ot">&lt;-</span></span>
-<span id="cb328-8"><a href="4.7-zenga-index-svyzenga.html#cb328-8" tabindex="-1"></a>  n.size <span class="sc">*</span> (<span class="fu">abs</span>(pop.df<span class="sc">$</span>C) <span class="sc">/</span> <span class="fu">sum</span>(<span class="fu">abs</span>(pop.df<span class="sc">$</span>C)))</span>
-<span id="cb328-9"><a href="4.7-zenga-index-svyzenga.html#cb328-9" tabindex="-1"></a></span>
-<span id="cb328-10"><a href="4.7-zenga-index-svyzenga.html#cb328-10" tabindex="-1"></a><span class="co"># calculate second order probabilities</span></span>
-<span id="cb328-11"><a href="4.7-zenga-index-svyzenga.html#cb328-11" tabindex="-1"></a>pikl <span class="ot">&lt;-</span> pop.df<span class="sc">$</span>pik <span class="sc">%*%</span> <span class="fu">t</span>(pop.df<span class="sc">$</span>pik)</span>
-<span id="cb328-12"><a href="4.7-zenga-index-svyzenga.html#cb328-12" tabindex="-1"></a><span class="fu">diag</span>(pikl) <span class="ot">&lt;-</span> pop.df<span class="sc">$</span>pik</span>
-<span id="cb328-13"><a href="4.7-zenga-index-svyzenga.html#cb328-13" tabindex="-1"></a></span>
-<span id="cb328-14"><a href="4.7-zenga-index-svyzenga.html#cb328-14" tabindex="-1"></a><span class="co"># set random number seed</span></span>
-<span id="cb328-15"><a href="4.7-zenga-index-svyzenga.html#cb328-15" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">1997</span>)</span>
-<span id="cb328-16"><a href="4.7-zenga-index-svyzenga.html#cb328-16" tabindex="-1"></a></span>
-<span id="cb328-17"><a href="4.7-zenga-index-svyzenga.html#cb328-17" tabindex="-1"></a><span class="co"># create list of survey design objects</span></span>
-<span id="cb328-18"><a href="4.7-zenga-index-svyzenga.html#cb328-18" tabindex="-1"></a><span class="co"># using poisson sampling</span></span>
-<span id="cb328-19"><a href="4.7-zenga-index-svyzenga.html#cb328-19" tabindex="-1"></a>survey.list <span class="ot">&lt;-</span></span>
-<span id="cb328-20"><a href="4.7-zenga-index-svyzenga.html#cb328-20" tabindex="-1"></a>  <span class="fu">lapply</span>(<span class="fu">seq_len</span>(mc.rep) ,</span>
-<span id="cb328-21"><a href="4.7-zenga-index-svyzenga.html#cb328-21" tabindex="-1"></a>         <span class="cf">function</span>(this.rep) {</span>
-<span id="cb328-22"><a href="4.7-zenga-index-svyzenga.html#cb328-22" tabindex="-1"></a>           smp.ind <span class="ot">&lt;-</span> <span class="fu">which</span>(<span class="fu">runif</span>(N.size) <span class="sc">&lt;=</span> pop.df<span class="sc">$</span>pik)</span>
-<span id="cb328-23"><a href="4.7-zenga-index-svyzenga.html#cb328-23" tabindex="-1"></a>           smp.df <span class="ot">&lt;-</span> pop.df[smp.ind , , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
-<span id="cb328-24"><a href="4.7-zenga-index-svyzenga.html#cb328-24" tabindex="-1"></a>           <span class="fu">svydesign</span>(</span>
-<span id="cb328-25"><a href="4.7-zenga-index-svyzenga.html#cb328-25" tabindex="-1"></a>             <span class="at">ids =</span> <span class="sc">~</span> nquest ,</span>
-<span id="cb328-26"><a href="4.7-zenga-index-svyzenga.html#cb328-26" tabindex="-1"></a>             <span class="at">data =</span> smp.df ,</span>
-<span id="cb328-27"><a href="4.7-zenga-index-svyzenga.html#cb328-27" tabindex="-1"></a>             <span class="at">fpc =</span> <span class="sc">~</span> pik ,</span>
-<span id="cb328-28"><a href="4.7-zenga-index-svyzenga.html#cb328-28" tabindex="-1"></a>             <span class="at">nest =</span> <span class="cn">FALSE</span> ,</span>
-<span id="cb328-29"><a href="4.7-zenga-index-svyzenga.html#cb328-29" tabindex="-1"></a>             <span class="at">pps =</span> <span class="fu">ppsmat</span>(pikl[smp.ind , smp.ind]) ,</span>
-<span id="cb328-30"><a href="4.7-zenga-index-svyzenga.html#cb328-30" tabindex="-1"></a>             <span class="at">variance =</span> <span class="st">&quot;HT&quot;</span></span>
-<span id="cb328-31"><a href="4.7-zenga-index-svyzenga.html#cb328-31" tabindex="-1"></a>           )</span>
-<span id="cb328-32"><a href="4.7-zenga-index-svyzenga.html#cb328-32" tabindex="-1"></a>         })</span></code></pre></div>
+<div class="sourceCode" id="cb327"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb327-1"><a href="4.7-zenga-index-svyzenga.html#cb327-1" tabindex="-1"></a><span class="co"># set up monte carlo attributes</span></span>
+<span id="cb327-2"><a href="4.7-zenga-index-svyzenga.html#cb327-2" tabindex="-1"></a>mc.rep <span class="ot">&lt;-</span> 5000L</span>
+<span id="cb327-3"><a href="4.7-zenga-index-svyzenga.html#cb327-3" tabindex="-1"></a>n.size <span class="ot">=</span> 1000L</span>
+<span id="cb327-4"><a href="4.7-zenga-index-svyzenga.html#cb327-4" tabindex="-1"></a>N.size <span class="ot">=</span> <span class="fu">nrow</span>(pop.df)</span>
+<span id="cb327-5"><a href="4.7-zenga-index-svyzenga.html#cb327-5" tabindex="-1"></a></span>
+<span id="cb327-6"><a href="4.7-zenga-index-svyzenga.html#cb327-6" tabindex="-1"></a><span class="co"># calculate first order probabilities</span></span>
+<span id="cb327-7"><a href="4.7-zenga-index-svyzenga.html#cb327-7" tabindex="-1"></a>pop.df<span class="sc">$</span>pik <span class="ot">&lt;-</span></span>
+<span id="cb327-8"><a href="4.7-zenga-index-svyzenga.html#cb327-8" tabindex="-1"></a>  n.size <span class="sc">*</span> (<span class="fu">abs</span>(pop.df<span class="sc">$</span>C) <span class="sc">/</span> <span class="fu">sum</span>(<span class="fu">abs</span>(pop.df<span class="sc">$</span>C)))</span>
+<span id="cb327-9"><a href="4.7-zenga-index-svyzenga.html#cb327-9" tabindex="-1"></a></span>
+<span id="cb327-10"><a href="4.7-zenga-index-svyzenga.html#cb327-10" tabindex="-1"></a><span class="co"># calculate second order probabilities</span></span>
+<span id="cb327-11"><a href="4.7-zenga-index-svyzenga.html#cb327-11" tabindex="-1"></a>pikl <span class="ot">&lt;-</span> pop.df<span class="sc">$</span>pik <span class="sc">%*%</span> <span class="fu">t</span>(pop.df<span class="sc">$</span>pik)</span>
+<span id="cb327-12"><a href="4.7-zenga-index-svyzenga.html#cb327-12" tabindex="-1"></a><span class="fu">diag</span>(pikl) <span class="ot">&lt;-</span> pop.df<span class="sc">$</span>pik</span>
+<span id="cb327-13"><a href="4.7-zenga-index-svyzenga.html#cb327-13" tabindex="-1"></a></span>
+<span id="cb327-14"><a href="4.7-zenga-index-svyzenga.html#cb327-14" tabindex="-1"></a><span class="co"># set random number seed</span></span>
+<span id="cb327-15"><a href="4.7-zenga-index-svyzenga.html#cb327-15" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">1997</span>)</span>
+<span id="cb327-16"><a href="4.7-zenga-index-svyzenga.html#cb327-16" tabindex="-1"></a></span>
+<span id="cb327-17"><a href="4.7-zenga-index-svyzenga.html#cb327-17" tabindex="-1"></a><span class="co"># create list of survey design objects</span></span>
+<span id="cb327-18"><a href="4.7-zenga-index-svyzenga.html#cb327-18" tabindex="-1"></a><span class="co"># using poisson sampling</span></span>
+<span id="cb327-19"><a href="4.7-zenga-index-svyzenga.html#cb327-19" tabindex="-1"></a>survey.list <span class="ot">&lt;-</span></span>
+<span id="cb327-20"><a href="4.7-zenga-index-svyzenga.html#cb327-20" tabindex="-1"></a>  <span class="fu">lapply</span>(<span class="fu">seq_len</span>(mc.rep) ,</span>
+<span id="cb327-21"><a href="4.7-zenga-index-svyzenga.html#cb327-21" tabindex="-1"></a>         <span class="cf">function</span>(this.rep) {</span>
+<span id="cb327-22"><a href="4.7-zenga-index-svyzenga.html#cb327-22" tabindex="-1"></a>           smp.ind <span class="ot">&lt;-</span> <span class="fu">which</span>(<span class="fu">runif</span>(N.size) <span class="sc">&lt;=</span> pop.df<span class="sc">$</span>pik)</span>
+<span id="cb327-23"><a href="4.7-zenga-index-svyzenga.html#cb327-23" tabindex="-1"></a>           smp.df <span class="ot">&lt;-</span> pop.df[smp.ind , , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
+<span id="cb327-24"><a href="4.7-zenga-index-svyzenga.html#cb327-24" tabindex="-1"></a>           <span class="fu">svydesign</span>(</span>
+<span id="cb327-25"><a href="4.7-zenga-index-svyzenga.html#cb327-25" tabindex="-1"></a>             <span class="at">ids =</span> <span class="sc">~</span> nquest ,</span>
+<span id="cb327-26"><a href="4.7-zenga-index-svyzenga.html#cb327-26" tabindex="-1"></a>             <span class="at">data =</span> smp.df ,</span>
+<span id="cb327-27"><a href="4.7-zenga-index-svyzenga.html#cb327-27" tabindex="-1"></a>             <span class="at">fpc =</span> <span class="sc">~</span> pik ,</span>
+<span id="cb327-28"><a href="4.7-zenga-index-svyzenga.html#cb327-28" tabindex="-1"></a>             <span class="at">nest =</span> <span class="cn">FALSE</span> ,</span>
+<span id="cb327-29"><a href="4.7-zenga-index-svyzenga.html#cb327-29" tabindex="-1"></a>             <span class="at">pps =</span> <span class="fu">ppsmat</span>(pikl[smp.ind , smp.ind]) ,</span>
+<span id="cb327-30"><a href="4.7-zenga-index-svyzenga.html#cb327-30" tabindex="-1"></a>             <span class="at">variance =</span> <span class="st">&quot;HT&quot;</span></span>
+<span id="cb327-31"><a href="4.7-zenga-index-svyzenga.html#cb327-31" tabindex="-1"></a>           )</span>
+<span id="cb327-32"><a href="4.7-zenga-index-svyzenga.html#cb327-32" tabindex="-1"></a>         })</span></code></pre></div>
 <p>… and estimate the Zenga index using each sample:</p>
-<div class="sourceCode" id="cb329"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb329-1"><a href="4.7-zenga-index-svyzenga.html#cb329-1" tabindex="-1"></a><span class="co"># estimate zenga index for each sample</span></span>
-<span id="cb329-2"><a href="4.7-zenga-index-svyzenga.html#cb329-2" tabindex="-1"></a>zenga.estimate.list <span class="ot">&lt;-</span></span>
-<span id="cb329-3"><a href="4.7-zenga-index-svyzenga.html#cb329-3" tabindex="-1"></a>  <span class="fu">lapply</span>(survey.list ,</span>
-<span id="cb329-4"><a href="4.7-zenga-index-svyzenga.html#cb329-4" tabindex="-1"></a>         <span class="cf">function</span>(this.sample) {</span>
-<span id="cb329-5"><a href="4.7-zenga-index-svyzenga.html#cb329-5" tabindex="-1"></a>           <span class="fu">svyzenga</span>( <span class="sc">~</span> x ,</span>
-<span id="cb329-6"><a href="4.7-zenga-index-svyzenga.html#cb329-6" tabindex="-1"></a>                     <span class="fu">subset</span>(this.sample , x <span class="sc">&gt;</span> <span class="dv">0</span>) ,</span>
-<span id="cb329-7"><a href="4.7-zenga-index-svyzenga.html#cb329-7" tabindex="-1"></a>                     <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
-<span id="cb329-8"><a href="4.7-zenga-index-svyzenga.html#cb329-8" tabindex="-1"></a>         })</span></code></pre></div>
+<div class="sourceCode" id="cb328"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb328-1"><a href="4.7-zenga-index-svyzenga.html#cb328-1" tabindex="-1"></a><span class="co"># estimate zenga index for each sample</span></span>
+<span id="cb328-2"><a href="4.7-zenga-index-svyzenga.html#cb328-2" tabindex="-1"></a>zenga.estimate.list <span class="ot">&lt;-</span></span>
+<span id="cb328-3"><a href="4.7-zenga-index-svyzenga.html#cb328-3" tabindex="-1"></a>  <span class="fu">lapply</span>(survey.list ,</span>
+<span id="cb328-4"><a href="4.7-zenga-index-svyzenga.html#cb328-4" tabindex="-1"></a>         <span class="cf">function</span>(this.sample) {</span>
+<span id="cb328-5"><a href="4.7-zenga-index-svyzenga.html#cb328-5" tabindex="-1"></a>           <span class="fu">svyzenga</span>( <span class="sc">~</span> x ,</span>
+<span id="cb328-6"><a href="4.7-zenga-index-svyzenga.html#cb328-6" tabindex="-1"></a>                     <span class="fu">subset</span>(this.sample , x <span class="sc">&gt;</span> <span class="dv">0</span>) ,</span>
+<span id="cb328-7"><a href="4.7-zenga-index-svyzenga.html#cb328-7" tabindex="-1"></a>                     <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
+<span id="cb328-8"><a href="4.7-zenga-index-svyzenga.html#cb328-8" tabindex="-1"></a>         })</span></code></pre></div>
 <p>Then, we evaluate the Percentage Relative Bias (PRB) of the Zenga index estimator. Under this scenario, the PRB of the Zenga index estimator is 0.3397%, a result similar to the <code>0.321</code> shown in Table 2.</p>
-<div class="sourceCode" id="cb330"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb330-1"><a href="4.7-zenga-index-svyzenga.html#cb330-1" tabindex="-1"></a><span class="co"># compute the (finite population) Zenga index parameter</span></span>
-<span id="cb330-2"><a href="4.7-zenga-index-svyzenga.html#cb330-2" tabindex="-1"></a>theta.pop <span class="ot">&lt;-</span></span>
-<span id="cb330-3"><a href="4.7-zenga-index-svyzenga.html#cb330-3" tabindex="-1"></a>  convey<span class="sc">:::</span><span class="fu">CalcZenga</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>))</span>
-<span id="cb330-4"><a href="4.7-zenga-index-svyzenga.html#cb330-4" tabindex="-1"></a></span>
-<span id="cb330-5"><a href="4.7-zenga-index-svyzenga.html#cb330-5" tabindex="-1"></a><span class="co"># estimate the expected value of the Zenga index estimator</span></span>
-<span id="cb330-6"><a href="4.7-zenga-index-svyzenga.html#cb330-6" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
-<span id="cb330-7"><a href="4.7-zenga-index-svyzenga.html#cb330-7" tabindex="-1"></a>theta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(zenga.estimate.list , coef))</span>
-<span id="cb330-8"><a href="4.7-zenga-index-svyzenga.html#cb330-8" tabindex="-1"></a></span>
-<span id="cb330-9"><a href="4.7-zenga-index-svyzenga.html#cb330-9" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
-<span id="cb330-10"><a href="4.7-zenga-index-svyzenga.html#cb330-10" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb329"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb329-1"><a href="4.7-zenga-index-svyzenga.html#cb329-1" tabindex="-1"></a><span class="co"># compute the (finite population) Zenga index parameter</span></span>
+<span id="cb329-2"><a href="4.7-zenga-index-svyzenga.html#cb329-2" tabindex="-1"></a>theta.pop <span class="ot">&lt;-</span></span>
+<span id="cb329-3"><a href="4.7-zenga-index-svyzenga.html#cb329-3" tabindex="-1"></a>  convey<span class="sc">:::</span><span class="fu">CalcZenga</span>(pop.df<span class="sc">$</span>x , <span class="fu">ifelse</span>(pop.df<span class="sc">$</span>x <span class="sc">&gt;</span> <span class="dv">0</span> , <span class="dv">1</span> , <span class="dv">0</span>))</span>
+<span id="cb329-4"><a href="4.7-zenga-index-svyzenga.html#cb329-4" tabindex="-1"></a></span>
+<span id="cb329-5"><a href="4.7-zenga-index-svyzenga.html#cb329-5" tabindex="-1"></a><span class="co"># estimate the expected value of the Zenga index estimator</span></span>
+<span id="cb329-6"><a href="4.7-zenga-index-svyzenga.html#cb329-6" tabindex="-1"></a><span class="co"># using the average of the estimates</span></span>
+<span id="cb329-7"><a href="4.7-zenga-index-svyzenga.html#cb329-7" tabindex="-1"></a>theta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(zenga.estimate.list , coef))</span>
+<span id="cb329-8"><a href="4.7-zenga-index-svyzenga.html#cb329-8" tabindex="-1"></a></span>
+<span id="cb329-9"><a href="4.7-zenga-index-svyzenga.html#cb329-9" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
+<span id="cb329-10"><a href="4.7-zenga-index-svyzenga.html#cb329-10" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (theta.exp <span class="sc">/</span> theta.pop <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
 <pre><code>## [1] 0.3396837</code></pre>
 <p>Then, we evaluate the PRB of the variance estimator of the Zenga index estimator. Under this scenario, the PRB of the Zenga index variance estimator is -0.4954%, another result similar to the <code>-0.600</code> shown in Table 2.</p>
-<div class="sourceCode" id="cb332"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb332-1"><a href="4.7-zenga-index-svyzenga.html#cb332-1" tabindex="-1"></a><span class="co"># estimate the variance of the Zenga index estimator</span></span>
-<span id="cb332-2"><a href="4.7-zenga-index-svyzenga.html#cb332-2" tabindex="-1"></a><span class="co"># using the variance of the estimates</span></span>
-<span id="cb332-3"><a href="4.7-zenga-index-svyzenga.html#cb332-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span> <span class="fu">var</span>(<span class="fu">sapply</span>(zenga.estimate.list , coef)))</span></code></pre></div>
+<div class="sourceCode" id="cb331"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb331-1"><a href="4.7-zenga-index-svyzenga.html#cb331-1" tabindex="-1"></a><span class="co"># estimate the variance of the Zenga index estimator</span></span>
+<span id="cb331-2"><a href="4.7-zenga-index-svyzenga.html#cb331-2" tabindex="-1"></a><span class="co"># using the variance of the estimates</span></span>
+<span id="cb331-3"><a href="4.7-zenga-index-svyzenga.html#cb331-3" tabindex="-1"></a>(vartheta.popest <span class="ot">&lt;-</span> <span class="fu">var</span>(<span class="fu">sapply</span>(zenga.estimate.list , coef)))</span></code></pre></div>
 <pre><code>## [1] 9.47244e-05</code></pre>
-<div class="sourceCode" id="cb334"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb334-1"><a href="4.7-zenga-index-svyzenga.html#cb334-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Zenga index variance estimator</span></span>
-<span id="cb334-2"><a href="4.7-zenga-index-svyzenga.html#cb334-2" tabindex="-1"></a><span class="co"># using the expected of the variance estimates</span></span>
-<span id="cb334-3"><a href="4.7-zenga-index-svyzenga.html#cb334-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(zenga.estimate.list , vcov)))</span></code></pre></div>
+<div class="sourceCode" id="cb333"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb333-1"><a href="4.7-zenga-index-svyzenga.html#cb333-1" tabindex="-1"></a><span class="co"># estimate the expected value of the Zenga index variance estimator</span></span>
+<span id="cb333-2"><a href="4.7-zenga-index-svyzenga.html#cb333-2" tabindex="-1"></a><span class="co"># using the expected of the variance estimates</span></span>
+<span id="cb333-3"><a href="4.7-zenga-index-svyzenga.html#cb333-3" tabindex="-1"></a>(vartheta.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">sapply</span>(zenga.estimate.list , vcov)))</span></code></pre></div>
 <pre><code>## [1] 9.425515e-05</code></pre>
-<div class="sourceCode" id="cb336"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb336-1"><a href="4.7-zenga-index-svyzenga.html#cb336-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
-<span id="cb336-2"><a href="4.7-zenga-index-svyzenga.html#cb336-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb335"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb335-1"><a href="4.7-zenga-index-svyzenga.html#cb335-1" tabindex="-1"></a><span class="co"># estimate the percentage relative bias</span></span>
+<span id="cb335-2"><a href="4.7-zenga-index-svyzenga.html#cb335-2" tabindex="-1"></a><span class="dv">100</span> <span class="sc">*</span> (vartheta.exp <span class="sc">/</span> vartheta.popest <span class="sc">-</span> <span class="dv">1</span>)</span></code></pre></div>
 <pre><code>## [1] -0.4953863</code></pre>
 <p>Next, we evaluate the Percentage Coverage Rate (PCR). In theory, under repeated sampling, the estimated 95% CIs should cover the population parameter 95% of the time. We can evaluate that using:</p>
-<div class="sourceCode" id="cb338"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb338-1"><a href="4.7-zenga-index-svyzenga.html#cb338-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Zenga index</span></span>
-<span id="cb338-2"><a href="4.7-zenga-index-svyzenga.html#cb338-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
-<span id="cb338-3"><a href="4.7-zenga-index-svyzenga.html#cb338-3" tabindex="-1"></a>est.cis <span class="ot">&lt;-</span></span>
-<span id="cb338-4"><a href="4.7-zenga-index-svyzenga.html#cb338-4" tabindex="-1"></a>  <span class="fu">t</span>(<span class="fu">sapply</span>(zenga.estimate.list, <span class="cf">function</span>(this.stat)</span>
-<span id="cb338-5"><a href="4.7-zenga-index-svyzenga.html#cb338-5" tabindex="-1"></a>    <span class="fu">c</span>(<span class="fu">confint</span>(this.stat))))</span>
-<span id="cb338-6"><a href="4.7-zenga-index-svyzenga.html#cb338-6" tabindex="-1"></a></span>
-<span id="cb338-7"><a href="4.7-zenga-index-svyzenga.html#cb338-7" tabindex="-1"></a><span class="co"># evaluate</span></span>
-<span id="cb338-8"><a href="4.7-zenga-index-svyzenga.html#cb338-8" tabindex="-1"></a><span class="fu">prop.table</span>(<span class="fu">table</span>((theta.pop <span class="sc">&gt;</span> est.cis[, <span class="dv">1</span>]) <span class="sc">&amp;</span></span>
-<span id="cb338-9"><a href="4.7-zenga-index-svyzenga.html#cb338-9" tabindex="-1"></a>                   (theta.pop <span class="sc">&lt;</span> est.cis[, <span class="dv">2</span>])))</span></code></pre></div>
+<div class="sourceCode" id="cb337"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb337-1"><a href="4.7-zenga-index-svyzenga.html#cb337-1" tabindex="-1"></a><span class="co"># estimate confidence intervals of the Zenga index</span></span>
+<span id="cb337-2"><a href="4.7-zenga-index-svyzenga.html#cb337-2" tabindex="-1"></a><span class="co"># for each of the samples</span></span>
+<span id="cb337-3"><a href="4.7-zenga-index-svyzenga.html#cb337-3" tabindex="-1"></a>est.cis <span class="ot">&lt;-</span></span>
+<span id="cb337-4"><a href="4.7-zenga-index-svyzenga.html#cb337-4" tabindex="-1"></a>  <span class="fu">t</span>(<span class="fu">sapply</span>(zenga.estimate.list, <span class="cf">function</span>(this.stat)</span>
+<span id="cb337-5"><a href="4.7-zenga-index-svyzenga.html#cb337-5" tabindex="-1"></a>    <span class="fu">c</span>(<span class="fu">confint</span>(this.stat))))</span>
+<span id="cb337-6"><a href="4.7-zenga-index-svyzenga.html#cb337-6" tabindex="-1"></a></span>
+<span id="cb337-7"><a href="4.7-zenga-index-svyzenga.html#cb337-7" tabindex="-1"></a><span class="co"># evaluate</span></span>
+<span id="cb337-8"><a href="4.7-zenga-index-svyzenga.html#cb337-8" tabindex="-1"></a><span class="fu">prop.table</span>(<span class="fu">table</span>((theta.pop <span class="sc">&gt;</span> est.cis[, <span class="dv">1</span>]) <span class="sc">&amp;</span></span>
+<span id="cb337-9"><a href="4.7-zenga-index-svyzenga.html#cb337-9" tabindex="-1"></a>                   (theta.pop <span class="sc">&lt;</span> est.cis[, <span class="dv">2</span>])))</span></code></pre></div>
 <pre><code>## 
 ##  FALSE   TRUE 
 ## 0.0548 0.9452</code></pre>
diff --git a/docs/4.8-social-welfare-function-based-measures.html b/docs/4.8-social-welfare-function-based-measures.html
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@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
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+++ b/docs/4.9-atkinson-index-svyatk.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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+<meta name="date" content="2023-11-07" />
 
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@@ -253,12 +253,12 @@
 <div class="col-sm-12">
 <div id="atkinson-index-svyatk" class="section level2" number="4.9">
 <h2><span class="header-section-number">4.9</span> Atkinson index (svyatk)</h2>
-<div class="sourceCode" id="cb340"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb340-1"><a href="4.9-atkinson-index-svyatk.html#cb340-1" tabindex="-1"></a>✔️ is defined <span class="cf">in</span> terms of an interpretable utility <span class="cf">function</span></span>
-<span id="cb340-2"><a href="4.9-atkinson-index-svyatk.html#cb340-2" tabindex="-1"></a>✔️ has a <span class="fu">direct</span> (but non<span class="sc">-</span>linear) relationship to <span class="st">`</span><span class="at">svygei</span><span class="st">`</span></span>
-<span id="cb340-3"><a href="4.9-atkinson-index-svyatk.html#cb340-3" tabindex="-1"></a>✔️ has an interpretable inequality aversion parameter</span>
-<span id="cb340-4"><a href="4.9-atkinson-index-svyatk.html#cb340-4" tabindex="-1"></a>❌ does not handle zeroes or negative incomes</span>
-<span id="cb340-5"><a href="4.9-atkinson-index-svyatk.html#cb340-5" tabindex="-1"></a>❌ the decomposition interpretation is not exactly the same as the GEI, but very <span class="fu">similar</span> (not implemented, though)</span>
-<span id="cb340-6"><a href="4.9-atkinson-index-svyatk.html#cb340-6" tabindex="-1"></a>❌ not very common</span></code></pre></div>
+<div class="sourceCode" id="cb339"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb339-1"><a href="4.9-atkinson-index-svyatk.html#cb339-1" tabindex="-1"></a>✔️ is defined <span class="cf">in</span> terms of an interpretable utility <span class="cf">function</span></span>
+<span id="cb339-2"><a href="4.9-atkinson-index-svyatk.html#cb339-2" tabindex="-1"></a>✔️ has a <span class="fu">direct</span> (but non<span class="sc">-</span>linear) relationship to <span class="st">`</span><span class="at">svygei</span><span class="st">`</span></span>
+<span id="cb339-3"><a href="4.9-atkinson-index-svyatk.html#cb339-3" tabindex="-1"></a>✔️ has an interpretable inequality aversion parameter</span>
+<span id="cb339-4"><a href="4.9-atkinson-index-svyatk.html#cb339-4" tabindex="-1"></a>❌ does not handle zeroes or negative incomes</span>
+<span id="cb339-5"><a href="4.9-atkinson-index-svyatk.html#cb339-5" tabindex="-1"></a>❌ the decomposition interpretation is not exactly the same as the GEI, but very <span class="fu">similar</span> (not implemented, though)</span>
+<span id="cb339-6"><a href="4.9-atkinson-index-svyatk.html#cb339-6" tabindex="-1"></a>❌ not very common</span></code></pre></div>
 <p><span class="citation">Dalton (<label for="tufte-mn-85" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-85" class="margin-toggle">1920<span class="marginnote">Dalton, Hugh. 1920. <span>“The Measurement of the Inequality of Incomes.”</span> <em>The Economic Journal</em> 30 (September). <a href="https://doi.org/10.2307/2223525">https://doi.org/10.2307/2223525</a>.</span>)</span> pointed out one of the most important facts about the economic theory
 of income inequality measurement: every income inequality measure has an implicit
 SWF.<label for="tufte-sn-6" class="margin-toggle sidenote-number">6</label><input type="checkbox" id="tufte-sn-6" class="margin-toggle"><span class="sidenote"><span class="sidenote-number">6</span> This is the subject of an interesting discussion between the British and the Italian schools of inequality measurement.</span>
@@ -326,38 +326,38 @@ <h2><span class="header-section-number">4.9</span> Atkinson index (svyatk)</h2>
 <h3><span class="header-section-number">4.9.1</span> Replication Example</h3>
 <p>In July 2006, <span class="citation">Jenkins (<label for="tufte-mn-92" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-92" class="margin-toggle">2008<span class="marginnote">Jenkins, Stephen. 2008. <span>“Estimation and Interpretation of Measures of Inequality, Poverty, and Social Welfare Using Stata.”</span> North American Stata Users' Group Meetings 2006. Stata Users Group. <a href="http://EconPapers.repec.org/RePEc:boc:asug06:16">http://EconPapers.repec.org/RePEc:boc:asug06:16</a>.</span>)</span> presented at the North American Stata Users’ Group Meetings on the stata Atkinson Index command. The example below reproduces those statistics.</p>
 <p>Load and prepare the same data set:</p>
-<div class="sourceCode" id="cb341"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb341-1"><a href="4.9-atkinson-index-svyatk.html#cb341-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb341-2"><a href="4.9-atkinson-index-svyatk.html#cb341-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb341-3"><a href="4.9-atkinson-index-svyatk.html#cb341-3" tabindex="-1"></a></span>
-<span id="cb341-4"><a href="4.9-atkinson-index-svyatk.html#cb341-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb341-5"><a href="4.9-atkinson-index-svyatk.html#cb341-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb341-6"><a href="4.9-atkinson-index-svyatk.html#cb341-6" tabindex="-1"></a></span>
-<span id="cb341-7"><a href="4.9-atkinson-index-svyatk.html#cb341-7" tabindex="-1"></a><span class="co"># load the foreign library</span></span>
-<span id="cb341-8"><a href="4.9-atkinson-index-svyatk.html#cb341-8" tabindex="-1"></a><span class="fu">library</span>(foreign)</span>
-<span id="cb341-9"><a href="4.9-atkinson-index-svyatk.html#cb341-9" tabindex="-1"></a></span>
-<span id="cb341-10"><a href="4.9-atkinson-index-svyatk.html#cb341-10" tabindex="-1"></a><span class="co"># create a temporary file on the local disk</span></span>
-<span id="cb341-11"><a href="4.9-atkinson-index-svyatk.html#cb341-11" tabindex="-1"></a>tf <span class="ot">&lt;-</span> <span class="fu">tempfile</span>()</span>
-<span id="cb341-12"><a href="4.9-atkinson-index-svyatk.html#cb341-12" tabindex="-1"></a></span>
-<span id="cb341-13"><a href="4.9-atkinson-index-svyatk.html#cb341-13" tabindex="-1"></a><span class="co"># store the location of the presentation file</span></span>
-<span id="cb341-14"><a href="4.9-atkinson-index-svyatk.html#cb341-14" tabindex="-1"></a>presentation_zip <span class="ot">&lt;-</span></span>
-<span id="cb341-15"><a href="4.9-atkinson-index-svyatk.html#cb341-15" tabindex="-1"></a>  <span class="st">&quot;http://repec.org/nasug2006/nasug2006_jenkins.zip&quot;</span></span>
-<span id="cb341-16"><a href="4.9-atkinson-index-svyatk.html#cb341-16" tabindex="-1"></a></span>
-<span id="cb341-17"><a href="4.9-atkinson-index-svyatk.html#cb341-17" tabindex="-1"></a><span class="co"># download jenkins&#39; presentation to the temporary file</span></span>
-<span id="cb341-18"><a href="4.9-atkinson-index-svyatk.html#cb341-18" tabindex="-1"></a><span class="fu">download.file</span>(presentation_zip , tf , <span class="at">mode =</span> <span class="st">&#39;wb&#39;</span>)</span>
-<span id="cb341-19"><a href="4.9-atkinson-index-svyatk.html#cb341-19" tabindex="-1"></a></span>
-<span id="cb341-20"><a href="4.9-atkinson-index-svyatk.html#cb341-20" tabindex="-1"></a><span class="co"># unzip the contents of the archive</span></span>
-<span id="cb341-21"><a href="4.9-atkinson-index-svyatk.html#cb341-21" tabindex="-1"></a>presentation_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> <span class="fu">tempdir</span>())</span>
-<span id="cb341-22"><a href="4.9-atkinson-index-svyatk.html#cb341-22" tabindex="-1"></a></span>
-<span id="cb341-23"><a href="4.9-atkinson-index-svyatk.html#cb341-23" tabindex="-1"></a><span class="co"># load the institute for fiscal studies&#39; 1981, 1985, and 1991 data.frame objects</span></span>
-<span id="cb341-24"><a href="4.9-atkinson-index-svyatk.html#cb341-24" tabindex="-1"></a>x81 <span class="ot">&lt;-</span></span>
-<span id="cb341-25"><a href="4.9-atkinson-index-svyatk.html#cb341-25" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs81&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb341-26"><a href="4.9-atkinson-index-svyatk.html#cb341-26" tabindex="-1"></a>x85 <span class="ot">&lt;-</span></span>
-<span id="cb341-27"><a href="4.9-atkinson-index-svyatk.html#cb341-27" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs85&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb341-28"><a href="4.9-atkinson-index-svyatk.html#cb341-28" tabindex="-1"></a>x91 <span class="ot">&lt;-</span></span>
-<span id="cb341-29"><a href="4.9-atkinson-index-svyatk.html#cb341-29" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs91&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
-<span id="cb341-30"><a href="4.9-atkinson-index-svyatk.html#cb341-30" tabindex="-1"></a></span>
-<span id="cb341-31"><a href="4.9-atkinson-index-svyatk.html#cb341-31" tabindex="-1"></a><span class="co"># stack each of these three years of data into a single data.frame</span></span>
-<span id="cb341-32"><a href="4.9-atkinson-index-svyatk.html#cb341-32" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">rbind</span>(x81 , x85 , x91)</span></code></pre></div>
+<div class="sourceCode" id="cb340"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb340-1"><a href="4.9-atkinson-index-svyatk.html#cb340-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb340-2"><a href="4.9-atkinson-index-svyatk.html#cb340-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb340-3"><a href="4.9-atkinson-index-svyatk.html#cb340-3" tabindex="-1"></a></span>
+<span id="cb340-4"><a href="4.9-atkinson-index-svyatk.html#cb340-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb340-5"><a href="4.9-atkinson-index-svyatk.html#cb340-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb340-6"><a href="4.9-atkinson-index-svyatk.html#cb340-6" tabindex="-1"></a></span>
+<span id="cb340-7"><a href="4.9-atkinson-index-svyatk.html#cb340-7" tabindex="-1"></a><span class="co"># load the foreign library</span></span>
+<span id="cb340-8"><a href="4.9-atkinson-index-svyatk.html#cb340-8" tabindex="-1"></a><span class="fu">library</span>(foreign)</span>
+<span id="cb340-9"><a href="4.9-atkinson-index-svyatk.html#cb340-9" tabindex="-1"></a></span>
+<span id="cb340-10"><a href="4.9-atkinson-index-svyatk.html#cb340-10" tabindex="-1"></a><span class="co"># create a temporary file on the local disk</span></span>
+<span id="cb340-11"><a href="4.9-atkinson-index-svyatk.html#cb340-11" tabindex="-1"></a>tf <span class="ot">&lt;-</span> <span class="fu">tempfile</span>()</span>
+<span id="cb340-12"><a href="4.9-atkinson-index-svyatk.html#cb340-12" tabindex="-1"></a></span>
+<span id="cb340-13"><a href="4.9-atkinson-index-svyatk.html#cb340-13" tabindex="-1"></a><span class="co"># store the location of the presentation file</span></span>
+<span id="cb340-14"><a href="4.9-atkinson-index-svyatk.html#cb340-14" tabindex="-1"></a>presentation_zip <span class="ot">&lt;-</span></span>
+<span id="cb340-15"><a href="4.9-atkinson-index-svyatk.html#cb340-15" tabindex="-1"></a>  <span class="st">&quot;http://repec.org/nasug2006/nasug2006_jenkins.zip&quot;</span></span>
+<span id="cb340-16"><a href="4.9-atkinson-index-svyatk.html#cb340-16" tabindex="-1"></a></span>
+<span id="cb340-17"><a href="4.9-atkinson-index-svyatk.html#cb340-17" tabindex="-1"></a><span class="co"># download jenkins&#39; presentation to the temporary file</span></span>
+<span id="cb340-18"><a href="4.9-atkinson-index-svyatk.html#cb340-18" tabindex="-1"></a><span class="fu">download.file</span>(presentation_zip , tf , <span class="at">mode =</span> <span class="st">&#39;wb&#39;</span>)</span>
+<span id="cb340-19"><a href="4.9-atkinson-index-svyatk.html#cb340-19" tabindex="-1"></a></span>
+<span id="cb340-20"><a href="4.9-atkinson-index-svyatk.html#cb340-20" tabindex="-1"></a><span class="co"># unzip the contents of the archive</span></span>
+<span id="cb340-21"><a href="4.9-atkinson-index-svyatk.html#cb340-21" tabindex="-1"></a>presentation_files <span class="ot">&lt;-</span> <span class="fu">unzip</span>(tf , <span class="at">exdir =</span> <span class="fu">tempdir</span>())</span>
+<span id="cb340-22"><a href="4.9-atkinson-index-svyatk.html#cb340-22" tabindex="-1"></a></span>
+<span id="cb340-23"><a href="4.9-atkinson-index-svyatk.html#cb340-23" tabindex="-1"></a><span class="co"># load the institute for fiscal studies&#39; 1981, 1985, and 1991 data.frame objects</span></span>
+<span id="cb340-24"><a href="4.9-atkinson-index-svyatk.html#cb340-24" tabindex="-1"></a>x81 <span class="ot">&lt;-</span></span>
+<span id="cb340-25"><a href="4.9-atkinson-index-svyatk.html#cb340-25" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs81&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb340-26"><a href="4.9-atkinson-index-svyatk.html#cb340-26" tabindex="-1"></a>x85 <span class="ot">&lt;-</span></span>
+<span id="cb340-27"><a href="4.9-atkinson-index-svyatk.html#cb340-27" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs85&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb340-28"><a href="4.9-atkinson-index-svyatk.html#cb340-28" tabindex="-1"></a>x91 <span class="ot">&lt;-</span></span>
+<span id="cb340-29"><a href="4.9-atkinson-index-svyatk.html#cb340-29" tabindex="-1"></a>  <span class="fu">read.dta</span>(<span class="fu">grep</span>(<span class="st">&quot;ifs91&quot;</span> , presentation_files , <span class="at">value =</span> <span class="cn">TRUE</span>))</span>
+<span id="cb340-30"><a href="4.9-atkinson-index-svyatk.html#cb340-30" tabindex="-1"></a></span>
+<span id="cb340-31"><a href="4.9-atkinson-index-svyatk.html#cb340-31" tabindex="-1"></a><span class="co"># stack each of these three years of data into a single data.frame</span></span>
+<span id="cb340-32"><a href="4.9-atkinson-index-svyatk.html#cb340-32" tabindex="-1"></a>x <span class="ot">&lt;-</span> <span class="fu">rbind</span>(x81 , x85 , x91)</span></code></pre></div>
 <p>Replicate the author’s survey design statement from stata code..</p>
 <pre><code>. * account for clustering within HHs 
 . version 8: svyset [pweight = wgt], psu(hrn)
@@ -365,11 +365,11 @@ <h3><span class="header-section-number">4.9.1</span> Replication Example</h3>
 psu is hrn
 construct an</code></pre>
 <p>.. into R code:</p>
-<div class="sourceCode" id="cb343"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb343-1"><a href="4.9-atkinson-index-svyatk.html#cb343-1" tabindex="-1"></a><span class="co"># initiate a linearized survey design object</span></span>
-<span id="cb343-2"><a href="4.9-atkinson-index-svyatk.html#cb343-2" tabindex="-1"></a>y <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="sc">~</span> hrn , <span class="at">data =</span> x , <span class="at">weights =</span> <span class="sc">~</span> wgt)</span>
-<span id="cb343-3"><a href="4.9-atkinson-index-svyatk.html#cb343-3" tabindex="-1"></a></span>
-<span id="cb343-4"><a href="4.9-atkinson-index-svyatk.html#cb343-4" tabindex="-1"></a><span class="co"># immediately run the `convey_prep` function on the survey design</span></span>
-<span id="cb343-5"><a href="4.9-atkinson-index-svyatk.html#cb343-5" tabindex="-1"></a>z <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(y)</span></code></pre></div>
+<div class="sourceCode" id="cb342"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb342-1"><a href="4.9-atkinson-index-svyatk.html#cb342-1" tabindex="-1"></a><span class="co"># initiate a linearized survey design object</span></span>
+<span id="cb342-2"><a href="4.9-atkinson-index-svyatk.html#cb342-2" tabindex="-1"></a>y <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="sc">~</span> hrn , <span class="at">data =</span> x , <span class="at">weights =</span> <span class="sc">~</span> wgt)</span>
+<span id="cb342-3"><a href="4.9-atkinson-index-svyatk.html#cb342-3" tabindex="-1"></a></span>
+<span id="cb342-4"><a href="4.9-atkinson-index-svyatk.html#cb342-4" tabindex="-1"></a><span class="co"># immediately run the `convey_prep` function on the survey design</span></span>
+<span id="cb342-5"><a href="4.9-atkinson-index-svyatk.html#cb342-5" tabindex="-1"></a>z <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(y)</span></code></pre></div>
 <p>Replicate the author’s subset statement and each of his svyatk results with stata..</p>
 <pre><code>. svyatk x if year == 1981
  
@@ -391,21 +391,21 @@ <h3><span class="header-section-number">4.9.1</span> Replication Example</h3>
 A(2.5)   |  .4992701   .06754311     7.39    0.000       .366888   .6316522
 ---------------------------------------------------------------------------</code></pre>
 <p>..using R code:</p>
-<div class="sourceCode" id="cb345"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb345-1"><a href="4.9-atkinson-index-svyatk.html#cb345-1" tabindex="-1"></a>z81 <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>)</span>
-<span id="cb345-2"><a href="4.9-atkinson-index-svyatk.html#cb345-2" tabindex="-1"></a></span>
-<span id="cb345-3"><a href="4.9-atkinson-index-svyatk.html#cb345-3" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="fl">0.5</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb344"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb344-1"><a href="4.9-atkinson-index-svyatk.html#cb344-1" tabindex="-1"></a>z81 <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span>)</span>
+<span id="cb344-2"><a href="4.9-atkinson-index-svyatk.html#cb344-2" tabindex="-1"></a></span>
+<span id="cb344-3"><a href="4.9-atkinson-index-svyatk.html#cb344-3" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="fl">0.5</span>)</span></code></pre></div>
 <pre><code>##        atkinson     SE
 ## eybhc0 0.054324 0.0011</code></pre>
-<div class="sourceCode" id="cb347"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb347-1"><a href="4.9-atkinson-index-svyatk.html#cb347-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>))</span></code></pre></div>
+<div class="sourceCode" id="cb346"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb346-1"><a href="4.9-atkinson-index-svyatk.html#cb346-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>))</span></code></pre></div>
 <pre><code>##        atkinson     SE
 ## eybhc0    0.108 0.0025</code></pre>
-<div class="sourceCode" id="cb349"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb349-1"><a href="4.9-atkinson-index-svyatk.html#cb349-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="fl">1.5</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb348"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb348-1"><a href="4.9-atkinson-index-svyatk.html#cb348-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="fl">1.5</span>)</span></code></pre></div>
 <pre><code>##        atkinson     SE
 ## eybhc0  0.17018 0.0067</code></pre>
-<div class="sourceCode" id="cb351"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb351-1"><a href="4.9-atkinson-index-svyatk.html#cb351-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb350"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb350-1"><a href="4.9-atkinson-index-svyatk.html#cb350-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
 <pre><code>##        atkinson    SE
 ## eybhc0  0.27558 0.026</code></pre>
-<div class="sourceCode" id="cb353"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb353-1"><a href="4.9-atkinson-index-svyatk.html#cb353-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="fl">2.5</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb352"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb352-1"><a href="4.9-atkinson-index-svyatk.html#cb352-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , <span class="fu">subset</span>(z81 , eybhc0 <span class="sc">&gt;</span> <span class="dv">0</span>) , <span class="at">epsilon =</span> <span class="fl">2.5</span>)</span></code></pre></div>
 <pre><code>##        atkinson     SE
 ## eybhc0  0.49927 0.0675</code></pre>
 <p>Confirm this replication applies for subsetted objects as well, comparing stata code..</p>
@@ -427,21 +427,21 @@ <h3><span class="header-section-number">4.9.1</span> Replication Example</h3>
 A(2.5)   |   .394787   .04155221     9.50    0.000      .3133461   .4762278
 ---------------------------------------------------------------------------</code></pre>
 <p>..to R code:</p>
-<div class="sourceCode" id="cb356"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb356-1"><a href="4.9-atkinson-index-svyatk.html#cb356-1" tabindex="-1"></a>z81_two <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span> <span class="sc">&amp;</span> eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>)</span>
-<span id="cb356-2"><a href="4.9-atkinson-index-svyatk.html#cb356-2" tabindex="-1"></a></span>
-<span id="cb356-3"><a href="4.9-atkinson-index-svyatk.html#cb356-3" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two , <span class="at">epsilon =</span> <span class="fl">0.5</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb355"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb355-1"><a href="4.9-atkinson-index-svyatk.html#cb355-1" tabindex="-1"></a>z81_two <span class="ot">&lt;-</span> <span class="fu">subset</span>(z , year <span class="sc">==</span> <span class="dv">1981</span> <span class="sc">&amp;</span> eybhc0 <span class="sc">&gt;</span> <span class="dv">1</span>)</span>
+<span id="cb355-2"><a href="4.9-atkinson-index-svyatk.html#cb355-2" tabindex="-1"></a></span>
+<span id="cb355-3"><a href="4.9-atkinson-index-svyatk.html#cb355-3" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two , <span class="at">epsilon =</span> <span class="fl">0.5</span>)</span></code></pre></div>
 <pre><code>##        atkinson     SE
 ## eybhc0 0.054006 0.0011</code></pre>
-<div class="sourceCode" id="cb358"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb358-1"><a href="4.9-atkinson-index-svyatk.html#cb358-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two)</span></code></pre></div>
+<div class="sourceCode" id="cb357"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb357-1"><a href="4.9-atkinson-index-svyatk.html#cb357-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two)</span></code></pre></div>
 <pre><code>##        atkinson     SE
 ## eybhc0  0.10661 0.0022</code></pre>
-<div class="sourceCode" id="cb360"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb360-1"><a href="4.9-atkinson-index-svyatk.html#cb360-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two , <span class="at">epsilon =</span> <span class="fl">1.5</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb359"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb359-1"><a href="4.9-atkinson-index-svyatk.html#cb359-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two , <span class="at">epsilon =</span> <span class="fl">1.5</span>)</span></code></pre></div>
 <pre><code>##        atkinson     SE
 ## eybhc0  0.16383 0.0048</code></pre>
-<div class="sourceCode" id="cb362"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb362-1"><a href="4.9-atkinson-index-svyatk.html#cb362-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb361"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb361-1"><a href="4.9-atkinson-index-svyatk.html#cb361-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two , <span class="at">epsilon =</span> <span class="dv">2</span>)</span></code></pre></div>
 <pre><code>##        atkinson     SE
 ## eybhc0  0.24432 0.0143</code></pre>
-<div class="sourceCode" id="cb364"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb364-1"><a href="4.9-atkinson-index-svyatk.html#cb364-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two , <span class="at">epsilon =</span> <span class="fl">2.5</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb363"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb363-1"><a href="4.9-atkinson-index-svyatk.html#cb363-1" tabindex="-1"></a><span class="fu">svyatk</span>( <span class="sc">~</span> eybhc0 , z81_two , <span class="at">epsilon =</span> <span class="fl">2.5</span>)</span></code></pre></div>
 <pre><code>##        atkinson     SE
 ## eybhc0  0.39479 0.0416</code></pre>
 <p>For additional usage examples of <code>svyatk</code>, type <code>?convey::svyatk</code> in the R console.</p>
diff --git a/docs/404.html b/docs/404.html
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+++ b/docs/404.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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+++ b/docs/5.1-richness-measures-svyrich.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
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@@ -253,13 +253,13 @@
 <div class="col-sm-12">
 <div id="richness-measures-svyrich" class="section level2" number="5.1">
 <h2><span class="header-section-number">5.1</span> Richness Measures (svyrich)</h2>
-<div class="sourceCode" id="cb449"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb449-1"><a href="5.1-richness-measures-svyrich.html#cb449-1" tabindex="-1"></a>✔️ focuses on the top <span class="sc">--</span> i.e., the <span class="st">&quot;rich&quot;</span></span>
-<span id="cb449-2"><a href="5.1-richness-measures-svyrich.html#cb449-2" tabindex="-1"></a>✔️ can have an inequality or polarization interpretation</span>
-<span id="cb449-3"><a href="5.1-richness-measures-svyrich.html#cb449-3" tabindex="-1"></a>✔️ interesting complementary approach to income inequality or polarization</span>
-<span id="cb449-4"><a href="5.1-richness-measures-svyrich.html#cb449-4" tabindex="-1"></a>❌ hard to interpret as parameters change</span>
-<span id="cb449-5"><a href="5.1-richness-measures-svyrich.html#cb449-5" tabindex="-1"></a>❌ convex richness measures are severely affected by outliers, unreliable <span class="cf">for</span> inference</span>
-<span id="cb449-6"><a href="5.1-richness-measures-svyrich.html#cb449-6" tabindex="-1"></a>❌ requires a richness line defition</span>
-<span id="cb449-7"><a href="5.1-richness-measures-svyrich.html#cb449-7" tabindex="-1"></a>❌ hardly ever used</span></code></pre></div>
+<div class="sourceCode" id="cb448"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb448-1"><a href="5.1-richness-measures-svyrich.html#cb448-1" tabindex="-1"></a>✔️ focuses on the top <span class="sc">--</span> i.e., the <span class="st">&quot;rich&quot;</span></span>
+<span id="cb448-2"><a href="5.1-richness-measures-svyrich.html#cb448-2" tabindex="-1"></a>✔️ can have an inequality or polarization interpretation</span>
+<span id="cb448-3"><a href="5.1-richness-measures-svyrich.html#cb448-3" tabindex="-1"></a>✔️ interesting complementary approach to income inequality or polarization</span>
+<span id="cb448-4"><a href="5.1-richness-measures-svyrich.html#cb448-4" tabindex="-1"></a>❌ hard to interpret as parameters change</span>
+<span id="cb448-5"><a href="5.1-richness-measures-svyrich.html#cb448-5" tabindex="-1"></a>❌ convex richness measures are severely affected by outliers, unreliable <span class="cf">for</span> inference</span>
+<span id="cb448-6"><a href="5.1-richness-measures-svyrich.html#cb448-6" tabindex="-1"></a>❌ requires a richness line defition</span>
+<span id="cb448-7"><a href="5.1-richness-measures-svyrich.html#cb448-7" tabindex="-1"></a>❌ hardly ever used</span></code></pre></div>
 <p><span class="citation">Peichl, Schaefer, and Scheicher (<label for="tufte-mn-101" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-101" class="margin-toggle">2010<span class="marginnote">Peichl, Andreas, Thilo Schaefer, and Christoph Scheicher. 2010. <span>“<span class="nocase">Measuring Richness and Poverty: A micro data application to Europe and Germany</span>.”</span> <em>Review of Income and Wealth</em> 56 (3): 597–619. https://doi.org/<a href="https://doi.org/10.1111/j.1475-4991.2010.00404.x">https://doi.org/10.1111/j.1475-4991.2010.00404.x</a>.</span>)</span> also presented a general class of richness measures, proposing three
 particular sub-classes: the (concave) Chakravarty class, the concave-FGT class and the convex-FGT class, defined at the population level as:</p>
 <p><span class="math display">\[
@@ -296,167 +296,167 @@ <h3><span class="header-section-number">5.1.1</span> Monte Carlo Simulation</h3>
 parameter!).</p>
 <p>For the sake of similarity, we start by simulating a large finite population (<span class="math inline">\(N = 10^5\)</span>)
 using the same distribution from <span class="citation">Brzezinski (<label for="tufte-mn-107" class="margin-toggle">&#8853;</label><input type="checkbox" id="tufte-mn-107" class="margin-toggle">2014<span class="marginnote">Brzezinski, Michal. 2014. <span>“Statistical Inference for Richness Measures.”</span> <em>Applied Economics</em> 46 (14): 1599–1608. <a href="https://doi.org/10.1080/00036846.2014.880106">https://doi.org/10.1080/00036846.2014.880106</a>.</span>)</span>:</p>
-<div class="sourceCode" id="cb450"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb450-1"><a href="5.1-richness-measures-svyrich.html#cb450-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
-<span id="cb450-2"><a href="5.1-richness-measures-svyrich.html#cb450-2" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb450-3"><a href="5.1-richness-measures-svyrich.html#cb450-3" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb450-4"><a href="5.1-richness-measures-svyrich.html#cb450-4" tabindex="-1"></a><span class="fu">library</span>(sampling)</span>
-<span id="cb450-5"><a href="5.1-richness-measures-svyrich.html#cb450-5" tabindex="-1"></a><span class="fu">library</span>(VGAM)</span>
-<span id="cb450-6"><a href="5.1-richness-measures-svyrich.html#cb450-6" tabindex="-1"></a></span>
-<span id="cb450-7"><a href="5.1-richness-measures-svyrich.html#cb450-7" tabindex="-1"></a><span class="co"># set random seed</span></span>
-<span id="cb450-8"><a href="5.1-richness-measures-svyrich.html#cb450-8" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">2023</span>)</span>
-<span id="cb450-9"><a href="5.1-richness-measures-svyrich.html#cb450-9" tabindex="-1"></a></span>
-<span id="cb450-10"><a href="5.1-richness-measures-svyrich.html#cb450-10" tabindex="-1"></a><span class="co"># superpopulation parameters</span></span>
-<span id="cb450-11"><a href="5.1-richness-measures-svyrich.html#cb450-11" tabindex="-1"></a>scale.x0 <span class="ot">&lt;-</span> <span class="dv">1</span></span>
-<span id="cb450-12"><a href="5.1-richness-measures-svyrich.html#cb450-12" tabindex="-1"></a>shape.theta <span class="ot">&lt;-</span> <span class="dv">2</span></span>
-<span id="cb450-13"><a href="5.1-richness-measures-svyrich.html#cb450-13" tabindex="-1"></a>cha.beta <span class="ot">&lt;-</span> <span class="dv">2</span></span>
-<span id="cb450-14"><a href="5.1-richness-measures-svyrich.html#cb450-14" tabindex="-1"></a>fgt.alpha <span class="ot">&lt;-</span> <span class="fl">1.5</span></span>
-<span id="cb450-15"><a href="5.1-richness-measures-svyrich.html#cb450-15" tabindex="-1"></a>n.pop <span class="ot">&lt;-</span> <span class="fu">as.integer</span>(<span class="dv">10</span> <span class="sc">^</span> <span class="dv">5</span>)</span>
-<span id="cb450-16"><a href="5.1-richness-measures-svyrich.html#cb450-16" tabindex="-1"></a></span>
-<span id="cb450-17"><a href="5.1-richness-measures-svyrich.html#cb450-17" tabindex="-1"></a><span class="co"># generate finite population</span></span>
-<span id="cb450-18"><a href="5.1-richness-measures-svyrich.html#cb450-18" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
-<span id="cb450-19"><a href="5.1-richness-measures-svyrich.html#cb450-19" tabindex="-1"></a>  <span class="fu">data.frame</span>(<span class="at">y1 =</span> <span class="fu">rparetoI</span>(n.pop  ,  scale.x0 , shape.theta))</span></code></pre></div>
+<div class="sourceCode" id="cb449"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb449-1"><a href="5.1-richness-measures-svyrich.html#cb449-1" tabindex="-1"></a><span class="co"># load libraries</span></span>
+<span id="cb449-2"><a href="5.1-richness-measures-svyrich.html#cb449-2" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb449-3"><a href="5.1-richness-measures-svyrich.html#cb449-3" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb449-4"><a href="5.1-richness-measures-svyrich.html#cb449-4" tabindex="-1"></a><span class="fu">library</span>(sampling)</span>
+<span id="cb449-5"><a href="5.1-richness-measures-svyrich.html#cb449-5" tabindex="-1"></a><span class="fu">library</span>(VGAM)</span>
+<span id="cb449-6"><a href="5.1-richness-measures-svyrich.html#cb449-6" tabindex="-1"></a></span>
+<span id="cb449-7"><a href="5.1-richness-measures-svyrich.html#cb449-7" tabindex="-1"></a><span class="co"># set random seed</span></span>
+<span id="cb449-8"><a href="5.1-richness-measures-svyrich.html#cb449-8" tabindex="-1"></a><span class="fu">set.seed</span>(<span class="dv">2023</span>)</span>
+<span id="cb449-9"><a href="5.1-richness-measures-svyrich.html#cb449-9" tabindex="-1"></a></span>
+<span id="cb449-10"><a href="5.1-richness-measures-svyrich.html#cb449-10" tabindex="-1"></a><span class="co"># superpopulation parameters</span></span>
+<span id="cb449-11"><a href="5.1-richness-measures-svyrich.html#cb449-11" tabindex="-1"></a>scale.x0 <span class="ot">&lt;-</span> <span class="dv">1</span></span>
+<span id="cb449-12"><a href="5.1-richness-measures-svyrich.html#cb449-12" tabindex="-1"></a>shape.theta <span class="ot">&lt;-</span> <span class="dv">2</span></span>
+<span id="cb449-13"><a href="5.1-richness-measures-svyrich.html#cb449-13" tabindex="-1"></a>cha.beta <span class="ot">&lt;-</span> <span class="dv">2</span></span>
+<span id="cb449-14"><a href="5.1-richness-measures-svyrich.html#cb449-14" tabindex="-1"></a>fgt.alpha <span class="ot">&lt;-</span> <span class="fl">1.5</span></span>
+<span id="cb449-15"><a href="5.1-richness-measures-svyrich.html#cb449-15" tabindex="-1"></a>n.pop <span class="ot">&lt;-</span> <span class="fu">as.integer</span>(<span class="dv">10</span> <span class="sc">^</span> <span class="dv">5</span>)</span>
+<span id="cb449-16"><a href="5.1-richness-measures-svyrich.html#cb449-16" tabindex="-1"></a></span>
+<span id="cb449-17"><a href="5.1-richness-measures-svyrich.html#cb449-17" tabindex="-1"></a><span class="co"># generate finite population</span></span>
+<span id="cb449-18"><a href="5.1-richness-measures-svyrich.html#cb449-18" tabindex="-1"></a>pop.df <span class="ot">&lt;-</span></span>
+<span id="cb449-19"><a href="5.1-richness-measures-svyrich.html#cb449-19" tabindex="-1"></a>  <span class="fu">data.frame</span>(<span class="at">y1 =</span> <span class="fu">rparetoI</span>(n.pop  ,  scale.x0 , shape.theta))</span></code></pre></div>
 <p>Then, we compute the finite population parameters using the simulated population:</p>
-<div class="sourceCode" id="cb451"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb451-1"><a href="5.1-richness-measures-svyrich.html#cb451-1" tabindex="-1"></a><span class="co"># richness measures: finite population parameters</span></span>
-<span id="cb451-2"><a href="5.1-richness-measures-svyrich.html#cb451-2" tabindex="-1"></a>cha.scores <span class="ot">&lt;-</span></span>
-<span id="cb451-3"><a href="5.1-richness-measures-svyrich.html#cb451-3" tabindex="-1"></a>  <span class="cf">function</span>(y , b , rho)</span>
-<span id="cb451-4"><a href="5.1-richness-measures-svyrich.html#cb451-4" tabindex="-1"></a>    <span class="fu">ifelse</span>(y <span class="sc">&gt;</span> rho , (<span class="dv">1</span> <span class="sc">-</span> (rho <span class="sc">/</span> y) <span class="sc">^</span> b) , <span class="dv">0</span>)</span>
-<span id="cb451-5"><a href="5.1-richness-measures-svyrich.html#cb451-5" tabindex="-1"></a>fgtt2.scores <span class="ot">&lt;-</span></span>
-<span id="cb451-6"><a href="5.1-richness-measures-svyrich.html#cb451-6" tabindex="-1"></a>  <span class="cf">function</span>(y , g , rho)</span>
-<span id="cb451-7"><a href="5.1-richness-measures-svyrich.html#cb451-7" tabindex="-1"></a>    <span class="fu">ifelse</span>(y <span class="sc">&gt;</span> rho , (y <span class="sc">/</span> rho <span class="sc">-</span> <span class="dv">1</span>) <span class="sc">^</span> a , <span class="dv">0</span>)</span>
-<span id="cb451-8"><a href="5.1-richness-measures-svyrich.html#cb451-8" tabindex="-1"></a>median.fp <span class="ot">&lt;-</span> <span class="fu">quantile</span>(pop.df<span class="sc">$</span>y1 , .<span class="dv">50</span>)</span>
-<span id="cb451-9"><a href="5.1-richness-measures-svyrich.html#cb451-9" tabindex="-1"></a>rho.fp <span class="ot">&lt;-</span> <span class="dv">3</span> <span class="sc">*</span> median.fp</span>
-<span id="cb451-10"><a href="5.1-richness-measures-svyrich.html#cb451-10" tabindex="-1"></a>rHC.fp <span class="ot">&lt;-</span> <span class="fu">mean</span>(pop.df<span class="sc">$</span>y1 <span class="sc">&gt;</span> rho.fp)</span>
-<span id="cb451-11"><a href="5.1-richness-measures-svyrich.html#cb451-11" tabindex="-1"></a>rCha.fp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">cha.scores</span>(pop.df<span class="sc">$</span>y1  , cha.beta , rho.fp))</span>
-<span id="cb451-12"><a href="5.1-richness-measures-svyrich.html#cb451-12" tabindex="-1"></a>rFGTT2.fp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">cha.scores</span>(pop.df<span class="sc">$</span>y1  , fgt.alpha , rho.fp))</span></code></pre></div>
+<div class="sourceCode" id="cb450"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb450-1"><a href="5.1-richness-measures-svyrich.html#cb450-1" tabindex="-1"></a><span class="co"># richness measures: finite population parameters</span></span>
+<span id="cb450-2"><a href="5.1-richness-measures-svyrich.html#cb450-2" tabindex="-1"></a>cha.scores <span class="ot">&lt;-</span></span>
+<span id="cb450-3"><a href="5.1-richness-measures-svyrich.html#cb450-3" tabindex="-1"></a>  <span class="cf">function</span>(y , b , rho)</span>
+<span id="cb450-4"><a href="5.1-richness-measures-svyrich.html#cb450-4" tabindex="-1"></a>    <span class="fu">ifelse</span>(y <span class="sc">&gt;</span> rho , (<span class="dv">1</span> <span class="sc">-</span> (rho <span class="sc">/</span> y) <span class="sc">^</span> b) , <span class="dv">0</span>)</span>
+<span id="cb450-5"><a href="5.1-richness-measures-svyrich.html#cb450-5" tabindex="-1"></a>fgtt2.scores <span class="ot">&lt;-</span></span>
+<span id="cb450-6"><a href="5.1-richness-measures-svyrich.html#cb450-6" tabindex="-1"></a>  <span class="cf">function</span>(y , g , rho)</span>
+<span id="cb450-7"><a href="5.1-richness-measures-svyrich.html#cb450-7" tabindex="-1"></a>    <span class="fu">ifelse</span>(y <span class="sc">&gt;</span> rho , (y <span class="sc">/</span> rho <span class="sc">-</span> <span class="dv">1</span>) <span class="sc">^</span> a , <span class="dv">0</span>)</span>
+<span id="cb450-8"><a href="5.1-richness-measures-svyrich.html#cb450-8" tabindex="-1"></a>median.fp <span class="ot">&lt;-</span> <span class="fu">quantile</span>(pop.df<span class="sc">$</span>y1 , .<span class="dv">50</span>)</span>
+<span id="cb450-9"><a href="5.1-richness-measures-svyrich.html#cb450-9" tabindex="-1"></a>rho.fp <span class="ot">&lt;-</span> <span class="dv">3</span> <span class="sc">*</span> median.fp</span>
+<span id="cb450-10"><a href="5.1-richness-measures-svyrich.html#cb450-10" tabindex="-1"></a>rHC.fp <span class="ot">&lt;-</span> <span class="fu">mean</span>(pop.df<span class="sc">$</span>y1 <span class="sc">&gt;</span> rho.fp)</span>
+<span id="cb450-11"><a href="5.1-richness-measures-svyrich.html#cb450-11" tabindex="-1"></a>rCha.fp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">cha.scores</span>(pop.df<span class="sc">$</span>y1  , cha.beta , rho.fp))</span>
+<span id="cb450-12"><a href="5.1-richness-measures-svyrich.html#cb450-12" tabindex="-1"></a>rFGTT2.fp <span class="ot">&lt;-</span> <span class="fu">mean</span>(<span class="fu">cha.scores</span>(pop.df<span class="sc">$</span>y1  , fgt.alpha , rho.fp))</span></code></pre></div>
 <p>For our sampling design, we select <span class="math inline">\(n = 1000\)</span> units using multinomial sampling,
 with the variable <code>x.aux</code> as the size variable for the inclusion probabilities:</p>
-<div class="sourceCode" id="cb452"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb452-1"><a href="5.1-richness-measures-svyrich.html#cb452-1" tabindex="-1"></a><span class="co"># define sample size</span></span>
-<span id="cb452-2"><a href="5.1-richness-measures-svyrich.html#cb452-2" tabindex="-1"></a>n.sample <span class="ot">&lt;-</span> 1000L</span>
-<span id="cb452-3"><a href="5.1-richness-measures-svyrich.html#cb452-3" tabindex="-1"></a></span>
-<span id="cb452-4"><a href="5.1-richness-measures-svyrich.html#cb452-4" tabindex="-1"></a><span class="co"># inclusion probability</span></span>
-<span id="cb452-5"><a href="5.1-richness-measures-svyrich.html#cb452-5" tabindex="-1"></a>pop.df<span class="sc">$</span>x.aux <span class="ot">&lt;-</span> <span class="fu">plogis</span>( pop.df<span class="sc">$</span>y1 ) <span class="sc">/</span> <span class="fl">1.1</span></span>
-<span id="cb452-6"><a href="5.1-richness-measures-svyrich.html#cb452-6" tabindex="-1"></a>pop.df<span class="sc">$</span>pi1 <span class="ot">&lt;-</span> sampling<span class="sc">::</span><span class="fu">inclusionprobabilities</span>( pop.df<span class="sc">$</span>x.aux , n.sample )</span></code></pre></div>
+<div class="sourceCode" id="cb451"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb451-1"><a href="5.1-richness-measures-svyrich.html#cb451-1" tabindex="-1"></a><span class="co"># define sample size</span></span>
+<span id="cb451-2"><a href="5.1-richness-measures-svyrich.html#cb451-2" tabindex="-1"></a>n.sample <span class="ot">&lt;-</span> 1000L</span>
+<span id="cb451-3"><a href="5.1-richness-measures-svyrich.html#cb451-3" tabindex="-1"></a></span>
+<span id="cb451-4"><a href="5.1-richness-measures-svyrich.html#cb451-4" tabindex="-1"></a><span class="co"># inclusion probability</span></span>
+<span id="cb451-5"><a href="5.1-richness-measures-svyrich.html#cb451-5" tabindex="-1"></a>pop.df<span class="sc">$</span>x.aux <span class="ot">&lt;-</span> <span class="fu">plogis</span>( pop.df<span class="sc">$</span>y1 ) <span class="sc">/</span> <span class="fl">1.1</span></span>
+<span id="cb451-6"><a href="5.1-richness-measures-svyrich.html#cb451-6" tabindex="-1"></a>pop.df<span class="sc">$</span>pi1 <span class="ot">&lt;-</span> sampling<span class="sc">::</span><span class="fu">inclusionprobabilities</span>( pop.df<span class="sc">$</span>x.aux , n.sample )</span></code></pre></div>
 <p>We run the procedure N and store the estimate objects using the code below:</p>
-<div class="sourceCode" id="cb453"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb453-1"><a href="5.1-richness-measures-svyrich.html#cb453-1" tabindex="-1"></a><span class="co"># define the number of simulation runs</span></span>
-<span id="cb453-2"><a href="5.1-richness-measures-svyrich.html#cb453-2" tabindex="-1"></a>mc.reps <span class="ot">&lt;-</span> 5000L</span>
-<span id="cb453-3"><a href="5.1-richness-measures-svyrich.html#cb453-3" tabindex="-1"></a></span>
-<span id="cb453-4"><a href="5.1-richness-measures-svyrich.html#cb453-4" tabindex="-1"></a><span class="co"># simulation runs</span></span>
-<span id="cb453-5"><a href="5.1-richness-measures-svyrich.html#cb453-5" tabindex="-1"></a>rep.list <span class="ot">&lt;-</span> <span class="fu">lapply</span>(<span class="fu">seq_len</span>(mc.reps) , <span class="cf">function</span>(this.iter) {</span>
-<span id="cb453-6"><a href="5.1-richness-measures-svyrich.html#cb453-6" tabindex="-1"></a>  <span class="co"># multinomial sampling</span></span>
-<span id="cb453-7"><a href="5.1-richness-measures-svyrich.html#cb453-7" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> sampling<span class="sc">::</span><span class="fu">UPmultinomial</span>(pop.df<span class="sc">$</span>pi1)</span>
-<span id="cb453-8"><a href="5.1-richness-measures-svyrich.html#cb453-8" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">rep</span>(<span class="dv">1</span><span class="sc">:</span>n.pop , this.sample)</span>
-<span id="cb453-9"><a href="5.1-richness-measures-svyrich.html#cb453-9" tabindex="-1"></a>  sample.df <span class="ot">&lt;-</span> pop.df[this.sample ,]</span>
-<span id="cb453-10"><a href="5.1-richness-measures-svyrich.html#cb453-10" tabindex="-1"></a>  sample.df<span class="sc">$</span>weights <span class="ot">&lt;-</span> <span class="dv">1</span> <span class="sc">/</span> sample.df<span class="sc">$</span>pi1</span>
-<span id="cb453-11"><a href="5.1-richness-measures-svyrich.html#cb453-11" tabindex="-1"></a>  des.obj <span class="ot">&lt;-</span></span>
-<span id="cb453-12"><a href="5.1-richness-measures-svyrich.html#cb453-12" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
-<span id="cb453-13"><a href="5.1-richness-measures-svyrich.html#cb453-13" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> <span class="dv">1</span> ,</span>
-<span id="cb453-14"><a href="5.1-richness-measures-svyrich.html#cb453-14" tabindex="-1"></a>      <span class="at">weights =</span> <span class="sc">~</span> weights ,</span>
-<span id="cb453-15"><a href="5.1-richness-measures-svyrich.html#cb453-15" tabindex="-1"></a>      <span class="at">data =</span> sample.df ,</span>
-<span id="cb453-16"><a href="5.1-richness-measures-svyrich.html#cb453-16" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
-<span id="cb453-17"><a href="5.1-richness-measures-svyrich.html#cb453-17" tabindex="-1"></a>    )</span>
-<span id="cb453-18"><a href="5.1-richness-measures-svyrich.html#cb453-18" tabindex="-1"></a>  </span>
-<span id="cb453-19"><a href="5.1-richness-measures-svyrich.html#cb453-19" tabindex="-1"></a>  <span class="co"># run estimation</span></span>
-<span id="cb453-20"><a href="5.1-richness-measures-svyrich.html#cb453-20" tabindex="-1"></a>  des.obj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des.obj)</span>
-<span id="cb453-21"><a href="5.1-richness-measures-svyrich.html#cb453-21" tabindex="-1"></a>  rCha.hat <span class="ot">&lt;-</span></span>
-<span id="cb453-22"><a href="5.1-richness-measures-svyrich.html#cb453-22" tabindex="-1"></a>    <span class="fu">svyrich</span>(</span>
-<span id="cb453-23"><a href="5.1-richness-measures-svyrich.html#cb453-23" tabindex="-1"></a>      <span class="sc">~</span> y1 ,</span>
-<span id="cb453-24"><a href="5.1-richness-measures-svyrich.html#cb453-24" tabindex="-1"></a>      des.obj ,</span>
-<span id="cb453-25"><a href="5.1-richness-measures-svyrich.html#cb453-25" tabindex="-1"></a>      <span class="at">type_measure =</span> <span class="st">&quot;Cha&quot;</span> ,</span>
-<span id="cb453-26"><a href="5.1-richness-measures-svyrich.html#cb453-26" tabindex="-1"></a>      <span class="at">g =</span> cha.beta ,</span>
-<span id="cb453-27"><a href="5.1-richness-measures-svyrich.html#cb453-27" tabindex="-1"></a>      <span class="at">type_thresh =</span> <span class="st">&quot;relq&quot;</span> ,</span>
-<span id="cb453-28"><a href="5.1-richness-measures-svyrich.html#cb453-28" tabindex="-1"></a>      <span class="at">percent =</span> <span class="dv">3</span></span>
-<span id="cb453-29"><a href="5.1-richness-measures-svyrich.html#cb453-29" tabindex="-1"></a>    )</span>
-<span id="cb453-30"><a href="5.1-richness-measures-svyrich.html#cb453-30" tabindex="-1"></a>  <span class="fu">suppressWarnings</span>(</span>
-<span id="cb453-31"><a href="5.1-richness-measures-svyrich.html#cb453-31" tabindex="-1"></a>    rHC.hat <span class="ot">&lt;-</span></span>
-<span id="cb453-32"><a href="5.1-richness-measures-svyrich.html#cb453-32" tabindex="-1"></a>      <span class="fu">svyrich</span>(</span>
-<span id="cb453-33"><a href="5.1-richness-measures-svyrich.html#cb453-33" tabindex="-1"></a>        <span class="sc">~</span> y1 ,</span>
-<span id="cb453-34"><a href="5.1-richness-measures-svyrich.html#cb453-34" tabindex="-1"></a>        des.obj ,</span>
-<span id="cb453-35"><a href="5.1-richness-measures-svyrich.html#cb453-35" tabindex="-1"></a>        <span class="at">type_measure =</span> <span class="st">&quot;FGTT1&quot;</span> ,</span>
-<span id="cb453-36"><a href="5.1-richness-measures-svyrich.html#cb453-36" tabindex="-1"></a>        <span class="at">g =</span> <span class="dv">0</span> ,</span>
-<span id="cb453-37"><a href="5.1-richness-measures-svyrich.html#cb453-37" tabindex="-1"></a>        <span class="at">type_thresh =</span> <span class="st">&quot;relq&quot;</span>  ,</span>
-<span id="cb453-38"><a href="5.1-richness-measures-svyrich.html#cb453-38" tabindex="-1"></a>        <span class="at">percent =</span> <span class="dv">3</span></span>
-<span id="cb453-39"><a href="5.1-richness-measures-svyrich.html#cb453-39" tabindex="-1"></a>      )</span>
-<span id="cb453-40"><a href="5.1-richness-measures-svyrich.html#cb453-40" tabindex="-1"></a>  )</span>
-<span id="cb453-41"><a href="5.1-richness-measures-svyrich.html#cb453-41" tabindex="-1"></a>  <span class="fu">suppressWarnings</span>(</span>
-<span id="cb453-42"><a href="5.1-richness-measures-svyrich.html#cb453-42" tabindex="-1"></a>    rFGTT2.hat <span class="ot">&lt;-</span></span>
-<span id="cb453-43"><a href="5.1-richness-measures-svyrich.html#cb453-43" tabindex="-1"></a>      <span class="fu">svyrich</span>(</span>
-<span id="cb453-44"><a href="5.1-richness-measures-svyrich.html#cb453-44" tabindex="-1"></a>        <span class="sc">~</span> y1 ,</span>
-<span id="cb453-45"><a href="5.1-richness-measures-svyrich.html#cb453-45" tabindex="-1"></a>        des.obj ,</span>
-<span id="cb453-46"><a href="5.1-richness-measures-svyrich.html#cb453-46" tabindex="-1"></a>        <span class="at">type_measure =</span> <span class="st">&quot;FGTT2&quot;</span> ,</span>
-<span id="cb453-47"><a href="5.1-richness-measures-svyrich.html#cb453-47" tabindex="-1"></a>        <span class="at">g =</span> fgt.alpha ,</span>
-<span id="cb453-48"><a href="5.1-richness-measures-svyrich.html#cb453-48" tabindex="-1"></a>        <span class="at">type_thresh =</span> <span class="st">&quot;relq&quot;</span>  ,</span>
-<span id="cb453-49"><a href="5.1-richness-measures-svyrich.html#cb453-49" tabindex="-1"></a>        <span class="at">percent =</span> <span class="dv">3</span></span>
-<span id="cb453-50"><a href="5.1-richness-measures-svyrich.html#cb453-50" tabindex="-1"></a>      )</span>
-<span id="cb453-51"><a href="5.1-richness-measures-svyrich.html#cb453-51" tabindex="-1"></a>  )</span>
-<span id="cb453-52"><a href="5.1-richness-measures-svyrich.html#cb453-52" tabindex="-1"></a>  est.list <span class="ot">&lt;-</span> <span class="fu">list</span>(rHC.hat , rCha.hat , rFGTT2.hat)</span>
-<span id="cb453-53"><a href="5.1-richness-measures-svyrich.html#cb453-53" tabindex="-1"></a>  est.list</span>
-<span id="cb453-54"><a href="5.1-richness-measures-svyrich.html#cb453-54" tabindex="-1"></a>  </span>
-<span id="cb453-55"><a href="5.1-richness-measures-svyrich.html#cb453-55" tabindex="-1"></a>})</span></code></pre></div>
+<div class="sourceCode" id="cb452"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb452-1"><a href="5.1-richness-measures-svyrich.html#cb452-1" tabindex="-1"></a><span class="co"># define the number of simulation runs</span></span>
+<span id="cb452-2"><a href="5.1-richness-measures-svyrich.html#cb452-2" tabindex="-1"></a>mc.reps <span class="ot">&lt;-</span> 5000L</span>
+<span id="cb452-3"><a href="5.1-richness-measures-svyrich.html#cb452-3" tabindex="-1"></a></span>
+<span id="cb452-4"><a href="5.1-richness-measures-svyrich.html#cb452-4" tabindex="-1"></a><span class="co"># simulation runs</span></span>
+<span id="cb452-5"><a href="5.1-richness-measures-svyrich.html#cb452-5" tabindex="-1"></a>rep.list <span class="ot">&lt;-</span> <span class="fu">lapply</span>(<span class="fu">seq_len</span>(mc.reps) , <span class="cf">function</span>(this.iter) {</span>
+<span id="cb452-6"><a href="5.1-richness-measures-svyrich.html#cb452-6" tabindex="-1"></a>  <span class="co"># multinomial sampling</span></span>
+<span id="cb452-7"><a href="5.1-richness-measures-svyrich.html#cb452-7" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> sampling<span class="sc">::</span><span class="fu">UPmultinomial</span>(pop.df<span class="sc">$</span>pi1)</span>
+<span id="cb452-8"><a href="5.1-richness-measures-svyrich.html#cb452-8" tabindex="-1"></a>  this.sample <span class="ot">&lt;-</span> <span class="fu">rep</span>(<span class="dv">1</span><span class="sc">:</span>n.pop , this.sample)</span>
+<span id="cb452-9"><a href="5.1-richness-measures-svyrich.html#cb452-9" tabindex="-1"></a>  sample.df <span class="ot">&lt;-</span> pop.df[this.sample ,]</span>
+<span id="cb452-10"><a href="5.1-richness-measures-svyrich.html#cb452-10" tabindex="-1"></a>  sample.df<span class="sc">$</span>weights <span class="ot">&lt;-</span> <span class="dv">1</span> <span class="sc">/</span> sample.df<span class="sc">$</span>pi1</span>
+<span id="cb452-11"><a href="5.1-richness-measures-svyrich.html#cb452-11" tabindex="-1"></a>  des.obj <span class="ot">&lt;-</span></span>
+<span id="cb452-12"><a href="5.1-richness-measures-svyrich.html#cb452-12" tabindex="-1"></a>    <span class="fu">svydesign</span>(</span>
+<span id="cb452-13"><a href="5.1-richness-measures-svyrich.html#cb452-13" tabindex="-1"></a>      <span class="at">ids =</span> <span class="sc">~</span> <span class="dv">1</span> ,</span>
+<span id="cb452-14"><a href="5.1-richness-measures-svyrich.html#cb452-14" tabindex="-1"></a>      <span class="at">weights =</span> <span class="sc">~</span> weights ,</span>
+<span id="cb452-15"><a href="5.1-richness-measures-svyrich.html#cb452-15" tabindex="-1"></a>      <span class="at">data =</span> sample.df ,</span>
+<span id="cb452-16"><a href="5.1-richness-measures-svyrich.html#cb452-16" tabindex="-1"></a>      <span class="at">nest =</span> <span class="cn">FALSE</span></span>
+<span id="cb452-17"><a href="5.1-richness-measures-svyrich.html#cb452-17" tabindex="-1"></a>    )</span>
+<span id="cb452-18"><a href="5.1-richness-measures-svyrich.html#cb452-18" tabindex="-1"></a>  </span>
+<span id="cb452-19"><a href="5.1-richness-measures-svyrich.html#cb452-19" tabindex="-1"></a>  <span class="co"># run estimation</span></span>
+<span id="cb452-20"><a href="5.1-richness-measures-svyrich.html#cb452-20" tabindex="-1"></a>  des.obj <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des.obj)</span>
+<span id="cb452-21"><a href="5.1-richness-measures-svyrich.html#cb452-21" tabindex="-1"></a>  rCha.hat <span class="ot">&lt;-</span></span>
+<span id="cb452-22"><a href="5.1-richness-measures-svyrich.html#cb452-22" tabindex="-1"></a>    <span class="fu">svyrich</span>(</span>
+<span id="cb452-23"><a href="5.1-richness-measures-svyrich.html#cb452-23" tabindex="-1"></a>      <span class="sc">~</span> y1 ,</span>
+<span id="cb452-24"><a href="5.1-richness-measures-svyrich.html#cb452-24" tabindex="-1"></a>      des.obj ,</span>
+<span id="cb452-25"><a href="5.1-richness-measures-svyrich.html#cb452-25" tabindex="-1"></a>      <span class="at">type_measure =</span> <span class="st">&quot;Cha&quot;</span> ,</span>
+<span id="cb452-26"><a href="5.1-richness-measures-svyrich.html#cb452-26" tabindex="-1"></a>      <span class="at">g =</span> cha.beta ,</span>
+<span id="cb452-27"><a href="5.1-richness-measures-svyrich.html#cb452-27" tabindex="-1"></a>      <span class="at">type_thresh =</span> <span class="st">&quot;relq&quot;</span> ,</span>
+<span id="cb452-28"><a href="5.1-richness-measures-svyrich.html#cb452-28" tabindex="-1"></a>      <span class="at">percent =</span> <span class="dv">3</span></span>
+<span id="cb452-29"><a href="5.1-richness-measures-svyrich.html#cb452-29" tabindex="-1"></a>    )</span>
+<span id="cb452-30"><a href="5.1-richness-measures-svyrich.html#cb452-30" tabindex="-1"></a>  <span class="fu">suppressWarnings</span>(</span>
+<span id="cb452-31"><a href="5.1-richness-measures-svyrich.html#cb452-31" tabindex="-1"></a>    rHC.hat <span class="ot">&lt;-</span></span>
+<span id="cb452-32"><a href="5.1-richness-measures-svyrich.html#cb452-32" tabindex="-1"></a>      <span class="fu">svyrich</span>(</span>
+<span id="cb452-33"><a href="5.1-richness-measures-svyrich.html#cb452-33" tabindex="-1"></a>        <span class="sc">~</span> y1 ,</span>
+<span id="cb452-34"><a href="5.1-richness-measures-svyrich.html#cb452-34" tabindex="-1"></a>        des.obj ,</span>
+<span id="cb452-35"><a href="5.1-richness-measures-svyrich.html#cb452-35" tabindex="-1"></a>        <span class="at">type_measure =</span> <span class="st">&quot;FGTT1&quot;</span> ,</span>
+<span id="cb452-36"><a href="5.1-richness-measures-svyrich.html#cb452-36" tabindex="-1"></a>        <span class="at">g =</span> <span class="dv">0</span> ,</span>
+<span id="cb452-37"><a href="5.1-richness-measures-svyrich.html#cb452-37" tabindex="-1"></a>        <span class="at">type_thresh =</span> <span class="st">&quot;relq&quot;</span>  ,</span>
+<span id="cb452-38"><a href="5.1-richness-measures-svyrich.html#cb452-38" tabindex="-1"></a>        <span class="at">percent =</span> <span class="dv">3</span></span>
+<span id="cb452-39"><a href="5.1-richness-measures-svyrich.html#cb452-39" tabindex="-1"></a>      )</span>
+<span id="cb452-40"><a href="5.1-richness-measures-svyrich.html#cb452-40" tabindex="-1"></a>  )</span>
+<span id="cb452-41"><a href="5.1-richness-measures-svyrich.html#cb452-41" tabindex="-1"></a>  <span class="fu">suppressWarnings</span>(</span>
+<span id="cb452-42"><a href="5.1-richness-measures-svyrich.html#cb452-42" tabindex="-1"></a>    rFGTT2.hat <span class="ot">&lt;-</span></span>
+<span id="cb452-43"><a href="5.1-richness-measures-svyrich.html#cb452-43" tabindex="-1"></a>      <span class="fu">svyrich</span>(</span>
+<span id="cb452-44"><a href="5.1-richness-measures-svyrich.html#cb452-44" tabindex="-1"></a>        <span class="sc">~</span> y1 ,</span>
+<span id="cb452-45"><a href="5.1-richness-measures-svyrich.html#cb452-45" tabindex="-1"></a>        des.obj ,</span>
+<span id="cb452-46"><a href="5.1-richness-measures-svyrich.html#cb452-46" tabindex="-1"></a>        <span class="at">type_measure =</span> <span class="st">&quot;FGTT2&quot;</span> ,</span>
+<span id="cb452-47"><a href="5.1-richness-measures-svyrich.html#cb452-47" tabindex="-1"></a>        <span class="at">g =</span> fgt.alpha ,</span>
+<span id="cb452-48"><a href="5.1-richness-measures-svyrich.html#cb452-48" tabindex="-1"></a>        <span class="at">type_thresh =</span> <span class="st">&quot;relq&quot;</span>  ,</span>
+<span id="cb452-49"><a href="5.1-richness-measures-svyrich.html#cb452-49" tabindex="-1"></a>        <span class="at">percent =</span> <span class="dv">3</span></span>
+<span id="cb452-50"><a href="5.1-richness-measures-svyrich.html#cb452-50" tabindex="-1"></a>      )</span>
+<span id="cb452-51"><a href="5.1-richness-measures-svyrich.html#cb452-51" tabindex="-1"></a>  )</span>
+<span id="cb452-52"><a href="5.1-richness-measures-svyrich.html#cb452-52" tabindex="-1"></a>  est.list <span class="ot">&lt;-</span> <span class="fu">list</span>(rHC.hat , rCha.hat , rFGTT2.hat)</span>
+<span id="cb452-53"><a href="5.1-richness-measures-svyrich.html#cb452-53" tabindex="-1"></a>  est.list</span>
+<span id="cb452-54"><a href="5.1-richness-measures-svyrich.html#cb452-54" tabindex="-1"></a>  </span>
+<span id="cb452-55"><a href="5.1-richness-measures-svyrich.html#cb452-55" tabindex="-1"></a>})</span></code></pre></div>
 <p>To study the behavior of the estimators, we estimate their expected values, empirical
 variance (for the main parameter) and mean squared error. To study the validity
 of the normal approximation, we also estimate the percent coverage rate of the nominal
 95% confidence interval. This is done using the function below:</p>
-<div class="sourceCode" id="cb454"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb454-1"><a href="5.1-richness-measures-svyrich.html#cb454-1" tabindex="-1"></a>sim.compile <span class="ot">&lt;-</span> <span class="cf">function</span>(ll ,</span>
-<span id="cb454-2"><a href="5.1-richness-measures-svyrich.html#cb454-2" tabindex="-1"></a>                        pv ,</span>
-<span id="cb454-3"><a href="5.1-richness-measures-svyrich.html#cb454-3" tabindex="-1"></a>                        <span class="at">level =</span> .<span class="dv">95</span> ,</span>
-<span id="cb454-4"><a href="5.1-richness-measures-svyrich.html#cb454-4" tabindex="-1"></a>                        <span class="at">na.rm =</span> <span class="cn">FALSE</span>) {</span>
-<span id="cb454-5"><a href="5.1-richness-measures-svyrich.html#cb454-5" tabindex="-1"></a>  <span class="co"># collect estimates</span></span>
-<span id="cb454-6"><a href="5.1-richness-measures-svyrich.html#cb454-6" tabindex="-1"></a>  mhat.vec <span class="ot">&lt;-</span> <span class="fu">sapply</span>(ll , coef)</span>
-<span id="cb454-7"><a href="5.1-richness-measures-svyrich.html#cb454-7" tabindex="-1"></a>  vhat.vec <span class="ot">&lt;-</span> <span class="fu">sapply</span>(ll , vcov)</span>
-<span id="cb454-8"><a href="5.1-richness-measures-svyrich.html#cb454-8" tabindex="-1"></a>  </span>
-<span id="cb454-9"><a href="5.1-richness-measures-svyrich.html#cb454-9" tabindex="-1"></a>  <span class="co"># estimate expected value</span></span>
-<span id="cb454-10"><a href="5.1-richness-measures-svyrich.html#cb454-10" tabindex="-1"></a>  mhat.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(mhat.vec , <span class="at">na.rm =</span> na.rm)</span>
-<span id="cb454-11"><a href="5.1-richness-measures-svyrich.html#cb454-11" tabindex="-1"></a>  vhat.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(vhat.vec , <span class="at">na.rm =</span> na.rm)</span>
-<span id="cb454-12"><a href="5.1-richness-measures-svyrich.html#cb454-12" tabindex="-1"></a>  </span>
-<span id="cb454-13"><a href="5.1-richness-measures-svyrich.html#cb454-13" tabindex="-1"></a>  <span class="co"># calculate empirical variance</span></span>
-<span id="cb454-14"><a href="5.1-richness-measures-svyrich.html#cb454-14" tabindex="-1"></a>  mhat.empvar <span class="ot">&lt;-</span> <span class="fu">var</span>(mhat.vec , <span class="at">na.rm =</span> na.rm)</span>
-<span id="cb454-15"><a href="5.1-richness-measures-svyrich.html#cb454-15" tabindex="-1"></a>  </span>
-<span id="cb454-16"><a href="5.1-richness-measures-svyrich.html#cb454-16" tabindex="-1"></a>  <span class="co"># estimate squared bias</span></span>
-<span id="cb454-17"><a href="5.1-richness-measures-svyrich.html#cb454-17" tabindex="-1"></a>  mhat.bias2 <span class="ot">&lt;-</span> (mhat.exp <span class="sc">-</span> pv) <span class="sc">^</span> <span class="dv">2</span></span>
-<span id="cb454-18"><a href="5.1-richness-measures-svyrich.html#cb454-18" tabindex="-1"></a>  vhat.bias2 <span class="ot">&lt;-</span> (vhat.exp <span class="sc">-</span> mhat.empvar) <span class="sc">^</span> <span class="dv">2</span></span>
-<span id="cb454-19"><a href="5.1-richness-measures-svyrich.html#cb454-19" tabindex="-1"></a>  </span>
-<span id="cb454-20"><a href="5.1-richness-measures-svyrich.html#cb454-20" tabindex="-1"></a>  <span class="co"># estimate mse</span></span>
-<span id="cb454-21"><a href="5.1-richness-measures-svyrich.html#cb454-21" tabindex="-1"></a>  mhat.mse <span class="ot">&lt;-</span> mhat.bias2 <span class="sc">+</span> mhat.empvar</span>
-<span id="cb454-22"><a href="5.1-richness-measures-svyrich.html#cb454-22" tabindex="-1"></a>  </span>
-<span id="cb454-23"><a href="5.1-richness-measures-svyrich.html#cb454-23" tabindex="-1"></a>  <span class="co"># estimate coverage rate</span></span>
-<span id="cb454-24"><a href="5.1-richness-measures-svyrich.html#cb454-24" tabindex="-1"></a>  ci.hats <span class="ot">&lt;-</span> <span class="fu">t</span>(<span class="fu">sapply</span>(ll , confint))</span>
-<span id="cb454-25"><a href="5.1-richness-measures-svyrich.html#cb454-25" tabindex="-1"></a>  ci.check <span class="ot">&lt;-</span></span>
-<span id="cb454-26"><a href="5.1-richness-measures-svyrich.html#cb454-26" tabindex="-1"></a>    <span class="fu">matrix</span>(<span class="fu">as.logical</span>(<span class="cn">NA</span>) , <span class="at">nrow =</span> <span class="fu">nrow</span>(ci.hats) , <span class="at">ncol =</span> <span class="dv">3</span>)</span>
-<span id="cb454-27"><a href="5.1-richness-measures-svyrich.html#cb454-27" tabindex="-1"></a>  ci.check[, <span class="dv">1</span>] <span class="ot">&lt;-</span> ci.hats[, <span class="dv">1</span>] <span class="sc">&lt;=</span> pv</span>
-<span id="cb454-28"><a href="5.1-richness-measures-svyrich.html#cb454-28" tabindex="-1"></a>  ci.check[, <span class="dv">2</span>] <span class="ot">&lt;-</span> ci.hats[, <span class="dv">2</span>] <span class="sc">&gt;=</span> pv</span>
-<span id="cb454-29"><a href="5.1-richness-measures-svyrich.html#cb454-29" tabindex="-1"></a>  ci.check[, <span class="dv">3</span>] <span class="ot">&lt;-</span> <span class="fu">apply</span>(ci.check[, <span class="dv">1</span><span class="sc">:</span><span class="dv">2</span>] , <span class="dv">1</span> , all)</span>
-<span id="cb454-30"><a href="5.1-richness-measures-svyrich.html#cb454-30" tabindex="-1"></a>  pcr.emp <span class="ot">&lt;-</span> <span class="fu">mean</span>(ci.check[, <span class="dv">3</span>] , <span class="at">na.rm =</span> na.rm)</span>
-<span id="cb454-31"><a href="5.1-richness-measures-svyrich.html#cb454-31" tabindex="-1"></a>  </span>
-<span id="cb454-32"><a href="5.1-richness-measures-svyrich.html#cb454-32" tabindex="-1"></a>  <span class="co"># setup final table</span></span>
-<span id="cb454-33"><a href="5.1-richness-measures-svyrich.html#cb454-33" tabindex="-1"></a>  <span class="fu">data.frame</span>(</span>
-<span id="cb454-34"><a href="5.1-richness-measures-svyrich.html#cb454-34" tabindex="-1"></a>    <span class="st">&quot;mc.reps&quot;</span> <span class="ot">=</span> <span class="fu">length</span>(ll) ,</span>
-<span id="cb454-35"><a href="5.1-richness-measures-svyrich.html#cb454-35" tabindex="-1"></a>    <span class="st">&quot;theta&quot;</span> <span class="ot">=</span> pv ,</span>
-<span id="cb454-36"><a href="5.1-richness-measures-svyrich.html#cb454-36" tabindex="-1"></a>    <span class="st">&quot;theta.hat&quot;</span> <span class="ot">=</span> mhat.exp ,</span>
-<span id="cb454-37"><a href="5.1-richness-measures-svyrich.html#cb454-37" tabindex="-1"></a>    <span class="st">&quot;theta.bias2&quot;</span> <span class="ot">=</span> mhat.bias2 ,</span>
-<span id="cb454-38"><a href="5.1-richness-measures-svyrich.html#cb454-38" tabindex="-1"></a>    <span class="st">&quot;theta.empvar&quot;</span> <span class="ot">=</span> mhat.empvar ,</span>
-<span id="cb454-39"><a href="5.1-richness-measures-svyrich.html#cb454-39" tabindex="-1"></a>    <span class="st">&quot;theta.hat.mse&quot;</span> <span class="ot">=</span> mhat.mse ,</span>
-<span id="cb454-40"><a href="5.1-richness-measures-svyrich.html#cb454-40" tabindex="-1"></a>    <span class="st">&quot;theta.varhat&quot;</span> <span class="ot">=</span> vhat.exp ,</span>
-<span id="cb454-41"><a href="5.1-richness-measures-svyrich.html#cb454-41" tabindex="-1"></a>    <span class="st">&quot;pcr&quot;</span> <span class="ot">=</span> pcr.emp</span>
-<span id="cb454-42"><a href="5.1-richness-measures-svyrich.html#cb454-42" tabindex="-1"></a>  )</span>
-<span id="cb454-43"><a href="5.1-richness-measures-svyrich.html#cb454-43" tabindex="-1"></a>}</span></code></pre></div>
+<div class="sourceCode" id="cb453"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb453-1"><a href="5.1-richness-measures-svyrich.html#cb453-1" tabindex="-1"></a>sim.compile <span class="ot">&lt;-</span> <span class="cf">function</span>(ll ,</span>
+<span id="cb453-2"><a href="5.1-richness-measures-svyrich.html#cb453-2" tabindex="-1"></a>                        pv ,</span>
+<span id="cb453-3"><a href="5.1-richness-measures-svyrich.html#cb453-3" tabindex="-1"></a>                        <span class="at">level =</span> .<span class="dv">95</span> ,</span>
+<span id="cb453-4"><a href="5.1-richness-measures-svyrich.html#cb453-4" tabindex="-1"></a>                        <span class="at">na.rm =</span> <span class="cn">FALSE</span>) {</span>
+<span id="cb453-5"><a href="5.1-richness-measures-svyrich.html#cb453-5" tabindex="-1"></a>  <span class="co"># collect estimates</span></span>
+<span id="cb453-6"><a href="5.1-richness-measures-svyrich.html#cb453-6" tabindex="-1"></a>  mhat.vec <span class="ot">&lt;-</span> <span class="fu">sapply</span>(ll , coef)</span>
+<span id="cb453-7"><a href="5.1-richness-measures-svyrich.html#cb453-7" tabindex="-1"></a>  vhat.vec <span class="ot">&lt;-</span> <span class="fu">sapply</span>(ll , vcov)</span>
+<span id="cb453-8"><a href="5.1-richness-measures-svyrich.html#cb453-8" tabindex="-1"></a>  </span>
+<span id="cb453-9"><a href="5.1-richness-measures-svyrich.html#cb453-9" tabindex="-1"></a>  <span class="co"># estimate expected value</span></span>
+<span id="cb453-10"><a href="5.1-richness-measures-svyrich.html#cb453-10" tabindex="-1"></a>  mhat.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(mhat.vec , <span class="at">na.rm =</span> na.rm)</span>
+<span id="cb453-11"><a href="5.1-richness-measures-svyrich.html#cb453-11" tabindex="-1"></a>  vhat.exp <span class="ot">&lt;-</span> <span class="fu">mean</span>(vhat.vec , <span class="at">na.rm =</span> na.rm)</span>
+<span id="cb453-12"><a href="5.1-richness-measures-svyrich.html#cb453-12" tabindex="-1"></a>  </span>
+<span id="cb453-13"><a href="5.1-richness-measures-svyrich.html#cb453-13" tabindex="-1"></a>  <span class="co"># calculate empirical variance</span></span>
+<span id="cb453-14"><a href="5.1-richness-measures-svyrich.html#cb453-14" tabindex="-1"></a>  mhat.empvar <span class="ot">&lt;-</span> <span class="fu">var</span>(mhat.vec , <span class="at">na.rm =</span> na.rm)</span>
+<span id="cb453-15"><a href="5.1-richness-measures-svyrich.html#cb453-15" tabindex="-1"></a>  </span>
+<span id="cb453-16"><a href="5.1-richness-measures-svyrich.html#cb453-16" tabindex="-1"></a>  <span class="co"># estimate squared bias</span></span>
+<span id="cb453-17"><a href="5.1-richness-measures-svyrich.html#cb453-17" tabindex="-1"></a>  mhat.bias2 <span class="ot">&lt;-</span> (mhat.exp <span class="sc">-</span> pv) <span class="sc">^</span> <span class="dv">2</span></span>
+<span id="cb453-18"><a href="5.1-richness-measures-svyrich.html#cb453-18" tabindex="-1"></a>  vhat.bias2 <span class="ot">&lt;-</span> (vhat.exp <span class="sc">-</span> mhat.empvar) <span class="sc">^</span> <span class="dv">2</span></span>
+<span id="cb453-19"><a href="5.1-richness-measures-svyrich.html#cb453-19" tabindex="-1"></a>  </span>
+<span id="cb453-20"><a href="5.1-richness-measures-svyrich.html#cb453-20" tabindex="-1"></a>  <span class="co"># estimate mse</span></span>
+<span id="cb453-21"><a href="5.1-richness-measures-svyrich.html#cb453-21" tabindex="-1"></a>  mhat.mse <span class="ot">&lt;-</span> mhat.bias2 <span class="sc">+</span> mhat.empvar</span>
+<span id="cb453-22"><a href="5.1-richness-measures-svyrich.html#cb453-22" tabindex="-1"></a>  </span>
+<span id="cb453-23"><a href="5.1-richness-measures-svyrich.html#cb453-23" tabindex="-1"></a>  <span class="co"># estimate coverage rate</span></span>
+<span id="cb453-24"><a href="5.1-richness-measures-svyrich.html#cb453-24" tabindex="-1"></a>  ci.hats <span class="ot">&lt;-</span> <span class="fu">t</span>(<span class="fu">sapply</span>(ll , confint))</span>
+<span id="cb453-25"><a href="5.1-richness-measures-svyrich.html#cb453-25" tabindex="-1"></a>  ci.check <span class="ot">&lt;-</span></span>
+<span id="cb453-26"><a href="5.1-richness-measures-svyrich.html#cb453-26" tabindex="-1"></a>    <span class="fu">matrix</span>(<span class="fu">as.logical</span>(<span class="cn">NA</span>) , <span class="at">nrow =</span> <span class="fu">nrow</span>(ci.hats) , <span class="at">ncol =</span> <span class="dv">3</span>)</span>
+<span id="cb453-27"><a href="5.1-richness-measures-svyrich.html#cb453-27" tabindex="-1"></a>  ci.check[, <span class="dv">1</span>] <span class="ot">&lt;-</span> ci.hats[, <span class="dv">1</span>] <span class="sc">&lt;=</span> pv</span>
+<span id="cb453-28"><a href="5.1-richness-measures-svyrich.html#cb453-28" tabindex="-1"></a>  ci.check[, <span class="dv">2</span>] <span class="ot">&lt;-</span> ci.hats[, <span class="dv">2</span>] <span class="sc">&gt;=</span> pv</span>
+<span id="cb453-29"><a href="5.1-richness-measures-svyrich.html#cb453-29" tabindex="-1"></a>  ci.check[, <span class="dv">3</span>] <span class="ot">&lt;-</span> <span class="fu">apply</span>(ci.check[, <span class="dv">1</span><span class="sc">:</span><span class="dv">2</span>] , <span class="dv">1</span> , all)</span>
+<span id="cb453-30"><a href="5.1-richness-measures-svyrich.html#cb453-30" tabindex="-1"></a>  pcr.emp <span class="ot">&lt;-</span> <span class="fu">mean</span>(ci.check[, <span class="dv">3</span>] , <span class="at">na.rm =</span> na.rm)</span>
+<span id="cb453-31"><a href="5.1-richness-measures-svyrich.html#cb453-31" tabindex="-1"></a>  </span>
+<span id="cb453-32"><a href="5.1-richness-measures-svyrich.html#cb453-32" tabindex="-1"></a>  <span class="co"># setup final table</span></span>
+<span id="cb453-33"><a href="5.1-richness-measures-svyrich.html#cb453-33" tabindex="-1"></a>  <span class="fu">data.frame</span>(</span>
+<span id="cb453-34"><a href="5.1-richness-measures-svyrich.html#cb453-34" tabindex="-1"></a>    <span class="st">&quot;mc.reps&quot;</span> <span class="ot">=</span> <span class="fu">length</span>(ll) ,</span>
+<span id="cb453-35"><a href="5.1-richness-measures-svyrich.html#cb453-35" tabindex="-1"></a>    <span class="st">&quot;theta&quot;</span> <span class="ot">=</span> pv ,</span>
+<span id="cb453-36"><a href="5.1-richness-measures-svyrich.html#cb453-36" tabindex="-1"></a>    <span class="st">&quot;theta.hat&quot;</span> <span class="ot">=</span> mhat.exp ,</span>
+<span id="cb453-37"><a href="5.1-richness-measures-svyrich.html#cb453-37" tabindex="-1"></a>    <span class="st">&quot;theta.bias2&quot;</span> <span class="ot">=</span> mhat.bias2 ,</span>
+<span id="cb453-38"><a href="5.1-richness-measures-svyrich.html#cb453-38" tabindex="-1"></a>    <span class="st">&quot;theta.empvar&quot;</span> <span class="ot">=</span> mhat.empvar ,</span>
+<span id="cb453-39"><a href="5.1-richness-measures-svyrich.html#cb453-39" tabindex="-1"></a>    <span class="st">&quot;theta.hat.mse&quot;</span> <span class="ot">=</span> mhat.mse ,</span>
+<span id="cb453-40"><a href="5.1-richness-measures-svyrich.html#cb453-40" tabindex="-1"></a>    <span class="st">&quot;theta.varhat&quot;</span> <span class="ot">=</span> vhat.exp ,</span>
+<span id="cb453-41"><a href="5.1-richness-measures-svyrich.html#cb453-41" tabindex="-1"></a>    <span class="st">&quot;pcr&quot;</span> <span class="ot">=</span> pcr.emp</span>
+<span id="cb453-42"><a href="5.1-richness-measures-svyrich.html#cb453-42" tabindex="-1"></a>  )</span>
+<span id="cb453-43"><a href="5.1-richness-measures-svyrich.html#cb453-43" tabindex="-1"></a>}</span></code></pre></div>
 <p>For the Headcount Richness Ratio (computed using the concave FGT measure), we have:</p>
-<div class="sourceCode" id="cb455"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb455-1"><a href="5.1-richness-measures-svyrich.html#cb455-1" tabindex="-1"></a>rhc.list <span class="ot">&lt;-</span> <span class="fu">lapply</span>(rep.list , <span class="st">`</span><span class="at">[[</span><span class="st">`</span> , <span class="dv">1</span>)</span>
-<span id="cb455-2"><a href="5.1-richness-measures-svyrich.html#cb455-2" tabindex="-1"></a><span class="fu">sim.compile</span>(rhc.list, rHC.fp)</span></code></pre></div>
+<div class="sourceCode" id="cb454"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb454-1"><a href="5.1-richness-measures-svyrich.html#cb454-1" tabindex="-1"></a>rhc.list <span class="ot">&lt;-</span> <span class="fu">lapply</span>(rep.list , <span class="st">`</span><span class="at">[[</span><span class="st">`</span> , <span class="dv">1</span>)</span>
+<span id="cb454-2"><a href="5.1-richness-measures-svyrich.html#cb454-2" tabindex="-1"></a><span class="fu">sim.compile</span>(rhc.list, rHC.fp)</span></code></pre></div>
 <pre><code>##   mc.reps   theta  theta.hat  theta.bias2 theta.empvar theta.hat.mse
 ## 1    5000 0.05469 0.05452618 2.683797e-08 4.112616e-05    4.1153e-05
 ##   theta.varhat    pcr
 ## 1 4.336252e-05 0.9524</code></pre>
-<div class="sourceCode" id="cb457"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb457-1"><a href="5.1-richness-measures-svyrich.html#cb457-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
-<span id="cb457-2"><a href="5.1-richness-measures-svyrich.html#cb457-2" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;theta.bias2&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;theta.hat.mse&quot;</span>] ,</span>
-<span id="cb457-3"><a href="5.1-richness-measures-svyrich.html#cb457-3" tabindex="-1"></a>  <span class="dv">4</span></span>
-<span id="cb457-4"><a href="5.1-richness-measures-svyrich.html#cb457-4" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.0007</span>)</span>
-<span id="cb457-5"><a href="5.1-richness-measures-svyrich.html#cb457-5" tabindex="-1"></a></span>
-<span id="cb457-6"><a href="5.1-richness-measures-svyrich.html#cb457-6" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
-<span id="cb457-7"><a href="5.1-richness-measures-svyrich.html#cb457-7" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;theta.varhat&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;theta.empvar&quot;</span>] ,</span>
-<span id="cb457-8"><a href="5.1-richness-measures-svyrich.html#cb457-8" tabindex="-1"></a>  <span class="dv">2</span></span>
-<span id="cb457-9"><a href="5.1-richness-measures-svyrich.html#cb457-9" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">1.05</span>)</span>
-<span id="cb457-10"><a href="5.1-richness-measures-svyrich.html#cb457-10" tabindex="-1"></a></span>
-<span id="cb457-11"><a href="5.1-richness-measures-svyrich.html#cb457-11" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;pcr&quot;</span>] , <span class="dv">4</span>) <span class="sc">==</span> <span class="fl">0.9524</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb456"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb456-1"><a href="5.1-richness-measures-svyrich.html#cb456-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
+<span id="cb456-2"><a href="5.1-richness-measures-svyrich.html#cb456-2" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;theta.bias2&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;theta.hat.mse&quot;</span>] ,</span>
+<span id="cb456-3"><a href="5.1-richness-measures-svyrich.html#cb456-3" tabindex="-1"></a>  <span class="dv">4</span></span>
+<span id="cb456-4"><a href="5.1-richness-measures-svyrich.html#cb456-4" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.0007</span>)</span>
+<span id="cb456-5"><a href="5.1-richness-measures-svyrich.html#cb456-5" tabindex="-1"></a></span>
+<span id="cb456-6"><a href="5.1-richness-measures-svyrich.html#cb456-6" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
+<span id="cb456-7"><a href="5.1-richness-measures-svyrich.html#cb456-7" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;theta.varhat&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;theta.empvar&quot;</span>] ,</span>
+<span id="cb456-8"><a href="5.1-richness-measures-svyrich.html#cb456-8" tabindex="-1"></a>  <span class="dv">2</span></span>
+<span id="cb456-9"><a href="5.1-richness-measures-svyrich.html#cb456-9" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">1.05</span>)</span>
+<span id="cb456-10"><a href="5.1-richness-measures-svyrich.html#cb456-10" tabindex="-1"></a></span>
+<span id="cb456-11"><a href="5.1-richness-measures-svyrich.html#cb456-11" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">sim.compile</span>(rhc.list, rHC.fp)[<span class="st">&quot;pcr&quot;</span>] , <span class="dv">4</span>) <span class="sc">==</span> <span class="fl">0.9524</span>)</span></code></pre></div>
 <p>Under this approach, the squared bias accounts for approx. 0.07% of the MSE, indicating
 that the MSE of the estimator is reasonably approximated by its variance. Additionally,
 the ratio between the expected value of the variance estimator and the empirical
@@ -465,23 +465,23 @@ <h3><span class="header-section-number">5.1.1</span> Monte Carlo Simulation</h3>
 Finally, the estimated percent coverage rate of 95.24% is close to the nominal
 level of 95%, indicating that the confidence intervals are approximately valid.</p>
 <p>For the Chakravarty measure, we have:</p>
-<div class="sourceCode" id="cb458"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb458-1"><a href="5.1-richness-measures-svyrich.html#cb458-1" tabindex="-1"></a>rcha.list <span class="ot">&lt;-</span> <span class="fu">lapply</span>(rep.list , <span class="st">`</span><span class="at">[[</span><span class="st">`</span> , <span class="dv">2</span>)</span>
-<span id="cb458-2"><a href="5.1-richness-measures-svyrich.html#cb458-2" tabindex="-1"></a><span class="fu">sim.compile</span>(rcha.list, rCha.fp)</span></code></pre></div>
+<div class="sourceCode" id="cb457"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb457-1"><a href="5.1-richness-measures-svyrich.html#cb457-1" tabindex="-1"></a>rcha.list <span class="ot">&lt;-</span> <span class="fu">lapply</span>(rep.list , <span class="st">`</span><span class="at">[[</span><span class="st">`</span> , <span class="dv">2</span>)</span>
+<span id="cb457-2"><a href="5.1-richness-measures-svyrich.html#cb457-2" tabindex="-1"></a><span class="fu">sim.compile</span>(rcha.list, rCha.fp)</span></code></pre></div>
 <pre><code>##   mc.reps      theta  theta.hat  theta.bias2 theta.empvar theta.hat.mse
 ## 1    5000 0.02743915 0.02737177 4.538966e-09 1.428639e-05  1.429093e-05
 ##   theta.varhat    pcr
 ## 1 1.402416e-05 0.9428</code></pre>
-<div class="sourceCode" id="cb460"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb460-1"><a href="5.1-richness-measures-svyrich.html#cb460-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
-<span id="cb460-2"><a href="5.1-richness-measures-svyrich.html#cb460-2" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;theta.bias2&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;theta.hat.mse&quot;</span>] ,</span>
-<span id="cb460-3"><a href="5.1-richness-measures-svyrich.html#cb460-3" tabindex="-1"></a>  <span class="dv">4</span></span>
-<span id="cb460-4"><a href="5.1-richness-measures-svyrich.html#cb460-4" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.0003</span>)</span>
-<span id="cb460-5"><a href="5.1-richness-measures-svyrich.html#cb460-5" tabindex="-1"></a></span>
-<span id="cb460-6"><a href="5.1-richness-measures-svyrich.html#cb460-6" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
-<span id="cb460-7"><a href="5.1-richness-measures-svyrich.html#cb460-7" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;theta.varhat&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;theta.empvar&quot;</span>] ,</span>
-<span id="cb460-8"><a href="5.1-richness-measures-svyrich.html#cb460-8" tabindex="-1"></a>  <span class="dv">2</span></span>
-<span id="cb460-9"><a href="5.1-richness-measures-svyrich.html#cb460-9" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.98</span>)</span>
-<span id="cb460-10"><a href="5.1-richness-measures-svyrich.html#cb460-10" tabindex="-1"></a></span>
-<span id="cb460-11"><a href="5.1-richness-measures-svyrich.html#cb460-11" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;pcr&quot;</span>] , <span class="dv">4</span>) <span class="sc">==</span> <span class="fl">0.9428</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb459"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb459-1"><a href="5.1-richness-measures-svyrich.html#cb459-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
+<span id="cb459-2"><a href="5.1-richness-measures-svyrich.html#cb459-2" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;theta.bias2&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;theta.hat.mse&quot;</span>] ,</span>
+<span id="cb459-3"><a href="5.1-richness-measures-svyrich.html#cb459-3" tabindex="-1"></a>  <span class="dv">4</span></span>
+<span id="cb459-4"><a href="5.1-richness-measures-svyrich.html#cb459-4" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.0003</span>)</span>
+<span id="cb459-5"><a href="5.1-richness-measures-svyrich.html#cb459-5" tabindex="-1"></a></span>
+<span id="cb459-6"><a href="5.1-richness-measures-svyrich.html#cb459-6" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
+<span id="cb459-7"><a href="5.1-richness-measures-svyrich.html#cb459-7" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;theta.varhat&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;theta.empvar&quot;</span>] ,</span>
+<span id="cb459-8"><a href="5.1-richness-measures-svyrich.html#cb459-8" tabindex="-1"></a>  <span class="dv">2</span></span>
+<span id="cb459-9"><a href="5.1-richness-measures-svyrich.html#cb459-9" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.98</span>)</span>
+<span id="cb459-10"><a href="5.1-richness-measures-svyrich.html#cb459-10" tabindex="-1"></a></span>
+<span id="cb459-11"><a href="5.1-richness-measures-svyrich.html#cb459-11" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">sim.compile</span>(rcha.list, rCha.fp)[<span class="st">&quot;pcr&quot;</span>] , <span class="dv">4</span>) <span class="sc">==</span> <span class="fl">0.9428</span>)</span></code></pre></div>
 <p>Under this approach, the squared bias is approx 0.03% of the MSE, indicating that
 the MSE of the estimator is reasonably approximated by its variance. Additionally,
 the ratio between the expected value of the variance estimator and the empirical
@@ -490,23 +490,23 @@ <h3><span class="header-section-number">5.1.1</span> Monte Carlo Simulation</h3>
 coverage rate of 94.28% is close to the nominal level of 95%, indicating that the
 confidence intervals are approximately valid.</p>
 <p>For the convex FGT measure, we have:</p>
-<div class="sourceCode" id="cb461"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb461-1"><a href="5.1-richness-measures-svyrich.html#cb461-1" tabindex="-1"></a>rfgtt2.list <span class="ot">&lt;-</span> <span class="fu">lapply</span>(rep.list , <span class="st">`</span><span class="at">[[</span><span class="st">`</span> , <span class="dv">3</span>)</span>
-<span id="cb461-2"><a href="5.1-richness-measures-svyrich.html#cb461-2" tabindex="-1"></a><span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)</span></code></pre></div>
+<div class="sourceCode" id="cb460"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb460-1"><a href="5.1-richness-measures-svyrich.html#cb460-1" tabindex="-1"></a>rfgtt2.list <span class="ot">&lt;-</span> <span class="fu">lapply</span>(rep.list , <span class="st">`</span><span class="at">[[</span><span class="st">`</span> , <span class="dv">3</span>)</span>
+<span id="cb460-2"><a href="5.1-richness-measures-svyrich.html#cb460-2" tabindex="-1"></a><span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)</span></code></pre></div>
 <pre><code>##   mc.reps      theta theta.hat theta.bias2 theta.empvar theta.hat.mse
 ## 1    5000 0.02349189 0.1045973  0.00657808   0.01865219    0.02523027
 ##   theta.varhat    pcr
 ## 1   0.01857144 0.5212</code></pre>
-<div class="sourceCode" id="cb463"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb463-1"><a href="5.1-richness-measures-svyrich.html#cb463-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
-<span id="cb463-2"><a href="5.1-richness-measures-svyrich.html#cb463-2" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;theta.bias2&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;theta.hat.mse&quot;</span>] ,</span>
-<span id="cb463-3"><a href="5.1-richness-measures-svyrich.html#cb463-3" tabindex="-1"></a>  <span class="dv">2</span></span>
-<span id="cb463-4"><a href="5.1-richness-measures-svyrich.html#cb463-4" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.26</span>)</span>
-<span id="cb463-5"><a href="5.1-richness-measures-svyrich.html#cb463-5" tabindex="-1"></a></span>
-<span id="cb463-6"><a href="5.1-richness-measures-svyrich.html#cb463-6" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
-<span id="cb463-7"><a href="5.1-richness-measures-svyrich.html#cb463-7" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;theta.varhat&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;theta.empvar&quot;</span>] ,</span>
-<span id="cb463-8"><a href="5.1-richness-measures-svyrich.html#cb463-8" tabindex="-1"></a>  <span class="dv">2</span></span>
-<span id="cb463-9"><a href="5.1-richness-measures-svyrich.html#cb463-9" tabindex="-1"></a>) <span class="sc">==</span> <span class="dv">1</span>)</span>
-<span id="cb463-10"><a href="5.1-richness-measures-svyrich.html#cb463-10" tabindex="-1"></a></span>
-<span id="cb463-11"><a href="5.1-richness-measures-svyrich.html#cb463-11" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;pcr&quot;</span>] , <span class="dv">4</span>) <span class="sc">==</span> <span class="fl">0.5212</span>)</span></code></pre></div>
+<div class="sourceCode" id="cb462"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb462-1"><a href="5.1-richness-measures-svyrich.html#cb462-1" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
+<span id="cb462-2"><a href="5.1-richness-measures-svyrich.html#cb462-2" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;theta.bias2&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;theta.hat.mse&quot;</span>] ,</span>
+<span id="cb462-3"><a href="5.1-richness-measures-svyrich.html#cb462-3" tabindex="-1"></a>  <span class="dv">2</span></span>
+<span id="cb462-4"><a href="5.1-richness-measures-svyrich.html#cb462-4" tabindex="-1"></a>) <span class="sc">==</span> <span class="fl">0.26</span>)</span>
+<span id="cb462-5"><a href="5.1-richness-measures-svyrich.html#cb462-5" tabindex="-1"></a></span>
+<span id="cb462-6"><a href="5.1-richness-measures-svyrich.html#cb462-6" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(</span>
+<span id="cb462-7"><a href="5.1-richness-measures-svyrich.html#cb462-7" tabindex="-1"></a>  <span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;theta.varhat&quot;</span>] <span class="sc">/</span> <span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;theta.empvar&quot;</span>] ,</span>
+<span id="cb462-8"><a href="5.1-richness-measures-svyrich.html#cb462-8" tabindex="-1"></a>  <span class="dv">2</span></span>
+<span id="cb462-9"><a href="5.1-richness-measures-svyrich.html#cb462-9" tabindex="-1"></a>) <span class="sc">==</span> <span class="dv">1</span>)</span>
+<span id="cb462-10"><a href="5.1-richness-measures-svyrich.html#cb462-10" tabindex="-1"></a></span>
+<span id="cb462-11"><a href="5.1-richness-measures-svyrich.html#cb462-11" tabindex="-1"></a><span class="fu">stopifnot</span>(<span class="fu">round</span>(<span class="fu">sim.compile</span>(rfgtt2.list, rFGTT2.fp)[<span class="st">&quot;pcr&quot;</span>] , <span class="dv">4</span>) <span class="sc">==</span> <span class="fl">0.5212</span>)</span></code></pre></div>
 <p>Under this approach, the squared bias is approx 26% of the MSE, indicating that
 the <em>bias is substantial</em>. The ratio between the expected value of the variance
 estimator and the empirical variance is approx. 1.00, indicating that the variance
diff --git a/docs/6-multidimensional-poverty.html b/docs/6-multidimensional-poverty.html
index 0b708ad..f48c5a1 100644
--- a/docs/6-multidimensional-poverty.html
+++ b/docs/6-multidimensional-poverty.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
diff --git a/docs/6.1-example-calculation.html b/docs/6.1-example-calculation.html
index 52f47fa..aed89de 100644
--- a/docs/6.1-example-calculation.html
+++ b/docs/6.1-example-calculation.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
diff --git a/docs/7-covariance-matrix.html b/docs/7-covariance-matrix.html
index 1bb25f2..5f9e32c 100644
--- a/docs/7-covariance-matrix.html
+++ b/docs/7-covariance-matrix.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -269,36 +269,36 @@ <h1><span class="header-section-number">Chapter 7</span> Covariance Matrix</h1>
 <p>Then, how can we estimate the covariance? The <code>survey</code> package already provides an
 approach for that using the <code>svyby</code>function. Based on the <code>?survey::svyby</code> examples,
 we have:</p>
-<div class="sourceCode" id="cb464"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb464-1"><a href="7-covariance-matrix.html#cb464-1" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb464-2"><a href="7-covariance-matrix.html#cb464-2" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb464-3"><a href="7-covariance-matrix.html#cb464-3" tabindex="-1"></a></span>
-<span id="cb464-4"><a href="7-covariance-matrix.html#cb464-4" tabindex="-1"></a><span class="co">#  load data set</span></span>
-<span id="cb464-5"><a href="7-covariance-matrix.html#cb464-5" tabindex="-1"></a><span class="fu">data</span>( api )</span>
-<span id="cb464-6"><a href="7-covariance-matrix.html#cb464-6" tabindex="-1"></a></span>
-<span id="cb464-7"><a href="7-covariance-matrix.html#cb464-7" tabindex="-1"></a><span class="co"># declare sampling design</span></span>
-<span id="cb464-8"><a href="7-covariance-matrix.html#cb464-8" tabindex="-1"></a>dclus1 <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="at">id=</span><span class="sc">~</span>dnum, <span class="at">weights=</span><span class="sc">~</span>pw, <span class="at">data=</span>apiclus1, <span class="at">fpc=</span><span class="sc">~</span>fpc )</span>
-<span id="cb464-9"><a href="7-covariance-matrix.html#cb464-9" tabindex="-1"></a></span>
-<span id="cb464-10"><a href="7-covariance-matrix.html#cb464-10" tabindex="-1"></a><span class="co"># estimate means</span></span>
-<span id="cb464-11"><a href="7-covariance-matrix.html#cb464-11" tabindex="-1"></a>mns <span class="ot">&lt;-</span><span class="fu">svyby</span>(<span class="sc">~</span>api99, <span class="sc">~</span>stype, dclus1, svymean,<span class="at">covmat=</span><span class="cn">TRUE</span>)</span>
-<span id="cb464-12"><a href="7-covariance-matrix.html#cb464-12" tabindex="-1"></a></span>
-<span id="cb464-13"><a href="7-covariance-matrix.html#cb464-13" tabindex="-1"></a><span class="co"># collect variacnce-covariance matrix of estimates</span></span>
-<span id="cb464-14"><a href="7-covariance-matrix.html#cb464-14" tabindex="-1"></a>( m <span class="ot">&lt;-</span> <span class="fu">vcov</span>( mns ) )</span></code></pre></div>
+<div class="sourceCode" id="cb463"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb463-1"><a href="7-covariance-matrix.html#cb463-1" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb463-2"><a href="7-covariance-matrix.html#cb463-2" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb463-3"><a href="7-covariance-matrix.html#cb463-3" tabindex="-1"></a></span>
+<span id="cb463-4"><a href="7-covariance-matrix.html#cb463-4" tabindex="-1"></a><span class="co">#  load data set</span></span>
+<span id="cb463-5"><a href="7-covariance-matrix.html#cb463-5" tabindex="-1"></a><span class="fu">data</span>( api )</span>
+<span id="cb463-6"><a href="7-covariance-matrix.html#cb463-6" tabindex="-1"></a></span>
+<span id="cb463-7"><a href="7-covariance-matrix.html#cb463-7" tabindex="-1"></a><span class="co"># declare sampling design</span></span>
+<span id="cb463-8"><a href="7-covariance-matrix.html#cb463-8" tabindex="-1"></a>dclus1 <span class="ot">&lt;-</span> <span class="fu">svydesign</span>( <span class="at">id=</span><span class="sc">~</span>dnum, <span class="at">weights=</span><span class="sc">~</span>pw, <span class="at">data=</span>apiclus1, <span class="at">fpc=</span><span class="sc">~</span>fpc )</span>
+<span id="cb463-9"><a href="7-covariance-matrix.html#cb463-9" tabindex="-1"></a></span>
+<span id="cb463-10"><a href="7-covariance-matrix.html#cb463-10" tabindex="-1"></a><span class="co"># estimate means</span></span>
+<span id="cb463-11"><a href="7-covariance-matrix.html#cb463-11" tabindex="-1"></a>mns <span class="ot">&lt;-</span><span class="fu">svyby</span>(<span class="sc">~</span>api99, <span class="sc">~</span>stype, dclus1, svymean,<span class="at">covmat=</span><span class="cn">TRUE</span>)</span>
+<span id="cb463-12"><a href="7-covariance-matrix.html#cb463-12" tabindex="-1"></a></span>
+<span id="cb463-13"><a href="7-covariance-matrix.html#cb463-13" tabindex="-1"></a><span class="co"># collect variacnce-covariance matrix of estimates</span></span>
+<span id="cb463-14"><a href="7-covariance-matrix.html#cb463-14" tabindex="-1"></a>( m <span class="ot">&lt;-</span> <span class="fu">vcov</span>( mns ) )</span></code></pre></div>
 <pre><code>##          E         H         M
 ## E 520.5973  573.0404  684.6562
 ## H 573.0404 1744.2317  747.1989
 ## M 684.6562  747.1989 1060.1954</code></pre>
-<div class="sourceCode" id="cb466"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb466-1"><a href="7-covariance-matrix.html#cb466-1" tabindex="-1"></a><span class="co"># compute variance terms</span></span>
-<span id="cb466-2"><a href="7-covariance-matrix.html#cb466-2" tabindex="-1"></a>var.naive <span class="ot">&lt;-</span> <span class="fu">sum</span>( <span class="fu">diag</span>( m[<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">3</span>),<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">3</span>)] ) )</span>
-<span id="cb466-3"><a href="7-covariance-matrix.html#cb466-3" tabindex="-1"></a>cov.term <span class="ot">&lt;-</span> <span class="fu">sum</span>( <span class="fu">diag</span>( m[ <span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">3</span>),<span class="fu">c</span>(<span class="dv">3</span>,<span class="dv">1</span>)] ) )</span>
-<span id="cb466-4"><a href="7-covariance-matrix.html#cb466-4" tabindex="-1"></a></span>
-<span id="cb466-5"><a href="7-covariance-matrix.html#cb466-5" tabindex="-1"></a><span class="co"># &quot;naive&quot; SE of the difference</span></span>
-<span id="cb466-6"><a href="7-covariance-matrix.html#cb466-6" tabindex="-1"></a><span class="fu">sqrt</span>( var.naive )</span></code></pre></div>
+<div class="sourceCode" id="cb465"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb465-1"><a href="7-covariance-matrix.html#cb465-1" tabindex="-1"></a><span class="co"># compute variance terms</span></span>
+<span id="cb465-2"><a href="7-covariance-matrix.html#cb465-2" tabindex="-1"></a>var.naive <span class="ot">&lt;-</span> <span class="fu">sum</span>( <span class="fu">diag</span>( m[<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">3</span>),<span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">3</span>)] ) )</span>
+<span id="cb465-3"><a href="7-covariance-matrix.html#cb465-3" tabindex="-1"></a>cov.term <span class="ot">&lt;-</span> <span class="fu">sum</span>( <span class="fu">diag</span>( m[ <span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">3</span>),<span class="fu">c</span>(<span class="dv">3</span>,<span class="dv">1</span>)] ) )</span>
+<span id="cb465-4"><a href="7-covariance-matrix.html#cb465-4" tabindex="-1"></a></span>
+<span id="cb465-5"><a href="7-covariance-matrix.html#cb465-5" tabindex="-1"></a><span class="co"># &quot;naive&quot; SE of the difference</span></span>
+<span id="cb465-6"><a href="7-covariance-matrix.html#cb465-6" tabindex="-1"></a><span class="fu">sqrt</span>( var.naive )</span></code></pre></div>
 <pre><code>## [1] 39.75918</code></pre>
-<div class="sourceCode" id="cb468"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb468-1"><a href="7-covariance-matrix.html#cb468-1" tabindex="-1"></a><span class="co"># SE of the difference</span></span>
-<span id="cb468-2"><a href="7-covariance-matrix.html#cb468-2" tabindex="-1"></a><span class="fu">sqrt</span>( var.naive <span class="sc">-</span> cov.term )</span></code></pre></div>
+<div class="sourceCode" id="cb467"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb467-1"><a href="7-covariance-matrix.html#cb467-1" tabindex="-1"></a><span class="co"># SE of the difference</span></span>
+<span id="cb467-2"><a href="7-covariance-matrix.html#cb467-2" tabindex="-1"></a><span class="fu">sqrt</span>( var.naive <span class="sc">-</span> cov.term )</span></code></pre></div>
 <pre><code>## [1] 14.54236</code></pre>
-<div class="sourceCode" id="cb470"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb470-1"><a href="7-covariance-matrix.html#cb470-1" tabindex="-1"></a><span class="co">#... or using svycontrast</span></span>
-<span id="cb470-2"><a href="7-covariance-matrix.html#cb470-2" tabindex="-1"></a><span class="fu">svycontrast</span>( mns , <span class="fu">c</span>(<span class="at">E =</span> <span class="dv">1</span>, <span class="at">M =</span> <span class="sc">-</span><span class="dv">1</span>) )</span></code></pre></div>
+<div class="sourceCode" id="cb469"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb469-1"><a href="7-covariance-matrix.html#cb469-1" tabindex="-1"></a><span class="co">#... or using svycontrast</span></span>
+<span id="cb469-2"><a href="7-covariance-matrix.html#cb469-2" tabindex="-1"></a><span class="fu">svycontrast</span>( mns , <span class="fu">c</span>(<span class="at">E =</span> <span class="dv">1</span>, <span class="at">M =</span> <span class="sc">-</span><span class="dv">1</span>) )</span></code></pre></div>
 <pre><code>##          contrast     SE
 ## contrast -0.80833 14.542</code></pre>
 <p>Notice that, because the covariance terms are positive, the (actual) variance of
diff --git a/docs/7.1-example-calculation-1.html b/docs/7.1-example-calculation-1.html
index 27768f1..89d9bcb 100644
--- a/docs/7.1-example-calculation-1.html
+++ b/docs/7.1-example-calculation-1.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -254,76 +254,76 @@
 <div id="example-calculation-1" class="section level2" number="7.1">
 <h2><span class="header-section-number">7.1</span> Example Calculation</h2>
 <p>We start by showing what has been implemented — the resampling based approach:</p>
-<div class="sourceCode" id="cb472"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb472-1"><a href="7.1-example-calculation-1.html#cb472-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
-<span id="cb472-2"><a href="7.1-example-calculation-1.html#cb472-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
-<span id="cb472-3"><a href="7.1-example-calculation-1.html#cb472-3" tabindex="-1"></a></span>
-<span id="cb472-4"><a href="7.1-example-calculation-1.html#cb472-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
-<span id="cb472-5"><a href="7.1-example-calculation-1.html#cb472-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
-<span id="cb472-6"><a href="7.1-example-calculation-1.html#cb472-6" tabindex="-1"></a></span>
-<span id="cb472-7"><a href="7.1-example-calculation-1.html#cb472-7" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
-<span id="cb472-8"><a href="7.1-example-calculation-1.html#cb472-8" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
-<span id="cb472-9"><a href="7.1-example-calculation-1.html#cb472-9" tabindex="-1"></a></span>
-<span id="cb472-10"><a href="7.1-example-calculation-1.html#cb472-10" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
-<span id="cb472-11"><a href="7.1-example-calculation-1.html#cb472-11" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
-<span id="cb472-12"><a href="7.1-example-calculation-1.html#cb472-12" tabindex="-1"></a></span>
-<span id="cb472-13"><a href="7.1-example-calculation-1.html#cb472-13" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
-<span id="cb472-14"><a href="7.1-example-calculation-1.html#cb472-14" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
-<span id="cb472-15"><a href="7.1-example-calculation-1.html#cb472-15" tabindex="-1"></a></span>
-<span id="cb472-16"><a href="7.1-example-calculation-1.html#cb472-16" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
-<span id="cb472-17"><a href="7.1-example-calculation-1.html#cb472-17" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
-<span id="cb472-18"><a href="7.1-example-calculation-1.html#cb472-18" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
-<span id="cb472-19"><a href="7.1-example-calculation-1.html#cb472-19" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
-<span id="cb472-20"><a href="7.1-example-calculation-1.html#cb472-20" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
-<span id="cb472-21"><a href="7.1-example-calculation-1.html#cb472-21" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
-<span id="cb472-22"><a href="7.1-example-calculation-1.html#cb472-22" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
-<span id="cb472-23"><a href="7.1-example-calculation-1.html#cb472-23" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
-<span id="cb472-24"><a href="7.1-example-calculation-1.html#cb472-24" tabindex="-1"></a>  )</span>
-<span id="cb472-25"><a href="7.1-example-calculation-1.html#cb472-25" tabindex="-1"></a></span>
-<span id="cb472-26"><a href="7.1-example-calculation-1.html#cb472-26" tabindex="-1"></a><span class="co"># create bootstrap-based design object</span></span>
-<span id="cb472-27"><a href="7.1-example-calculation-1.html#cb472-27" tabindex="-1"></a>des_eusilc_rep <span class="ot">&lt;-</span> <span class="fu">as.svrepdesign</span>( des_eusilc , <span class="at">type =</span> <span class="st">&quot;bootstrap&quot;</span> )</span>
-<span id="cb472-28"><a href="7.1-example-calculation-1.html#cb472-28" tabindex="-1"></a></span>
-<span id="cb472-29"><a href="7.1-example-calculation-1.html#cb472-29" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
-<span id="cb472-30"><a href="7.1-example-calculation-1.html#cb472-30" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>( des_eusilc )</span>
-<span id="cb472-31"><a href="7.1-example-calculation-1.html#cb472-31" tabindex="-1"></a>des_eusilc_rep <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc_rep)</span>
-<span id="cb472-32"><a href="7.1-example-calculation-1.html#cb472-32" tabindex="-1"></a></span>
-<span id="cb472-33"><a href="7.1-example-calculation-1.html#cb472-33" tabindex="-1"></a><span class="co"># estimate gini by gender, with and without covariance matrices</span></span>
-<span id="cb472-34"><a href="7.1-example-calculation-1.html#cb472-34" tabindex="-1"></a>ginis.rep <span class="ot">&lt;-</span> <span class="fu">svyby</span>( <span class="sc">~</span> py010n , <span class="sc">~</span>rb090 , des_eusilc_rep , svygini , <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">covmat =</span> <span class="cn">TRUE</span> )</span>
-<span id="cb472-35"><a href="7.1-example-calculation-1.html#cb472-35" tabindex="-1"></a>ginis.rep.nocov <span class="ot">&lt;-</span> <span class="fu">svyby</span>( <span class="sc">~</span> py010n , <span class="sc">~</span>rb090 , des_eusilc_rep , svygini , <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">covmat =</span> <span class="cn">FALSE</span> )</span>
-<span id="cb472-36"><a href="7.1-example-calculation-1.html#cb472-36" tabindex="-1"></a></span>
-<span id="cb472-37"><a href="7.1-example-calculation-1.html#cb472-37" tabindex="-1"></a><span class="co"># variance of the gini difference: naive</span></span>
-<span id="cb472-38"><a href="7.1-example-calculation-1.html#cb472-38" tabindex="-1"></a><span class="fu">svycontrast</span>( ginis.rep.nocov , <span class="fu">quote</span>( <span class="st">`</span><span class="at">male</span><span class="st">`</span> <span class="sc">-</span> <span class="st">`</span><span class="at">female</span><span class="st">`</span> ) )</span></code></pre></div>
+<div class="sourceCode" id="cb471"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb471-1"><a href="7.1-example-calculation-1.html#cb471-1" tabindex="-1"></a><span class="co"># load the convey package</span></span>
+<span id="cb471-2"><a href="7.1-example-calculation-1.html#cb471-2" tabindex="-1"></a><span class="fu">library</span>(convey)</span>
+<span id="cb471-3"><a href="7.1-example-calculation-1.html#cb471-3" tabindex="-1"></a></span>
+<span id="cb471-4"><a href="7.1-example-calculation-1.html#cb471-4" tabindex="-1"></a><span class="co"># load the survey library</span></span>
+<span id="cb471-5"><a href="7.1-example-calculation-1.html#cb471-5" tabindex="-1"></a><span class="fu">library</span>(survey)</span>
+<span id="cb471-6"><a href="7.1-example-calculation-1.html#cb471-6" tabindex="-1"></a></span>
+<span id="cb471-7"><a href="7.1-example-calculation-1.html#cb471-7" tabindex="-1"></a><span class="co"># load the laeken library</span></span>
+<span id="cb471-8"><a href="7.1-example-calculation-1.html#cb471-8" tabindex="-1"></a><span class="fu">library</span>(laeken)</span>
+<span id="cb471-9"><a href="7.1-example-calculation-1.html#cb471-9" tabindex="-1"></a></span>
+<span id="cb471-10"><a href="7.1-example-calculation-1.html#cb471-10" tabindex="-1"></a><span class="co"># load the synthetic EU statistics on income &amp; living conditions</span></span>
+<span id="cb471-11"><a href="7.1-example-calculation-1.html#cb471-11" tabindex="-1"></a><span class="fu">data</span>(eusilc)</span>
+<span id="cb471-12"><a href="7.1-example-calculation-1.html#cb471-12" tabindex="-1"></a></span>
+<span id="cb471-13"><a href="7.1-example-calculation-1.html#cb471-13" tabindex="-1"></a><span class="co"># make all column names lowercase</span></span>
+<span id="cb471-14"><a href="7.1-example-calculation-1.html#cb471-14" tabindex="-1"></a><span class="fu">names</span>(eusilc) <span class="ot">&lt;-</span> <span class="fu">tolower</span>(<span class="fu">names</span>(eusilc))</span>
+<span id="cb471-15"><a href="7.1-example-calculation-1.html#cb471-15" tabindex="-1"></a></span>
+<span id="cb471-16"><a href="7.1-example-calculation-1.html#cb471-16" tabindex="-1"></a><span class="co"># construct a survey.design</span></span>
+<span id="cb471-17"><a href="7.1-example-calculation-1.html#cb471-17" tabindex="-1"></a><span class="co"># using our recommended setup</span></span>
+<span id="cb471-18"><a href="7.1-example-calculation-1.html#cb471-18" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span></span>
+<span id="cb471-19"><a href="7.1-example-calculation-1.html#cb471-19" tabindex="-1"></a>  <span class="fu">svydesign</span>(</span>
+<span id="cb471-20"><a href="7.1-example-calculation-1.html#cb471-20" tabindex="-1"></a>    <span class="at">ids =</span> <span class="sc">~</span> rb030 ,</span>
+<span id="cb471-21"><a href="7.1-example-calculation-1.html#cb471-21" tabindex="-1"></a>    <span class="at">strata =</span> <span class="sc">~</span> db040 ,</span>
+<span id="cb471-22"><a href="7.1-example-calculation-1.html#cb471-22" tabindex="-1"></a>    <span class="at">weights =</span> <span class="sc">~</span> rb050 ,</span>
+<span id="cb471-23"><a href="7.1-example-calculation-1.html#cb471-23" tabindex="-1"></a>    <span class="at">data =</span> eusilc</span>
+<span id="cb471-24"><a href="7.1-example-calculation-1.html#cb471-24" tabindex="-1"></a>  )</span>
+<span id="cb471-25"><a href="7.1-example-calculation-1.html#cb471-25" tabindex="-1"></a></span>
+<span id="cb471-26"><a href="7.1-example-calculation-1.html#cb471-26" tabindex="-1"></a><span class="co"># create bootstrap-based design object</span></span>
+<span id="cb471-27"><a href="7.1-example-calculation-1.html#cb471-27" tabindex="-1"></a>des_eusilc_rep <span class="ot">&lt;-</span> <span class="fu">as.svrepdesign</span>( des_eusilc , <span class="at">type =</span> <span class="st">&quot;bootstrap&quot;</span> )</span>
+<span id="cb471-28"><a href="7.1-example-calculation-1.html#cb471-28" tabindex="-1"></a></span>
+<span id="cb471-29"><a href="7.1-example-calculation-1.html#cb471-29" tabindex="-1"></a><span class="co"># immediately run the convey_prep function on it</span></span>
+<span id="cb471-30"><a href="7.1-example-calculation-1.html#cb471-30" tabindex="-1"></a>des_eusilc <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>( des_eusilc )</span>
+<span id="cb471-31"><a href="7.1-example-calculation-1.html#cb471-31" tabindex="-1"></a>des_eusilc_rep <span class="ot">&lt;-</span> <span class="fu">convey_prep</span>(des_eusilc_rep)</span>
+<span id="cb471-32"><a href="7.1-example-calculation-1.html#cb471-32" tabindex="-1"></a></span>
+<span id="cb471-33"><a href="7.1-example-calculation-1.html#cb471-33" tabindex="-1"></a><span class="co"># estimate gini by gender, with and without covariance matrices</span></span>
+<span id="cb471-34"><a href="7.1-example-calculation-1.html#cb471-34" tabindex="-1"></a>ginis.rep <span class="ot">&lt;-</span> <span class="fu">svyby</span>( <span class="sc">~</span> py010n , <span class="sc">~</span>rb090 , des_eusilc_rep , svygini , <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">covmat =</span> <span class="cn">TRUE</span> )</span>
+<span id="cb471-35"><a href="7.1-example-calculation-1.html#cb471-35" tabindex="-1"></a>ginis.rep.nocov <span class="ot">&lt;-</span> <span class="fu">svyby</span>( <span class="sc">~</span> py010n , <span class="sc">~</span>rb090 , des_eusilc_rep , svygini , <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">covmat =</span> <span class="cn">FALSE</span> )</span>
+<span id="cb471-36"><a href="7.1-example-calculation-1.html#cb471-36" tabindex="-1"></a></span>
+<span id="cb471-37"><a href="7.1-example-calculation-1.html#cb471-37" tabindex="-1"></a><span class="co"># variance of the gini difference: naive</span></span>
+<span id="cb471-38"><a href="7.1-example-calculation-1.html#cb471-38" tabindex="-1"></a><span class="fu">svycontrast</span>( ginis.rep.nocov , <span class="fu">quote</span>( <span class="st">`</span><span class="at">male</span><span class="st">`</span> <span class="sc">-</span> <span class="st">`</span><span class="at">female</span><span class="st">`</span> ) )</span></code></pre></div>
 <pre><code>## Warning in vcov.svyby(stat): Only diagonal elements of vcov() available</code></pre>
 <pre><code>##             nlcon     SE
 ## contrast -0.15006 0.0065</code></pre>
-<div class="sourceCode" id="cb475"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb475-1"><a href="7.1-example-calculation-1.html#cb475-1" tabindex="-1"></a><span class="co"># variance of the gini difference: accounting for covariance</span></span>
-<span id="cb475-2"><a href="7.1-example-calculation-1.html#cb475-2" tabindex="-1"></a><span class="fu">svycontrast</span>( ginis.rep , <span class="fu">quote</span>( <span class="st">`</span><span class="at">male</span><span class="st">`</span> <span class="sc">-</span> <span class="st">`</span><span class="at">female</span><span class="st">`</span> ) )</span></code></pre></div>
+<div class="sourceCode" id="cb474"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb474-1"><a href="7.1-example-calculation-1.html#cb474-1" tabindex="-1"></a><span class="co"># variance of the gini difference: accounting for covariance</span></span>
+<span id="cb474-2"><a href="7.1-example-calculation-1.html#cb474-2" tabindex="-1"></a><span class="fu">svycontrast</span>( ginis.rep , <span class="fu">quote</span>( <span class="st">`</span><span class="at">male</span><span class="st">`</span> <span class="sc">-</span> <span class="st">`</span><span class="at">female</span><span class="st">`</span> ) )</span></code></pre></div>
 <pre><code>##             nlcon     SE
 ## contrast -0.15006 0.0068</code></pre>
 <p>While not implemented yet, a linearization-based approach can be applied using:</p>
-<div class="sourceCode" id="cb477"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb477-1"><a href="7.1-example-calculation-1.html#cb477-1" tabindex="-1"></a><span class="co"># estimate gini by gender, with and without covariance matrices</span></span>
-<span id="cb477-2"><a href="7.1-example-calculation-1.html#cb477-2" tabindex="-1"></a>ginis.lin.nocov <span class="ot">&lt;-</span> <span class="fu">svyby</span>( <span class="sc">~</span> py010n , <span class="sc">~</span>rb090 , des_eusilc , svygini , <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">covmat =</span> <span class="cn">FALSE</span> )</span>
-<span id="cb477-3"><a href="7.1-example-calculation-1.html#cb477-3" tabindex="-1"></a>gini.female <span class="ot">&lt;-</span> <span class="fu">svygini</span>( <span class="sc">~</span> py010n , <span class="fu">subset</span>( des_eusilc , rb090 <span class="sc">==</span> <span class="st">&quot;female&quot;</span> ), <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">influence =</span> <span class="cn">TRUE</span> )</span>
-<span id="cb477-4"><a href="7.1-example-calculation-1.html#cb477-4" tabindex="-1"></a>gini.male   <span class="ot">&lt;-</span> <span class="fu">svygini</span>( <span class="sc">~</span> py010n , <span class="fu">subset</span>( des_eusilc , rb090 <span class="sc">==</span> <span class="st">&quot;male&quot;</span> ), <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">influence =</span> <span class="cn">TRUE</span> )</span>
-<span id="cb477-5"><a href="7.1-example-calculation-1.html#cb477-5" tabindex="-1"></a></span>
-<span id="cb477-6"><a href="7.1-example-calculation-1.html#cb477-6" tabindex="-1"></a><span class="co"># variance of the gini difference: naive</span></span>
-<span id="cb477-7"><a href="7.1-example-calculation-1.html#cb477-7" tabindex="-1"></a>linmat <span class="ot">&lt;-</span> <span class="fu">rep</span>( <span class="dv">0</span> , <span class="fu">nrow</span>( des_eusilc<span class="sc">$</span>variables ) )</span>
-<span id="cb477-8"><a href="7.1-example-calculation-1.html#cb477-8" tabindex="-1"></a>linmat[ <span class="fu">attr</span>( gini.female , <span class="st">&quot;index&quot;</span> ) ] <span class="ot">&lt;-</span> <span class="fu">attr</span>( gini.female , <span class="st">&quot;influence&quot;</span> )</span>
-<span id="cb477-9"><a href="7.1-example-calculation-1.html#cb477-9" tabindex="-1"></a>linmat[ <span class="fu">attr</span>( gini.male , <span class="st">&quot;index&quot;</span> ) ] <span class="ot">&lt;-</span> <span class="fu">attr</span>( gini.male , <span class="st">&quot;influence&quot;</span> )</span>
-<span id="cb477-10"><a href="7.1-example-calculation-1.html#cb477-10" tabindex="-1"></a>linmat <span class="ot">&lt;-</span> linmat <span class="sc">*</span> des_eusilc<span class="sc">$</span>prob</span>
-<span id="cb477-11"><a href="7.1-example-calculation-1.html#cb477-11" tabindex="-1"></a>lintot <span class="ot">&lt;-</span> <span class="fu">svyby</span>( linmat , <span class="sc">~</span>rb090 , des_eusilc , svytotal , <span class="at">covmat =</span> <span class="cn">TRUE</span> )</span>
-<span id="cb477-12"><a href="7.1-example-calculation-1.html#cb477-12" tabindex="-1"></a></span>
-<span id="cb477-13"><a href="7.1-example-calculation-1.html#cb477-13" tabindex="-1"></a><span class="co"># collect covariance matrix</span></span>
-<span id="cb477-14"><a href="7.1-example-calculation-1.html#cb477-14" tabindex="-1"></a>( m <span class="ot">&lt;-</span> <span class="fu">vcov</span>( lintot ) )</span></code></pre></div>
+<div class="sourceCode" id="cb476"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb476-1"><a href="7.1-example-calculation-1.html#cb476-1" tabindex="-1"></a><span class="co"># estimate gini by gender, with and without covariance matrices</span></span>
+<span id="cb476-2"><a href="7.1-example-calculation-1.html#cb476-2" tabindex="-1"></a>ginis.lin.nocov <span class="ot">&lt;-</span> <span class="fu">svyby</span>( <span class="sc">~</span> py010n , <span class="sc">~</span>rb090 , des_eusilc , svygini , <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">covmat =</span> <span class="cn">FALSE</span> )</span>
+<span id="cb476-3"><a href="7.1-example-calculation-1.html#cb476-3" tabindex="-1"></a>gini.female <span class="ot">&lt;-</span> <span class="fu">svygini</span>( <span class="sc">~</span> py010n , <span class="fu">subset</span>( des_eusilc , rb090 <span class="sc">==</span> <span class="st">&quot;female&quot;</span> ), <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">influence =</span> <span class="cn">TRUE</span> )</span>
+<span id="cb476-4"><a href="7.1-example-calculation-1.html#cb476-4" tabindex="-1"></a>gini.male   <span class="ot">&lt;-</span> <span class="fu">svygini</span>( <span class="sc">~</span> py010n , <span class="fu">subset</span>( des_eusilc , rb090 <span class="sc">==</span> <span class="st">&quot;male&quot;</span> ), <span class="at">na.rm =</span> <span class="cn">TRUE</span> , <span class="at">influence =</span> <span class="cn">TRUE</span> )</span>
+<span id="cb476-5"><a href="7.1-example-calculation-1.html#cb476-5" tabindex="-1"></a></span>
+<span id="cb476-6"><a href="7.1-example-calculation-1.html#cb476-6" tabindex="-1"></a><span class="co"># variance of the gini difference: naive</span></span>
+<span id="cb476-7"><a href="7.1-example-calculation-1.html#cb476-7" tabindex="-1"></a>linmat <span class="ot">&lt;-</span> <span class="fu">rep</span>( <span class="dv">0</span> , <span class="fu">nrow</span>( des_eusilc<span class="sc">$</span>variables ) )</span>
+<span id="cb476-8"><a href="7.1-example-calculation-1.html#cb476-8" tabindex="-1"></a>linmat[ <span class="fu">attr</span>( gini.female , <span class="st">&quot;index&quot;</span> ) ] <span class="ot">&lt;-</span> <span class="fu">attr</span>( gini.female , <span class="st">&quot;influence&quot;</span> )</span>
+<span id="cb476-9"><a href="7.1-example-calculation-1.html#cb476-9" tabindex="-1"></a>linmat[ <span class="fu">attr</span>( gini.male , <span class="st">&quot;index&quot;</span> ) ] <span class="ot">&lt;-</span> <span class="fu">attr</span>( gini.male , <span class="st">&quot;influence&quot;</span> )</span>
+<span id="cb476-10"><a href="7.1-example-calculation-1.html#cb476-10" tabindex="-1"></a>linmat <span class="ot">&lt;-</span> linmat <span class="sc">*</span> des_eusilc<span class="sc">$</span>prob</span>
+<span id="cb476-11"><a href="7.1-example-calculation-1.html#cb476-11" tabindex="-1"></a>lintot <span class="ot">&lt;-</span> <span class="fu">svyby</span>( linmat , <span class="sc">~</span>rb090 , des_eusilc , svytotal , <span class="at">covmat =</span> <span class="cn">TRUE</span> )</span>
+<span id="cb476-12"><a href="7.1-example-calculation-1.html#cb476-12" tabindex="-1"></a></span>
+<span id="cb476-13"><a href="7.1-example-calculation-1.html#cb476-13" tabindex="-1"></a><span class="co"># collect covariance matrix</span></span>
+<span id="cb476-14"><a href="7.1-example-calculation-1.html#cb476-14" tabindex="-1"></a>( m <span class="ot">&lt;-</span> <span class="fu">vcov</span>( lintot ) )</span></code></pre></div>
 <pre><code>##                male       female
 ## male   2.954413e-05 2.764584e-10
 ## female 2.764584e-10 2.292063e-05</code></pre>
-<div class="sourceCode" id="cb479"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb479-1"><a href="7.1-example-calculation-1.html#cb479-1" tabindex="-1"></a><span class="co"># SE of the gini difference: naive</span></span>
-<span id="cb479-2"><a href="7.1-example-calculation-1.html#cb479-2" tabindex="-1"></a><span class="fu">SE</span>( <span class="fu">svycontrast</span>( ginis.lin.nocov , <span class="fu">quote</span>( <span class="st">`</span><span class="at">male</span><span class="st">`</span> <span class="sc">-</span> <span class="st">`</span><span class="at">female</span><span class="st">`</span> ) ) )</span></code></pre></div>
+<div class="sourceCode" id="cb478"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb478-1"><a href="7.1-example-calculation-1.html#cb478-1" tabindex="-1"></a><span class="co"># SE of the gini difference: naive</span></span>
+<span id="cb478-2"><a href="7.1-example-calculation-1.html#cb478-2" tabindex="-1"></a><span class="fu">SE</span>( <span class="fu">svycontrast</span>( ginis.lin.nocov , <span class="fu">quote</span>( <span class="st">`</span><span class="at">male</span><span class="st">`</span> <span class="sc">-</span> <span class="st">`</span><span class="at">female</span><span class="st">`</span> ) ) )</span></code></pre></div>
 <pre><code>## Warning in vcov.svyby(stat): Only diagonal elements of vcov() available</code></pre>
 <pre><code>##    contrast 
 ## 0.007243256</code></pre>
-<div class="sourceCode" id="cb482"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb482-1"><a href="7.1-example-calculation-1.html#cb482-1" tabindex="-1"></a><span class="co"># SE of the gini difference: accounting for covariance</span></span>
-<span id="cb482-2"><a href="7.1-example-calculation-1.html#cb482-2" tabindex="-1"></a><span class="fu">SE</span>( <span class="fu">svycontrast</span>( lintot , <span class="fu">quote</span>( <span class="st">`</span><span class="at">male</span><span class="st">`</span> <span class="sc">-</span> <span class="st">`</span><span class="at">female</span><span class="st">`</span> ) ) )</span></code></pre></div>
+<div class="sourceCode" id="cb481"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb481-1"><a href="7.1-example-calculation-1.html#cb481-1" tabindex="-1"></a><span class="co"># SE of the gini difference: accounting for covariance</span></span>
+<span id="cb481-2"><a href="7.1-example-calculation-1.html#cb481-2" tabindex="-1"></a><span class="fu">SE</span>( <span class="fu">svycontrast</span>( lintot , <span class="fu">quote</span>( <span class="st">`</span><span class="at">male</span><span class="st">`</span> <span class="sc">-</span> <span class="st">`</span><span class="at">female</span><span class="st">`</span> ) ) )</span></code></pre></div>
 <pre><code>##    contrast 
 ## 0.007243218</code></pre>
 
diff --git a/docs/index.html b/docs/index.html
index 8bd2b05..2edd204 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -13,7 +13,7 @@
 
 <meta name="author" content="By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the convey software and this accompanying textbook." />
 
-<meta name="date" content="2023-11-04" />
+<meta name="date" content="2023-11-07" />
 
 <script type="text/x-mathjax-config">
 MathJax.Hub.Config({
@@ -254,7 +254,7 @@
 <div id="header">
 <h1 class="title">Poverty and Inequality with Complex Survey Data</h1>
 <h4 class="author"><em>By Guilherme Jacob, Anthony Damico, and Djalma Pessoa. The authors received no external funding for the <code>convey</code> software and this accompanying textbook.</em></h4>
-<h4 class="date"><em>2023-11-04</em></h4>
+<h4 class="date"><em>2023-11-07</em></h4>
 </div>
 <div id="intro" class="section level1" number="1">
 <h1><span class="header-section-number">Chapter 1</span> Intro</h1>