fix resids being off when there is no constant term

README.md

@@ -224,9 +224,9 @@ All formats have their own format options, which can be passed into the `format_
 - **coefficient_column_name** (default = `'coefficient'`): Column name storing model coefficients.
 - **strip_quotes** (default = `True`): If true, strip outer quotes from column names if provided; if false, always use string literals.
 
-These options are only available when `method='chol'`:
+These options are available for `format='long'` only when `method='chol'`:
 
-- **calculate_standard_error** (default = `'calculate_standard_error'`): If true, provide the standard error in the output.
+- **calculate_standard_error** (default = `True if not alpha else False`): If true, provide the standard error in the output.
 - **standard_error_column_name** (default = `'standard_error'`): Column name storing the standard error for the parameter.
 -- **t_statistic_column_name** (default = `'t_statistic'`): Column name storing the t-statistic for the parameter.
 

integration_tests/tests/test_collinear_matrix_1var_without_const.sql

@@ -2,7 +2,7 @@ with
 
 expected as (
 
-  select 'x1' as variable_name, 30.500076644845674 as coefficient
+  select 'x1' as variable_name, 30.500076644845674 as coefficient, 0.8396121329329627 as standard_error, 36.326388636502585 as t_statistic
 
 )
 
@@ -11,5 +11,10 @@ from {{ ref('collinear_matrix_1var_without_const') }} as base
 full outer join expected
 on base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
+  or round(base.standard_error, 7) != round(expected.standard_error, 7)
+  or round(base.t_statistic, 7) != round(expected.t_statistic, 7)
   or base.coefficient is null
+  or base.standard_error is null
+  or base.t_statistic is null
+  or expected.coefficient is null

integration_tests/tests/test_collinear_matrix_2var_without_const.sql

@@ -2,9 +2,9 @@ with
 
 expected as (
 
-  select 'x1' as variable_name, 63.18154691334764 as coefficient
+  select 'x1' as variable_name, 63.18154691334764 as coefficient, 0.4056389914380657 as standard_error, 155.75807120848344 as t_statistic
   union all
-  select 'x2' as variable_name, 55.39820150046505 as coefficient
+  select 'x2' as variable_name, 55.39820150046505 as coefficient, 0.2738669097295638 as standard_error, 202.2814715190283 as t_statistic
 
 )
 
@@ -13,5 +13,10 @@ from {{ ref('collinear_matrix_2var_without_const') }} as base
 full outer join expected
 on base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
+  or round(base.standard_error, 7) != round(expected.standard_error, 7)
+  or round(base.t_statistic, 7) != round(expected.t_statistic, 7)
   or base.coefficient is null
+  or base.standard_error is null
+  or base.t_statistic is null
+  or expected.coefficient is null

integration_tests/tests/test_collinear_matrix_3var_without_const.sql

@@ -2,11 +2,11 @@ with
 
 expected as (
 
-  select 'x1' as variable_name, 20.090207982897063 as coefficient
+  select 'x1' as variable_name, 20.090207982897063 as coefficient, 0.5196176972417176 as standard_error, 38.6634406209445 as t_statistic
   union all
-  select 'x2' as variable_name, -16.533211090826203 as coefficient
+  select 'x2' as variable_name, -16.533211090826203 as coefficient, 0.7481701784700665 as standard_error, -22.098195793682894 as t_statistic
   union all
-  select 'x3' as variable_name, 35.00389104686492 as coefficient
+  select 'x3' as variable_name, 35.00389104686492 as coefficient, 0.351617515124373 as standard_error, 99.55104493154575 as t_statistic
 
 )
 
@@ -15,5 +15,10 @@ from {{ ref('collinear_matrix_3var_without_const') }} as base
 full outer join expected
 on base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
+  or round(base.standard_error, 7) != round(expected.standard_error, 7)
+  or round(base.t_statistic, 7) != round(expected.t_statistic, 7)
   or base.coefficient is null
+  or base.standard_error is null
+  or base.t_statistic is null
+  or expected.coefficient is null

integration_tests/tests/test_collinear_matrix_4var_without_const.sql

@@ -2,13 +2,13 @@ with
 
 expected as (
 
-  select 'x1' as variable_name, 20.587532776354163 as coefficient
+  select 'x1' as variable_name, 20.587532776354163 as coefficient, 0.5176259827853541 as standard_error, 39.772989496339235 as t_statistic
   union all
-  select 'x2' as variable_name, -20.41001520357013 as coefficient
+  select 'x2' as variable_name, -20.41001520357013 as coefficient, 0.8103907603637923 as standard_error, -25.185399688426696 as t_statistic
   union all
-  select 'x3' as variable_name, 35.084935774341524 as coefficient
+  select 'x3' as variable_name, 35.084935774341524 as coefficient, 0.34920588221192245 as standard_error, 100.4706322588505 as t_statistic
   union all
-  select 'x4' as variable_name, 1.8960558858899716 as coefficient
+  select 'x4' as variable_name, 1.8960558858899716 as coefficient, 0.1583538085466205 as standard_error, 11.973541421529871 as t_statistic
 
 )
 
@@ -17,5 +17,10 @@ from {{ ref('collinear_matrix_4var_without_const') }} as base
 full outer join expected
 on base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
+  or round(base.standard_error, 7) != round(expected.standard_error, 7)
+  or round(base.t_statistic, 7) != round(expected.t_statistic, 7)
   or base.coefficient is null
+  or base.standard_error is null
+  or base.t_statistic is null
+  or expected.coefficient is null

integration_tests/tests/test_collinear_matrix_5var_without_const.sql

@@ -2,15 +2,15 @@ with
 
 expected as (
 
-  select 'x1' as variable_name, 11.392300499659957 as coefficient
+  select 'x1' as variable_name, 11.392300499659957 as coefficient, 0.5240533254061608 as standard_error, 21.73881921430515 as t_statistic
   union all
-  select 'x2' as variable_name, 2.333060182571783 as coefficient
+  select 'x2' as variable_name, 2.333060182571783 as coefficient, 0.9201150492406911 as standard_error, 2.5356178931070636 as t_statistic
   union all
-  select 'x3' as variable_name, 21.895814737788875 as coefficient
+  select 'x3' as variable_name, 21.895814737788875 as coefficient, 0.44810399169425286 as standard_error, 48.8632441210849 as t_statistic
   union all
-  select 'x4' as variable_name, 3.4480236159406785 as coefficient
+  select 'x4' as variable_name, 3.4480236159406785 as coefficient, 0.1504072830205524 as standard_error, 22.92457882820424 as t_statistic
   union all
-  select 'x5' as variable_name, 15.766951731565559 as coefficient
+  select 'x5' as variable_name, 15.766951731565559 as coefficient, 0.37297028350495787 as standard_error, 42.274015997727524 as t_statistic
 
 )
 
@@ -19,5 +19,10 @@ from {{ ref('collinear_matrix_5var_without_const') }} as base
 full outer join expected
 on base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
+  or round(base.standard_error, 7) != round(expected.standard_error, 7)
+  or round(base.t_statistic, 7) != round(expected.t_statistic, 7)
   or base.coefficient is null
+  or base.standard_error is null
+  or base.t_statistic is null
+  or expected.coefficient is null

integration_tests/tests/test_collinear_matrix_regression_chol.sql

@@ -2,24 +2,29 @@ with
 
 expected as (
 
-  select 'const' as variable_name, 19.757104885315176 as coefficient
+  select 'const' as variable_name, 19.757104885315176 as coefficient, 2.992803142237603 as standard_error, 6.601538406078909 as t_statistic
   union all
-  select 'x1' as variable_name, 9.90708767581426 as coefficient
+  select 'x1' as variable_name, 9.90708767581426 as coefficient, 0.5692826957191374 as standard_error, 17.402755696445837 as t_statistic
   union all
-  select 'x2' as variable_name, 6.187473206056227 as coefficient
+  select 'x2' as variable_name, 6.187473206056227 as coefficient, 1.0880807259333622 as standard_error, 5.686593888287631 as t_statistic
   union all
-  select 'x3' as variable_name, 19.66874583168642 as coefficient
+  select 'x3' as variable_name, 19.66874583168642 as coefficient, 0.5601379212447676 as standard_error, 35.11411223146169 as t_statistic
   union all
-  select 'x4' as variable_name, 3.7192417102253468 as coefficient
+  select 'x4' as variable_name, 3.7192417102253468 as coefficient, 0.15560940177101745 as standard_error, 23.901137514160553 as t_statistic
   union all
-  select 'x5' as variable_name, 13.444273483323244 as coefficient
+  select 'x5' as variable_name, 13.444273483323244 as coefficient, 0.5121595119107619 as standard_error, 26.250168493728488 as t_statistic
 
 )
 
-select base.variable_name
+select base.*
 from {{ ref('collinear_matrix_regression_chol') }} as base
 full outer join expected
 on base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
+  or round(base.standard_error, 7) != round(expected.standard_error, 7)
+  or round(base.t_statistic, 7) != round(expected.t_statistic, 7)
   or base.coefficient is null
+  or base.standard_error is null
+  or base.t_statistic is null
+  or expected.coefficient is null

integration_tests/tests/test_collinear_matrix_regression_chol_unoptimized.sql

@@ -2,24 +2,29 @@ with
 
 expected as (
 
-  select 'const' as variable_name, 19.757104885315176 as coefficient
+  select 'const' as variable_name, 19.757104885315176 as coefficient, 2.992803142237603 as standard_error, 6.601538406078909 as t_statistic
   union all
-  select 'x1' as variable_name, 9.90708767581426 as coefficient
+  select 'x1' as variable_name, 9.90708767581426 as coefficient, 0.5692826957191374 as standard_error, 17.402755696445837 as t_statistic
   union all
-  select 'x2' as variable_name, 6.187473206056227 as coefficient
+  select 'x2' as variable_name, 6.187473206056227 as coefficient, 1.0880807259333622 as standard_error, 5.686593888287631 as t_statistic
   union all
-  select 'x3' as variable_name, 19.66874583168642 as coefficient
+  select 'x3' as variable_name, 19.66874583168642 as coefficient, 0.5601379212447676 as standard_error, 35.11411223146169 as t_statistic
   union all
-  select 'x4' as variable_name, 3.7192417102253468 as coefficient
+  select 'x4' as variable_name, 3.7192417102253468 as coefficient, 0.15560940177101745 as standard_error, 23.901137514160553 as t_statistic
   union all
-  select 'x5' as variable_name, 13.444273483323244 as coefficient
+  select 'x5' as variable_name, 13.444273483323244 as coefficient, 0.5121595119107619 as standard_error, 26.250168493728488 as t_statistic
 
 )
 
-select base.variable_name
+select base.*
 from {{ ref('collinear_matrix_regression_chol_unoptimized') }} as base
 full outer join expected
 on base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
+  or round(base.standard_error, 7) != round(expected.standard_error, 7)
+  or round(base.t_statistic, 7) != round(expected.t_statistic, 7)
   or base.coefficient is null
+  or base.standard_error is null
+  or base.t_statistic is null
+  or expected.coefficient is null

integration_tests/tests/test_collinear_matrix_regression_fwl.sql

@@ -21,5 +21,6 @@ from {{ ref('collinear_matrix_regression_fwl') }} as base
 full outer join expected
 on base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
   or base.coefficient is null
+  or expected.coefficient is null

integration_tests/tests/test_groups_matrix_regression_chol.sql

@@ -2,21 +2,21 @@ with
 
 expected as (
 
-  select 'a' as gb_var, 'const' as variable_name, -0.06563066041472207 as coefficient
+  select 'a' as gb_var, 'const' as variable_name, -0.06563066041472207 as coefficient, 0.053945103940799474 as standard_error, -1.2166194078844779 as t_statistic
   union all
-  select 'a' as gb_var, 'x1' as variable_name, 0.9905419281557593 as coefficient
+  select 'a' as gb_var, 'x1' as variable_name, 0.9905419281557593 as coefficient, 0.015209571618398615 as standard_error, 65.12622136954383 as t_statistic
   union all
-  select 'a' as gb_var, 'x2' as variable_name, 4.948221700496285 as coefficient
+  select 'a' as gb_var, 'x2' as variable_name, 4.948221700496285 as coefficient, 0.02906881854690807 as standard_error, 170.2243829590593 as t_statistic
   union all
-  select 'a' as gb_var, 'x3' as variable_name, 0.031234030051974747 as coefficient
+  select 'a' as gb_var, 'x3' as variable_name, 0.031234030051974747 as coefficient, 0.014337008978330493 as standard_error, 2.178559705108859 as t_statistic
   union all
-  select 'b' as gb_var, 'const' as variable_name, 2.0117130483709955 as coefficient
+  select 'b' as gb_var, 'const' as variable_name, 2.0117130483709955 as coefficient, 0.035587045398501334 as standard_error, 56.529364150464545 as t_statistic
   union all
-  select 'b' as gb_var, 'x1' as variable_name, 2.996331112245573 as coefficient
+  select 'b' as gb_var, 'x1' as variable_name, 2.996331112245573 as coefficient, 0.006731681784764358 as standard_error, 445.1088462064698 as t_statistic
   union all
-  select 'b' as gb_var, 'x2' as variable_name, 9.019683491736044 as coefficient
+  select 'b' as gb_var, 'x2' as variable_name, 9.019683491736044 as coefficient, 0.008744674914389008 as standard_error, 1031.4486907791759 as t_statistic
   union all
-  select 'b' as gb_var, 'x3' as variable_name, 0.016151316166848173 as coefficient
+  select 'b' as gb_var, 'x3' as variable_name, 0.016151316166848173 as coefficient, 0.0072206704541224525 as standard_error, 2.2368166875178472 as t_statistic
 
 )
 
@@ -27,5 +27,10 @@ on
   base.gb_var = expected.gb_var
   and base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
+  or round(base.standard_error, 7) != round(expected.standard_error, 7)
+  or round(base.t_statistic, 7) != round(expected.t_statistic, 7)
   or base.coefficient is null
+  or base.standard_error is null
+  or base.t_statistic is null
+  or expected.coefficient is null

integration_tests/tests/test_groups_matrix_regression_chol_unoptimized.sql

@@ -2,21 +2,21 @@ with
 
 expected as (
 
-  select 'a' as gb_var, 'const' as variable_name, -0.06563066041472207 as coefficient
+  select 'a' as gb_var, 'const' as variable_name, -0.06563066041472207 as coefficient, 0.053945103940799474 as standard_error, -1.2166194078844779 as t_statistic
   union all
-  select 'a' as gb_var, 'x1' as variable_name, 0.9905419281557593 as coefficient
+  select 'a' as gb_var, 'x1' as variable_name, 0.9905419281557593 as coefficient, 0.015209571618398615 as standard_error, 65.12622136954383 as t_statistic
   union all
-  select 'a' as gb_var, 'x2' as variable_name, 4.948221700496285 as coefficient
+  select 'a' as gb_var, 'x2' as variable_name, 4.948221700496285 as coefficient, 0.02906881854690807 as standard_error, 170.2243829590593 as t_statistic
   union all
-  select 'a' as gb_var, 'x3' as variable_name, 0.031234030051974747 as coefficient
+  select 'a' as gb_var, 'x3' as variable_name, 0.031234030051974747 as coefficient, 0.014337008978330493 as standard_error, 2.178559705108859 as t_statistic
   union all
-  select 'b' as gb_var, 'const' as variable_name, 2.0117130483709955 as coefficient
+  select 'b' as gb_var, 'const' as variable_name, 2.0117130483709955 as coefficient, 0.035587045398501334 as standard_error, 56.529364150464545 as t_statistic
   union all
-  select 'b' as gb_var, 'x1' as variable_name, 2.996331112245573 as coefficient
+  select 'b' as gb_var, 'x1' as variable_name, 2.996331112245573 as coefficient, 0.006731681784764358 as standard_error, 445.1088462064698 as t_statistic
   union all
-  select 'b' as gb_var, 'x2' as variable_name, 9.019683491736044 as coefficient
+  select 'b' as gb_var, 'x2' as variable_name, 9.019683491736044 as coefficient, 0.008744674914389008 as standard_error, 1031.4486907791759 as t_statistic
   union all
-  select 'b' as gb_var, 'x3' as variable_name, 0.016151316166848173 as coefficient
+  select 'b' as gb_var, 'x3' as variable_name, 0.016151316166848173 as coefficient, 0.0072206704541224525 as standard_error, 2.2368166875178472 as t_statistic
 
 )
 
@@ -27,5 +27,10 @@ on
   base.gb_var = expected.gb_var
   and base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
+  or round(base.standard_error, 7) != round(expected.standard_error, 7)
+  or round(base.t_statistic, 7) != round(expected.t_statistic, 7)
   or base.coefficient is null
+  or base.standard_error is null
+  or base.t_statistic is null
+  or expected.coefficient is null

integration_tests/tests/test_groups_matrix_regression_fwl.sql

@@ -30,5 +30,6 @@ on
   base.gb_var = expected.gb_var
   and base.variable_name = expected.variable_name
 where
-  round(base.coefficient, 7) - round(expected.coefficient, 7)
+  round(base.coefficient, 7) != round(expected.coefficient, 7)
   or base.coefficient is null
+  or expected.coefficient is null

macros/linear_regression/ols_impl_chol/_ols_impl_chol.sql

@@ -110,7 +110,12 @@
 {%- endif %}
 {%- set subquery_optimization = method_options.get('subquery_optimization', True) %}
 {%- set safe_sqrt = method_options.get('safe', True) %}
-{%- set calculate_standard_error = format_options.get('calculate_standard_error', True) and format == 'long' %}
+{%- set calculate_standard_error = format_options.get('calculate_standard_error', (not alpha)) and format == 'long' %}
+{%- if alpha and calculate_standard_error %}
+  {% do log(
+    'Warning: Standard errors are NOT designed to take into account ridge regression regularization.'
+  ) %}
+{%- endif %}
 {%- if add_constant %}
   {% set xmin = 0 %}
 {%- else %}
@@ -264,11 +269,11 @@ _dbt_linreg_final_coefs as (
 _dbt_linreg_resid as (
   select
     {{ dbt_linreg._gb_cols(group_by, trailing_comma=True, prefix='b') | indent(4) }}
-    var_pop(y
+    avg(pow(y
       {%- for x in xcols %}
       - x{{ x }} * x{{ x }}_coef
       {%- endfor %}
-    ) as resid_var,
+    , 2)) as resid_square_mean,
     count(*) as n
   from
     _dbt_linreg_base as b
@@ -282,7 +287,7 @@ _dbt_linreg_stderrs as (
   select
     {{ dbt_linreg._gb_cols(group_by, trailing_comma=True, prefix='b') | indent(4) }}
     {%- for x in xcols %}
-    sqrt(inv_x{{ x }}x{{ x }} * resid_var * n / (n - {{ xcols | length }})) as x{{ x }}_stderr
+    sqrt(inv_x{{ x }}x{{ x }} * resid_square_mean * n / (n - {{ xcols | length }})) as x{{ x }}_stderr
     {%- if not loop.last -%}
     ,
     {%- endif %}

run

@@ -2,8 +2,6 @@
 
 set -eo pipefail
 
-
-
 function setup {
 	poetry install
 	poetry run pre-commit install
@@ -17,7 +15,6 @@ function testloc {
   poetry run dbt run --project-dir ./integration_tests --select tag:perftest
 }
 
-
 function test {
   # rm -f integration_tests/dbt.duckdb
   export DBT_PROFILES_DIR=./integration_tests/profiles

scripts.py

@@ -248,13 +248,14 @@ def _run_model(cond=None):
             ).fit_regularized(L1_wt=0, alpha=alpha_arr)
         else:
             model = sm.OLS(y, x_mat).fit()
+        res_df = pd.DataFrame(index=x_mat.columns)
+        res_df["coef"] = model.params
+        res_df["stderr"] = model.bse
+        res_df["tstat"] = res_df["coef"] / res_df["stderr"]
         click.echo(
             tabulate(
-                pd.DataFrame(
-                    {"coefficient": model.params},
-                    index=x_mat.columns
-                ),
-                headers=["coefficient", "value"],
+                res_df,
+                headers=["column name", "coef", "stderr", "tstat"],
                 disable_numparse=True,
                 tablefmt="psql",
             )