-
Notifications
You must be signed in to change notification settings - Fork 0
/
graphical_data_exploration_exercise_solutions.html
949 lines (860 loc) · 53.3 KB
/
graphical_data_exploration_exercise_solutions.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<title>Exercises</title>
<script src="site_libs/header-attrs-2.26/header-attrs.js"></script>
<script src="site_libs/jquery-3.6.0/jquery-3.6.0.min.js"></script>
<meta name="viewport" content="width=device-width, initial-scale=1" />
<link href="site_libs/bootstrap-3.3.5/css/flatly.min.css" rel="stylesheet" />
<script src="site_libs/bootstrap-3.3.5/js/bootstrap.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/html5shiv.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/respond.min.js"></script>
<style>h1 {font-size: 34px;}
h1.title {font-size: 38px;}
h2 {font-size: 30px;}
h3 {font-size: 24px;}
h4 {font-size: 18px;}
h5 {font-size: 16px;}
h6 {font-size: 12px;}
code {color: inherit; background-color: rgba(0, 0, 0, 0.04);}
pre:not([class]) { background-color: white }</style>
<script src="site_libs/navigation-1.1/tabsets.js"></script>
<script src="site_libs/navigation-1.1/codefolding.js"></script>
<link href="site_libs/font-awesome-6.4.2/css/all.min.css" rel="stylesheet" />
<link href="site_libs/font-awesome-6.4.2/css/v4-shims.min.css" rel="stylesheet" />
<style type="text/css">
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
span.underline{text-decoration: underline;}
div.column{display: inline-block; vertical-align: top; width: 50%;}
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
ul.task-list{list-style: none;}
</style>
<style type="text/css">
code {
white-space: pre;
}
.sourceCode {
overflow: visible;
}
</style>
<style type="text/css" data-origin="pandoc">
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
color: #aaaaaa;
}
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }
div.sourceCode
{ background-color: #f8f8f8; }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ef2929; } /* Alert */
code span.an { color: #8f5902; font-weight: bold; font-style: italic; } /* Annotation */
code span.at { color: #204a87; } /* Attribute */
code span.bn { color: #0000cf; } /* BaseN */
code span.cf { color: #204a87; font-weight: bold; } /* ControlFlow */
code span.ch { color: #4e9a06; } /* Char */
code span.cn { color: #8f5902; } /* Constant */
code span.co { color: #8f5902; font-style: italic; } /* Comment */
code span.cv { color: #8f5902; font-weight: bold; font-style: italic; } /* CommentVar */
code span.do { color: #8f5902; font-weight: bold; font-style: italic; } /* Documentation */
code span.dt { color: #204a87; } /* DataType */
code span.dv { color: #0000cf; } /* DecVal */
code span.er { color: #a40000; font-weight: bold; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #0000cf; } /* Float */
code span.fu { color: #204a87; font-weight: bold; } /* Function */
code span.im { } /* Import */
code span.in { color: #8f5902; font-weight: bold; font-style: italic; } /* Information */
code span.kw { color: #204a87; font-weight: bold; } /* Keyword */
code span.op { color: #ce5c00; font-weight: bold; } /* Operator */
code span.ot { color: #8f5902; } /* Other */
code span.pp { color: #8f5902; font-style: italic; } /* Preprocessor */
code span.sc { color: #ce5c00; font-weight: bold; } /* SpecialChar */
code span.ss { color: #4e9a06; } /* SpecialString */
code span.st { color: #4e9a06; } /* String */
code span.va { color: #000000; } /* Variable */
code span.vs { color: #4e9a06; } /* VerbatimString */
code span.wa { color: #8f5902; font-weight: bold; font-style: italic; } /* Warning */
.sourceCode .row {
width: 100%;
}
.sourceCode {
overflow-x: auto;
}
.code-folding-btn {
margin-right: -30px;
}
</style>
<script>
// apply pandoc div.sourceCode style to pre.sourceCode instead
(function() {
var sheets = document.styleSheets;
for (var i = 0; i < sheets.length; i++) {
if (sheets[i].ownerNode.dataset["origin"] !== "pandoc") continue;
try { var rules = sheets[i].cssRules; } catch (e) { continue; }
var j = 0;
while (j < rules.length) {
var rule = rules[j];
// check if there is a div.sourceCode rule
if (rule.type !== rule.STYLE_RULE || rule.selectorText !== "div.sourceCode") {
j++;
continue;
}
var style = rule.style.cssText;
// check if color or background-color is set
if (rule.style.color === '' && rule.style.backgroundColor === '') {
j++;
continue;
}
// replace div.sourceCode by a pre.sourceCode rule
sheets[i].deleteRule(j);
sheets[i].insertRule('pre.sourceCode{' + style + '}', j);
}
}
})();
</script>
<style type = "text/css">
.main-container {
max-width: 940px;
margin-left: auto;
margin-right: auto;
}
img {
max-width:100%;
}
.tabbed-pane {
padding-top: 12px;
}
.html-widget {
margin-bottom: 20px;
}
button.code-folding-btn:focus {
outline: none;
}
summary {
display: list-item;
}
details > summary > p:only-child {
display: inline;
}
pre code {
padding: 0;
}
</style>
<style type="text/css">
.dropdown-submenu {
position: relative;
}
.dropdown-submenu>.dropdown-menu {
top: 0;
left: 100%;
margin-top: -6px;
margin-left: -1px;
border-radius: 0 6px 6px 6px;
}
.dropdown-submenu:hover>.dropdown-menu {
display: block;
}
.dropdown-submenu>a:after {
display: block;
content: " ";
float: right;
width: 0;
height: 0;
border-color: transparent;
border-style: solid;
border-width: 5px 0 5px 5px;
border-left-color: #cccccc;
margin-top: 5px;
margin-right: -10px;
}
.dropdown-submenu:hover>a:after {
border-left-color: #adb5bd;
}
.dropdown-submenu.pull-left {
float: none;
}
.dropdown-submenu.pull-left>.dropdown-menu {
left: -100%;
margin-left: 10px;
border-radius: 6px 0 6px 6px;
}
</style>
<script type="text/javascript">
// manage active state of menu based on current page
$(document).ready(function () {
// active menu anchor
href = window.location.pathname
href = href.substr(href.lastIndexOf('/') + 1)
if (href === "")
href = "index.html";
var menuAnchor = $('a[href="' + href + '"]');
// mark the anchor link active (and if it's in a dropdown, also mark that active)
var dropdown = menuAnchor.closest('li.dropdown');
if (window.bootstrap) { // Bootstrap 4+
menuAnchor.addClass('active');
dropdown.find('> .dropdown-toggle').addClass('active');
} else { // Bootstrap 3
menuAnchor.parent().addClass('active');
dropdown.addClass('active');
}
// Navbar adjustments
var navHeight = $(".navbar").first().height() + 15;
var style = document.createElement('style');
var pt = "padding-top: " + navHeight + "px; ";
var mt = "margin-top: -" + navHeight + "px; ";
var css = "";
// offset scroll position for anchor links (for fixed navbar)
for (var i = 1; i <= 6; i++) {
css += ".section h" + i + "{ " + pt + mt + "}\n";
}
style.innerHTML = "body {" + pt + "padding-bottom: 40px; }\n" + css;
document.head.appendChild(style);
});
</script>
<!-- tabsets -->
<style type="text/css">
.tabset-dropdown > .nav-tabs {
display: inline-table;
max-height: 500px;
min-height: 44px;
overflow-y: auto;
border: 1px solid #ddd;
border-radius: 4px;
}
.tabset-dropdown > .nav-tabs > li.active:before, .tabset-dropdown > .nav-tabs.nav-tabs-open:before {
content: "\e259";
font-family: 'Glyphicons Halflings';
display: inline-block;
padding: 10px;
border-right: 1px solid #ddd;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li.active:before {
content: "\e258";
font-family: 'Glyphicons Halflings';
border: none;
}
.tabset-dropdown > .nav-tabs > li.active {
display: block;
}
.tabset-dropdown > .nav-tabs > li > a,
.tabset-dropdown > .nav-tabs > li > a:focus,
.tabset-dropdown > .nav-tabs > li > a:hover {
border: none;
display: inline-block;
border-radius: 4px;
background-color: transparent;
}
.tabset-dropdown > .nav-tabs.nav-tabs-open > li {
display: block;
float: none;
}
.tabset-dropdown > .nav-tabs > li {
display: none;
}
</style>
<!-- code folding -->
<style type="text/css">
.code-folding-btn { margin-bottom: 4px; }
</style>
</head>
<body>
<div class="container-fluid main-container">
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-bs-toggle="collapse" data-target="#navbar" data-bs-target="#navbar">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="index.html">PGR-LM</a>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="index.html">
<span class="fa fa-home"></span>
Home
</a>
</li>
<li>
<a href="setup.html">
<span class="fa fa-cog"></span>
Setup
</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
<span class="fa fa-book"></span>
R Book
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="https://intro2r.com">
<span class="fa fa-firefox"></span>
Web book
</a>
</li>
<li class="divider"></li>
<li>
<a href="https://github.com/alexd106/Rbook/raw/master/docs/Rbook.pdf">
<span class="fa fa-file-pdf"></span>
PDF book
</a>
</li>
</ul>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
<span class="fa fa-book"></span>
Exercises
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="exercises.html">
<span class="fa fa-book"></span>
Exercises
</a>
</li>
<li class="divider"></li>
<li>
<a href="exercise_solutions.html">
<span class="fa fa-book"></span>
Exercise Solutions
</a>
</li>
</ul>
</li>
<li>
<a href="data.html">
<span class="fa fa-download"></span>
Data
</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
<span class="fa fa-question-circle"></span>
Info
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="syllabus.html">
<span class="fa fa-graduation-cap"></span>
Syllabus
</a>
</li>
<li>
<a href="People.html">
<span class="fa fa-user-friends"></span>
People
</a>
</li>
<li class="divider"></li>
<li>
<a href="resources.html">
<span class="fa fa-book"></span>
Resources
</a>
</li>
<li>
<a href="https://forms.gle/8xYAqv19x8SSAdfUA">
<span class="fa fa-commenting"></span>
Feedback
</a>
</li>
<li>
<a href="People.html">
<span class="fa fa-envelope fa-lg"></span>
Contact
</a>
</li>
<li class="divider"></li>
<li>
<a href="https://github.com/alexd106/PGR-LM">
<span class="fa fa-github fa-lg"></span>
Source code
</a>
</li>
<li>
<a href="https://twitter.com/Scedacity">
<span class="fa fa-twitter fa-lg"></span>
Twitter
</a>
</li>
</ul>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
<div id="header">
<div class="btn-group pull-right float-right">
<button type="button" class="btn btn-default btn-xs btn-secondary btn-sm dropdown-toggle" data-toggle="dropdown" data-bs-toggle="dropdown" aria-haspopup="true" aria-expanded="false"><span>Code</span> <span class="caret"></span></button>
<ul class="dropdown-menu dropdown-menu-right" style="min-width: 50px;">
<li><a id="rmd-show-all-code" href="#">Show All Code</a></li>
<li><a id="rmd-hide-all-code" href="#">Hide All Code</a></li>
</ul>
</div>
<h1 class="title toc-ignore">Exercises</h1>
</div>
<p> </p>
<div id="exercise-graphical-data-exploration-using-r"
class="section level2">
<h2>Exercise: Graphical data exploration using R</h2>
<p> </p>
<p>1. Start RStudio on your computer. If you haven’t already done so,
create a new RStudio Project (select File –> New Project on the main
menu). Create the Project in a new directory by selecting ‘New
Directory’ and then select ‘New Project’. Give the Project a suitable
name (‘pgr_stats’ maybe) in the ‘Directory name:’ box and choose where
you would like to create this Project directory by clicking on the
‘Browse’ button. Finally create the project by clicking on the ‘Create
Project’ button. This will be your main RStudio Project file and
directory which you will use throughout this course. See <a
href="https://intro2r.com/rsprojs.html#rsprojs">Section 1.6</a> of the
Introduction to R book for more information about RStudio Projects and
<a
href="https://alexd106.github.io/PGR-LM/howto.html#rstudio_proj-vid">here</a>
for a short video.</p>
<p>Now create a new R script inside this Project by selecting File –>
New File –> R Script from the main menu (or use the shortcut button).
Before you start writing any code save this script by selecting File
–> Save from the main menu. Call this script
‘graphical_data_exploration’ or something similar. Click on the ‘Files’
tab in the bottom right RStudio pane to see whether your file has been
saved in the correct location. Ok, at the top of almost every R script
(there are very few exceptions to this!) you should include some
metadata to help your collaborators (and the future you) know who wrote
the script, when it was written and what the script does (amongst other
things). Include this information at the top of your R script making
sure that you place a # at the beginning of every line to let R know
this is a comment. See <a
href="https://intro2r.com/proj-doc.html">Section 1.10</a> for a little
more detail.</p>
<p> </p>
<p>2. If you haven’t already, download the data file
<em>‘loyn.xlsx’</em> from the <strong><a
href="data.html"><i class="fa fa-download"></i> Data</a></strong> link
and save it to the <code>data</code> directory. Open this file in
Microsoft Excel (or even better use an open source equivalent - <a
href="https://www.libreoffice.org/download/download/">LibreOffice</a> is
a good free alternative) and save it as a tab delimited file type. Name
the file <em>‘loyn.txt’</em> and also save it to the <code>data</code>
directory.</p>
<p> </p>
<p>3. These data are from a study originally conducted by Loyn
(1987)<sup>1</sup> and subsequently re-analysed by Quinn and Keough
(2002)<sup>2</sup> and Zuur et al (2009)<sup>3</sup>. Note, I have had
to do some slight ‘tweaking’ of these data to improve usability for this
course. The aim of the study was to relate bird density in 67 forest
patches to a number of different environmental variables and management
practices. A summary of the variables is: <strong>ABUND</strong>:
Density of birds, continuous response variable; <strong>AREA</strong>:
Size of forest patch, continuous explanatory variable;
<strong>DIST</strong>: Distance to nearest patch, continuous
explanatory; <strong>LDIST</strong>: Distance to nearest larger patch,
continuous explanatory; <strong>ALT</strong>: Mean altitude of patch,
continuous explanatory; <strong>YR.ISOL</strong>: Year of isolation of
clearance, continuous explanatory; <strong>GRAZE</strong>: Index of
livestock grazing intensity, 5 level categorical explanatory 1= low
graze, 5 = high graze. Copy this information to your R script (make sure
you comment it out with a <code>#</code> - can you remember the keyboard
<a href="https://intro2r.com/proj_doc.html#proj_doc">shortcut</a>?) and
clearly highlight which variable is the response variable and which
variables are potential explanatory variables.</p>
<p> </p>
<p>4. Import your tab delimited file from Q2 (<em>‘loyn.txt’</em>) into
R using the <code>read.table()</code> function and assign it to an
object called <code>loyn</code> (checkout <a
href="https://intro2r.com/importing-data.html#import_fnc">Section
3.3.2</a> if you need a reminder). Use the <code>str()</code> function
to display the structure of the dataset and the <code>summary()</code>
function to summarise the dataset. Copy and paste the output of
<code>str()</code> and <code>Summary()</code> to your R code as a
record. Don’t forget to comment this code with a <code>#</code> at the
beginning of each line (use the keyboard to comment code blocks <a
href="https://intro2r.com/proj_doc.html#proj_doc">shortcut</a>?).</p>
<p>How many observations are in this dataset? How many variables does
the dataframe contain?</p>
<p>Are there any missing values (coded as <code>NA</code>) in any
variable?</p>
<p>How is the variable <code>GRAZE</code> coded? (as a number or a
string?). If you think this will cause a problem (hint: it will!),
create a new variable called <code>FGRAZE</code> <strong>in the
dataframe</strong> with <code>GRAZE</code> recoded as a factor. See <a
href="https://intro2r.com/data-types.html#data-types">here</a> to see
how to convert/coerce a numeric variable into a factor (TL;DR: use the
<code>as.factor()</code> or <code>factor()</code> function).</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" tabindex="-1"></a>loyn <span class="ot"><-</span> <span class="fu">read.table</span>(<span class="st">"./data/loyn.txt"</span>, <span class="at">header =</span> <span class="cn">TRUE</span>, </span>
<span id="cb1-2"><a href="#cb1-2" tabindex="-1"></a> <span class="at">stringsAsFactors =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-3"><a href="#cb1-3" tabindex="-1"></a><span class="fu">str</span>(loyn)</span>
<span id="cb1-4"><a href="#cb1-4" tabindex="-1"></a><span class="do">## 'data.frame': 67 obs. of 8 variables:</span></span>
<span id="cb1-5"><a href="#cb1-5" tabindex="-1"></a><span class="do">## $ SITE : int 1 60 2 3 61 4 5 6 7 8 ...</span></span>
<span id="cb1-6"><a href="#cb1-6" tabindex="-1"></a><span class="do">## $ ABUND : num 5.3 10 2 1.5 13 17.1 13.8 14.1 3.8 2.2 ...</span></span>
<span id="cb1-7"><a href="#cb1-7" tabindex="-1"></a><span class="do">## $ AREA : num 0.1 0.2 0.5 0.5 0.6 1 1 1 1 1 ...</span></span>
<span id="cb1-8"><a href="#cb1-8" tabindex="-1"></a><span class="do">## $ DIST : int 39 142 234 104 191 66 246 234 467 284 ...</span></span>
<span id="cb1-9"><a href="#cb1-9" tabindex="-1"></a><span class="do">## $ LDIST : int 39 142 234 311 357 66 246 285 467 1829 ...</span></span>
<span id="cb1-10"><a href="#cb1-10" tabindex="-1"></a><span class="do">## $ YR.ISOL: int 1968 1961 1920 1900 1957 1966 1918 1965 1955 1920 ...</span></span>
<span id="cb1-11"><a href="#cb1-11" tabindex="-1"></a><span class="do">## $ GRAZE : int 2 2 5 5 2 3 5 3 5 5 ...</span></span>
<span id="cb1-12"><a href="#cb1-12" tabindex="-1"></a><span class="do">## $ ALT : int 160 180 60 140 185 160 140 130 90 60 ...</span></span>
<span id="cb1-13"><a href="#cb1-13" tabindex="-1"></a></span>
<span id="cb1-14"><a href="#cb1-14" tabindex="-1"></a><span class="co"># 67 observations and 8 variables (from str())</span></span>
<span id="cb1-15"><a href="#cb1-15" tabindex="-1"></a></span>
<span id="cb1-16"><a href="#cb1-16" tabindex="-1"></a><span class="fu">summary</span>(loyn)</span>
<span id="cb1-17"><a href="#cb1-17" tabindex="-1"></a><span class="do">## SITE ABUND AREA DIST LDIST YR.ISOL GRAZE ALT </span></span>
<span id="cb1-18"><a href="#cb1-18" tabindex="-1"></a><span class="do">## Min. : 1.0 Min. : 1.50 Min. : 0.1 Min. : 26.0 Min. : 26.0 Min. :1890 Min. :1.00 Min. : 60.0 </span></span>
<span id="cb1-19"><a href="#cb1-19" tabindex="-1"></a><span class="do">## 1st Qu.:17.5 1st Qu.:12.10 1st Qu.: 2.0 1st Qu.: 112.0 1st Qu.: 157.5 1st Qu.:1946 1st Qu.:2.00 1st Qu.:120.0 </span></span>
<span id="cb1-20"><a href="#cb1-20" tabindex="-1"></a><span class="do">## Median :34.0 Median :19.40 Median : 7.0 Median : 208.0 Median : 345.0 Median :1963 Median :3.00 Median :150.0 </span></span>
<span id="cb1-21"><a href="#cb1-21" tabindex="-1"></a><span class="do">## Mean :34.0 Mean :18.76 Mean : 58.7 Mean : 241.8 Mean : 678.0 Mean :1952 Mean :3.03 Mean :150.4 </span></span>
<span id="cb1-22"><a href="#cb1-22" tabindex="-1"></a><span class="do">## 3rd Qu.:50.5 3rd Qu.:27.45 3rd Qu.: 20.5 3rd Qu.: 334.5 3rd Qu.: 826.0 3rd Qu.:1966 3rd Qu.:4.00 3rd Qu.:187.5 </span></span>
<span id="cb1-23"><a href="#cb1-23" tabindex="-1"></a><span class="do">## Max. :67.0 Max. :39.60 Max. :1771.0 Max. :1427.0 Max. :4426.0 Max. :1976 Max. :5.00 Max. :260.0</span></span>
<span id="cb1-24"><a href="#cb1-24" tabindex="-1"></a></span>
<span id="cb1-25"><a href="#cb1-25" tabindex="-1"></a><span class="co"># GRAZE is coded as numeric (i.e. 1,2,3,5)</span></span>
<span id="cb1-26"><a href="#cb1-26" tabindex="-1"></a></span>
<span id="cb1-27"><a href="#cb1-27" tabindex="-1"></a><span class="co"># create a new factor variable variable FGRAZE which is a factor of GRAZE</span></span>
<span id="cb1-28"><a href="#cb1-28" tabindex="-1"></a>loyn<span class="sc">$</span>FGRAZE <span class="ot"><-</span> <span class="fu">factor</span>(loyn<span class="sc">$</span>GRAZE)</span></code></pre></div>
<p> </p>
<p>5. Use the function <code>table()</code> (or <code>xtabs()</code>) to
determine how many observations were recorded for each
<code>FGRAZE</code> category (level). See <a
href="https://intro2r.com/summarising-data-frames.html">section 3.5</a>
of the Introduction to R book to remind yourself how to do this.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" tabindex="-1"></a><span class="fu">table</span>(loyn<span class="sc">$</span>FGRAZE)</span>
<span id="cb2-2"><a href="#cb2-2" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb2-3"><a href="#cb2-3" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb2-4"><a href="#cb2-4" tabindex="-1"></a><span class="do">## 13 11 17 13 13</span></span>
<span id="cb2-5"><a href="#cb2-5" tabindex="-1"></a></span>
<span id="cb2-6"><a href="#cb2-6" tabindex="-1"></a><span class="co"># or use xtabs function</span></span>
<span id="cb2-7"><a href="#cb2-7" tabindex="-1"></a><span class="fu">xtabs</span>(<span class="sc">~</span> FGRAZE, <span class="at">data =</span> loyn)</span>
<span id="cb2-8"><a href="#cb2-8" tabindex="-1"></a><span class="do">## FGRAZE</span></span>
<span id="cb2-9"><a href="#cb2-9" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb2-10"><a href="#cb2-10" tabindex="-1"></a><span class="do">## 13 11 17 13 13</span></span></code></pre></div>
<p> </p>
<p>6. Using the <code>tapply()</code> function what is the mean bird
abundance (<code>ABUND</code>) for each level of
<code>FGRAZE</code>?</p>
<p>Can you also determine the variance for each <code>FGRAZE</code>
level? Again see <a
href="https://intro2r.com/summarising-data-frames.html">section 3.5</a>
of the Introduction to R book to remind yourself how to do this.</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" tabindex="-1"></a><span class="co"># mean abundance of birds for each level of FGRAZE</span></span>
<span id="cb3-2"><a href="#cb3-2" tabindex="-1"></a><span class="fu">tapply</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>FGRAZE, mean, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb3-3"><a href="#cb3-3" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb3-4"><a href="#cb3-4" tabindex="-1"></a><span class="do">## 28.623077 19.418182 20.164706 18.961538 6.292308</span></span>
<span id="cb3-5"><a href="#cb3-5" tabindex="-1"></a></span>
<span id="cb3-6"><a href="#cb3-6" tabindex="-1"></a><span class="co"># variance in the abundance of birds for each level of FGRAZE</span></span>
<span id="cb3-7"><a href="#cb3-7" tabindex="-1"></a><span class="fu">tapply</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>FGRAZE, var, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb3-8"><a href="#cb3-8" tabindex="-1"></a><span class="do">## 1 2 3 4 5 </span></span>
<span id="cb3-9"><a href="#cb3-9" tabindex="-1"></a><span class="do">## 32.63859 73.13364 89.42243 50.62923 23.10744</span></span>
<span id="cb3-10"><a href="#cb3-10" tabindex="-1"></a></span>
<span id="cb3-11"><a href="#cb3-11" tabindex="-1"></a><span class="co"># OR use the summary function</span></span>
<span id="cb3-12"><a href="#cb3-12" tabindex="-1"></a><span class="fu">tapply</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>FGRAZE, summary, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb3-13"><a href="#cb3-13" tabindex="-1"></a><span class="do">## $`1`</span></span>
<span id="cb3-14"><a href="#cb3-14" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-15"><a href="#cb3-15" tabindex="-1"></a><span class="do">## 14.60 27.30 29.50 28.62 30.90 39.60 </span></span>
<span id="cb3-16"><a href="#cb3-16" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb3-17"><a href="#cb3-17" tabindex="-1"></a><span class="do">## $`2`</span></span>
<span id="cb3-18"><a href="#cb3-18" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-19"><a href="#cb3-19" tabindex="-1"></a><span class="do">## 5.30 14.00 19.40 19.42 25.20 34.40 </span></span>
<span id="cb3-20"><a href="#cb3-20" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb3-21"><a href="#cb3-21" tabindex="-1"></a><span class="do">## $`3`</span></span>
<span id="cb3-22"><a href="#cb3-22" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-23"><a href="#cb3-23" tabindex="-1"></a><span class="do">## 2.90 14.10 19.50 20.16 27.60 37.70 </span></span>
<span id="cb3-24"><a href="#cb3-24" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb3-25"><a href="#cb3-25" tabindex="-1"></a><span class="do">## $`4`</span></span>
<span id="cb3-26"><a href="#cb3-26" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-27"><a href="#cb3-27" tabindex="-1"></a><span class="do">## 3.30 15.00 19.90 18.96 25.00 27.80 </span></span>
<span id="cb3-28"><a href="#cb3-28" tabindex="-1"></a><span class="do">## </span></span>
<span id="cb3-29"><a href="#cb3-29" tabindex="-1"></a><span class="do">## $`5`</span></span>
<span id="cb3-30"><a href="#cb3-30" tabindex="-1"></a><span class="do">## Min. 1st Qu. Median Mean 3rd Qu. Max. </span></span>
<span id="cb3-31"><a href="#cb3-31" tabindex="-1"></a><span class="do">## 1.500 2.200 3.800 6.292 11.500 13.800</span></span></code></pre></div>
<p> </p>
<p>7. Now onto some plotting action. Plot a Cleveland dotchart (<a
href="https://intro2r.com/simple-base-r-plots.html#dotcharts">Section
4.2.4</a>) of each <strong>numeric</strong> variable separately to
assess whether there are any outliers (unusually large or small values)
in the response variable (<code>ABUND</code>) or any of the continuous
explanatory variables (see Q3).</p>
<p>If you feel in the mood, output these plots to an external PDF file
in an <code>output</code> directory within your RStudio project (don’t
forget to create the directory first if required). If you would like to
include all of the plots on a single ‘page’ (technically a device) then
you can split your page into two rows and three columns using
<code>par(mfrow = c(2,3))</code> before you run your plot code for each
plot. Make a note of which variables contain outliers.</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" tabindex="-1"></a><span class="co"># first split the plotting device into 2 rows</span></span>
<span id="cb4-2"><a href="#cb4-2" tabindex="-1"></a><span class="co"># and 3 columns</span></span>
<span id="cb4-3"><a href="#cb4-3" tabindex="-1"></a><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">2</span>,<span class="dv">3</span>))</span>
<span id="cb4-4"><a href="#cb4-4" tabindex="-1"></a></span>
<span id="cb4-5"><a href="#cb4-5" tabindex="-1"></a><span class="co"># now produce the plots</span></span>
<span id="cb4-6"><a href="#cb4-6" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>AREA, <span class="at">main =</span> <span class="st">"Area"</span>)</span>
<span id="cb4-7"><a href="#cb4-7" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>DIST, <span class="at">main =</span> <span class="st">"Distance"</span>)</span>
<span id="cb4-8"><a href="#cb4-8" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>LDIST, <span class="at">main =</span> <span class="st">"Distance to larger patch"</span>)</span>
<span id="cb4-9"><a href="#cb4-9" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>YR.ISOL, <span class="at">main =</span> <span class="st">"Year of isolation"</span>)</span>
<span id="cb4-10"><a href="#cb4-10" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>ALT, <span class="at">main =</span> <span class="st">"Altitude"</span>)</span>
<span id="cb4-11"><a href="#cb4-11" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>GRAZE, <span class="at">main =</span> <span class="st">"Grazing levels"</span>)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q7a-1.png" width="672" /></p>
<p> </p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" tabindex="-1"></a><span class="co"># A fancier version of a dotplot - just for fun!</span></span>
<span id="cb5-2"><a href="#cb5-2" tabindex="-1"></a>Z <span class="ot"><-</span> <span class="fu">cbind</span>(loyn<span class="sc">$</span>ABUND, loyn<span class="sc">$</span>AREA, loyn<span class="sc">$</span>DIST,</span>
<span id="cb5-3"><a href="#cb5-3" tabindex="-1"></a> loyn<span class="sc">$</span>LDIST,loyn<span class="sc">$</span>YR.ISOL,loyn<span class="sc">$</span>ALT,</span>
<span id="cb5-4"><a href="#cb5-4" tabindex="-1"></a> loyn<span class="sc">$</span>GRAZE)</span>
<span id="cb5-5"><a href="#cb5-5" tabindex="-1"></a></span>
<span id="cb5-6"><a href="#cb5-6" tabindex="-1"></a><span class="fu">colnames</span>(Z) <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"Abundance"</span>, <span class="st">"Area"</span>,<span class="st">"Distance"</span>,</span>
<span id="cb5-7"><a href="#cb5-7" tabindex="-1"></a> <span class="st">"larger dist"</span>,<span class="st">"year of isolation"</span>,</span>
<span id="cb5-8"><a href="#cb5-8" tabindex="-1"></a> <span class="st">"Altitude"</span>, <span class="st">"Grazing"</span>)</span>
<span id="cb5-9"><a href="#cb5-9" tabindex="-1"></a> </span>
<span id="cb5-10"><a href="#cb5-10" tabindex="-1"></a><span class="fu">library</span>(lattice)</span>
<span id="cb5-11"><a href="#cb5-11" tabindex="-1"></a><span class="fu">dotplot</span>(<span class="fu">as.matrix</span>(Z),</span>
<span id="cb5-12"><a href="#cb5-12" tabindex="-1"></a> <span class="at">groups=</span><span class="cn">FALSE</span>,</span>
<span id="cb5-13"><a href="#cb5-13" tabindex="-1"></a> <span class="at">strip =</span> <span class="fu">strip.custom</span>(<span class="at">bg =</span> <span class="st">'white'</span>,</span>
<span id="cb5-14"><a href="#cb5-14" tabindex="-1"></a> <span class="at">par.strip.text =</span> <span class="fu">list</span>(<span class="at">cex =</span> <span class="fl">0.8</span>)),</span>
<span id="cb5-15"><a href="#cb5-15" tabindex="-1"></a> <span class="at">scales =</span> <span class="fu">list</span>(<span class="at">x =</span> <span class="fu">list</span>(<span class="at">relation =</span> <span class="st">"free"</span>),</span>
<span id="cb5-16"><a href="#cb5-16" tabindex="-1"></a> <span class="at">y =</span> <span class="fu">list</span>(<span class="at">relation =</span> <span class="st">"free"</span>),</span>
<span id="cb5-17"><a href="#cb5-17" tabindex="-1"></a> <span class="at">draw =</span> <span class="cn">FALSE</span>),</span>
<span id="cb5-18"><a href="#cb5-18" tabindex="-1"></a> <span class="at">col=</span><span class="dv">1</span>, <span class="at">cex =</span><span class="fl">0.5</span>, <span class="at">pch =</span> <span class="dv">16</span>,</span>
<span id="cb5-19"><a href="#cb5-19" tabindex="-1"></a> <span class="at">xlab =</span> <span class="st">"Value of the variable"</span>,</span>
<span id="cb5-20"><a href="#cb5-20" tabindex="-1"></a> <span class="at">ylab =</span> <span class="st">"Order of the data from text file"</span>)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q7b-1.png" width="672" /></p>
<p>8. If you do spot any unusual observations have a think about what
you want to do with them (NOTE: do <strong>not</strong> just remove them
without justification!). If you’re unsure, please speak to an instructor
to discuss your options during the practical session. Perhaps you should
apply a data transformation to see if this reduces the magnitude of any
outlier. The best thing to do here is to play around with different
transformations (i.e. <code>log10</code>, <code>sqrt</code>) to see
which transformation does what you want it to do. When applying a data
transformation to a variable, it’s best practice to create a new
variable <strong>in your dataframe</strong> to contain your transformed
variable rather than overwrite your original data.</p>
<p>After you have applied these data transformations make sure you
re-plot your dotcharts with any transformed variable to double check
whether the transformation is doing something sensible. Hint: a
log<sub>10</sub> transformation might help reduce the magnitude of the
outliers for some of the variables.</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" tabindex="-1"></a><span class="co"># There appears to be two unusually large forest patches compared to the rest</span></span>
<span id="cb6-2"><a href="#cb6-2" tabindex="-1"></a><span class="co"># Also one potentially large distance in DIST</span></span>
<span id="cb6-3"><a href="#cb6-3" tabindex="-1"></a><span class="co"># One option would be to log10 transform AREA, DIST </span></span>
<span id="cb6-4"><a href="#cb6-4" tabindex="-1"></a><span class="co"># log base 10 transform variables </span></span>
<span id="cb6-5"><a href="#cb6-5" tabindex="-1"></a></span>
<span id="cb6-6"><a href="#cb6-6" tabindex="-1"></a>loyn<span class="sc">$</span>LOGAREA <span class="ot"><-</span> <span class="fu">log10</span>(loyn<span class="sc">$</span>AREA)</span>
<span id="cb6-7"><a href="#cb6-7" tabindex="-1"></a>loyn<span class="sc">$</span>LOGDIST <span class="ot"><-</span> <span class="fu">log10</span>(loyn<span class="sc">$</span>DIST)</span>
<span id="cb6-8"><a href="#cb6-8" tabindex="-1"></a></span>
<span id="cb6-9"><a href="#cb6-9" tabindex="-1"></a><span class="co"># check the dataframe</span></span>
<span id="cb6-10"><a href="#cb6-10" tabindex="-1"></a><span class="fu">str</span>(loyn)</span>
<span id="cb6-11"><a href="#cb6-11" tabindex="-1"></a><span class="do">## 'data.frame': 67 obs. of 11 variables:</span></span>
<span id="cb6-12"><a href="#cb6-12" tabindex="-1"></a><span class="do">## $ SITE : int 1 60 2 3 61 4 5 6 7 8 ...</span></span>
<span id="cb6-13"><a href="#cb6-13" tabindex="-1"></a><span class="do">## $ ABUND : num 5.3 10 2 1.5 13 17.1 13.8 14.1 3.8 2.2 ...</span></span>
<span id="cb6-14"><a href="#cb6-14" tabindex="-1"></a><span class="do">## $ AREA : num 0.1 0.2 0.5 0.5 0.6 1 1 1 1 1 ...</span></span>
<span id="cb6-15"><a href="#cb6-15" tabindex="-1"></a><span class="do">## $ DIST : int 39 142 234 104 191 66 246 234 467 284 ...</span></span>
<span id="cb6-16"><a href="#cb6-16" tabindex="-1"></a><span class="do">## $ LDIST : int 39 142 234 311 357 66 246 285 467 1829 ...</span></span>
<span id="cb6-17"><a href="#cb6-17" tabindex="-1"></a><span class="do">## $ YR.ISOL: int 1968 1961 1920 1900 1957 1966 1918 1965 1955 1920 ...</span></span>
<span id="cb6-18"><a href="#cb6-18" tabindex="-1"></a><span class="do">## $ GRAZE : int 2 2 5 5 2 3 5 3 5 5 ...</span></span>
<span id="cb6-19"><a href="#cb6-19" tabindex="-1"></a><span class="do">## $ ALT : int 160 180 60 140 185 160 140 130 90 60 ...</span></span>
<span id="cb6-20"><a href="#cb6-20" tabindex="-1"></a><span class="do">## $ FGRAZE : Factor w/ 5 levels "1","2","3","4",..: 2 2 5 5 2 3 5 3 5 5 ...</span></span>
<span id="cb6-21"><a href="#cb6-21" tabindex="-1"></a><span class="do">## $ LOGAREA: num -1 -0.699 -0.301 -0.301 -0.222 ...</span></span>
<span id="cb6-22"><a href="#cb6-22" tabindex="-1"></a><span class="do">## $ LOGDIST: num 1.59 2.15 2.37 2.02 2.28 ...</span></span>
<span id="cb6-23"><a href="#cb6-23" tabindex="-1"></a></span>
<span id="cb6-24"><a href="#cb6-24" tabindex="-1"></a><span class="co"># first split the plotting device into 2 rows</span></span>
<span id="cb6-25"><a href="#cb6-25" tabindex="-1"></a><span class="co"># and 3 columns</span></span>
<span id="cb6-26"><a href="#cb6-26" tabindex="-1"></a><span class="fu">par</span>(<span class="at">mfrow =</span> <span class="fu">c</span>(<span class="dv">1</span>,<span class="dv">2</span>))</span>
<span id="cb6-27"><a href="#cb6-27" tabindex="-1"></a></span>
<span id="cb6-28"><a href="#cb6-28" tabindex="-1"></a><span class="co"># now plot the transformed variables</span></span>
<span id="cb6-29"><a href="#cb6-29" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>LOGAREA, <span class="at">main =</span> <span class="st">"LOG Area"</span>)</span>
<span id="cb6-30"><a href="#cb6-30" tabindex="-1"></a><span class="fu">dotchart</span>(loyn<span class="sc">$</span>LOGDIST, <span class="at">main =</span> <span class="st">"LOG Distance"</span>)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q8-1.png" width="672" /></p>
<p> </p>
<p>9. Next, check if there is any potential collinearity between any of
the <strong>explanatory variables</strong>. Remember, collinearity is
<em>strong</em> relationships between your explanatory variables. Plot
these variables using the <code>pairs()</code> function (<a
href="https://intro2r.com/simple-base-r-plots.html#pairs-plots">Section
4.2.5</a>).</p>
<p>You will need to extract your explanatory variables from the
<code>loyn</code> dataframe (using <code>[]</code>) either before you
use the <code>pairs()</code> function or whilst using it (don’t forget
to plot the transformed versions of any variables from Q8).</p>
<p>Optionally, include the correlation coefficient between variables in
the upper panel of the pairs plot (see <a
href="https://intro2r.com/simple-base-r-plots.html#pairs-plots">section
4.2.5</a> of the introduction to R book for details) to help you decide
whether collinearity is an issue.</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" tabindex="-1"></a><span class="co"># Vanilla pairs plot</span></span>
<span id="cb7-2"><a href="#cb7-2" tabindex="-1"></a></span>
<span id="cb7-3"><a href="#cb7-3" tabindex="-1"></a><span class="fu">pairs</span>(loyn[,<span class="fu">c</span>(<span class="st">"LOGAREA"</span>, <span class="st">"LOGDIST"</span>, <span class="st">"LDIST"</span>,</span>
<span id="cb7-4"><a href="#cb7-4" tabindex="-1"></a> <span class="st">"YR.ISOL"</span>, <span class="st">"ALT"</span>, <span class="st">"GRAZE"</span>)])</span>
<span id="cb7-5"><a href="#cb7-5" tabindex="-1"></a></span>
<span id="cb7-6"><a href="#cb7-6" tabindex="-1"></a><span class="co"># or first create a new dataframe and then use this </span></span>
<span id="cb7-7"><a href="#cb7-7" tabindex="-1"></a><span class="co"># data frame with the pairs function</span></span>
<span id="cb7-8"><a href="#cb7-8" tabindex="-1"></a></span>
<span id="cb7-9"><a href="#cb7-9" tabindex="-1"></a>explan_vars <span class="ot"><-</span> loyn[,<span class="fu">c</span>(<span class="st">"LOGAREA"</span>, <span class="st">"LOGDIST"</span>, <span class="st">"LDIST"</span>,</span>
<span id="cb7-10"><a href="#cb7-10" tabindex="-1"></a> <span class="st">"YR.ISOL"</span>, <span class="st">"ALT"</span>, <span class="st">"GRAZE"</span>)]</span>
<span id="cb7-11"><a href="#cb7-11" tabindex="-1"></a><span class="fu">pairs</span>(explan_vars)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q9a-1.png" width="672" /></p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" tabindex="-1"></a><span class="co"># And with correlations in the upper panel</span></span>
<span id="cb8-2"><a href="#cb8-2" tabindex="-1"></a></span>
<span id="cb8-3"><a href="#cb8-3" tabindex="-1"></a><span class="co"># first need to define the panel.cor function</span></span>
<span id="cb8-4"><a href="#cb8-4" tabindex="-1"></a>panel.cor <span class="ot"><-</span> <span class="cf">function</span>(x, y, <span class="at">digits =</span> <span class="dv">2</span>, <span class="at">prefix =</span> <span class="st">""</span>, cex.cor, ...){</span>
<span id="cb8-5"><a href="#cb8-5" tabindex="-1"></a> usr <span class="ot"><-</span> <span class="fu">par</span>(<span class="st">"usr"</span>); <span class="fu">on.exit</span>(<span class="fu">par</span>(usr))</span>
<span id="cb8-6"><a href="#cb8-6" tabindex="-1"></a> <span class="fu">par</span>(<span class="at">usr =</span> <span class="fu">c</span>(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">0</span>, <span class="dv">1</span>))</span>
<span id="cb8-7"><a href="#cb8-7" tabindex="-1"></a> r <span class="ot"><-</span> <span class="fu">abs</span>(<span class="fu">cor</span>(x, y))</span>
<span id="cb8-8"><a href="#cb8-8" tabindex="-1"></a> txt <span class="ot"><-</span> <span class="fu">format</span>(<span class="fu">c</span>(r, <span class="fl">0.123456789</span>), <span class="at">digits =</span> digits)[<span class="dv">1</span>]</span>
<span id="cb8-9"><a href="#cb8-9" tabindex="-1"></a> txt <span class="ot"><-</span> <span class="fu">paste0</span>(prefix, txt)</span>
<span id="cb8-10"><a href="#cb8-10" tabindex="-1"></a> <span class="cf">if</span>(<span class="fu">missing</span>(cex.cor)) cex.cor <span class="ot"><-</span> <span class="fl">0.8</span><span class="sc">/</span><span class="fu">strwidth</span>(txt)</span>
<span id="cb8-11"><a href="#cb8-11" tabindex="-1"></a> <span class="fu">text</span>(<span class="fl">0.5</span>, <span class="fl">0.5</span>, txt, <span class="at">cex =</span> cex.cor <span class="sc">*</span> r)</span>
<span id="cb8-12"><a href="#cb8-12" tabindex="-1"></a>}</span>
<span id="cb8-13"><a href="#cb8-13" tabindex="-1"></a></span>
<span id="cb8-14"><a href="#cb8-14" tabindex="-1"></a><span class="co"># then use the panel.cor function when we use pairs</span></span>
<span id="cb8-15"><a href="#cb8-15" tabindex="-1"></a><span class="fu">pairs</span>(loyn[,<span class="fu">c</span>(<span class="st">"LOGAREA"</span>,<span class="st">"LOGDIST"</span>, <span class="st">"LDIST"</span>,</span>
<span id="cb8-16"><a href="#cb8-16" tabindex="-1"></a> <span class="st">"YR.ISOL"</span>,<span class="st">"ALT"</span>,<span class="st">"GRAZE"</span>)],</span>
<span id="cb8-17"><a href="#cb8-17" tabindex="-1"></a> <span class="at">upper.panel =</span> panel.cor)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q9b-1.png" width="672" /></p>
<p> </p>
<p>10. Now that we’ve checked for collinearity let’s assess whether
there are any clear relationships between the response variable
(<code>ABUND</code>) and individual explanatory variables. Use
appropriate plotting functions (<code>plot()</code>,
<code>boxplot()</code>, <code>pairs()</code> etc) to visualise these
relationships.</p>
<p>Don’t forget, if you have applied a data transformation to any of
your variables (Q8) you will need to plot these transformed variables
instead of the original variables.</p>
<p>Also, don’t forget, you can split your plotting device up to allow
you to plot multiple graphs (<a
href="https://intro2r.com/mult_graphs.html#mult_graphs">Section 4.4</a>)
or again use a function like <code>pairs()</code> to create a
multi-panel plot. Output these plots to the <code>output</code>
directory as PDFs. Add some comments in your R code to summarise your
findings.</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" tabindex="-1"></a><span class="fu">pairs</span>(loyn[,<span class="fu">c</span>(<span class="st">"ABUND"</span>,<span class="st">"LOGAREA"</span>,<span class="st">"LOGDIST"</span>, <span class="st">"LDIST"</span>,</span>
<span id="cb9-2"><a href="#cb9-2" tabindex="-1"></a> <span class="st">"YR.ISOL"</span>,<span class="st">"ALT"</span>,<span class="st">"GRAZE"</span>)],</span>
<span id="cb9-3"><a href="#cb9-3" tabindex="-1"></a> <span class="at">lower.panel =</span> panel.cor)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q10a-1.png" width="672" /></p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" tabindex="-1"></a><span class="fu">plot</span>(loyn<span class="sc">$</span>LOGAREA, loyn<span class="sc">$</span>ABUND, <span class="at">xlab =</span> <span class="st">"log area"</span>, <span class="at">ylab =</span> <span class="st">"bird abundance"</span>)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q10b-1.png" width="672" /></p>
<p> </p>
<p>11. One of the main aims of this study was to determine whether
management practices such as grazing intensity (<code>GRAZE</code>) and
size of the forest (<code>AREA</code>) affected the abundance of birds
(<code>ABUND</code>). One hypothesis was that the size of the forest
affected the number of birds, but this was dependent on the intensity of
the grazing regime (in other words, there is an interaction between
<code>AREA</code> and <code>GRAZE</code> - don’t worry if you haven’t
heard of an interaction term, we will go through this later on in the
course).</p>
<p>Use an appropriate plotting function to explore these data for such
an interaction (perhaps a <code>coplot()</code> or <code>xyplot()</code>
in <a
href="https://intro2r.com/simple-base-r-plots.html#coplots">Section
4.2.6</a> might be helpful?).</p>
<p>Again, don’t forget, if you have applied a data transformation to
your <code>AREA</code> variable you need to use the transformed variable
in this plot <strong>not</strong> the original <code>AREA</code>
variable. Likewise, as we’ve converted the <code>GRAZE</code> variable
into a factor type variable we should use our new factor
<code>FGRAZE</code> (or whatever you have called it).</p>
<p>Save this plot as a PDF to your <code>output</code> directory and add
some comments to your R code to describe any patterns you observe.</p>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1" tabindex="-1"></a><span class="co"># Interaction between LOGAREA and FGRAZE? </span></span>
<span id="cb11-2"><a href="#cb11-2" tabindex="-1"></a><span class="co"># Do the slopes look similar or different? </span></span>
<span id="cb11-3"><a href="#cb11-3" tabindex="-1"></a><span class="fu">coplot</span>(ABUND <span class="sc">~</span> LOGAREA <span class="sc">|</span> FGRAZE, <span class="at">data =</span> loyn)</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q11a-1.png" width="672" /></p>
<p> </p>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" tabindex="-1"></a><span class="co"># Fancier version of the above plot </span></span>
<span id="cb12-2"><a href="#cb12-2" tabindex="-1"></a><span class="co"># with a line of best fit included just for fun</span></span>
<span id="cb12-3"><a href="#cb12-3" tabindex="-1"></a><span class="fu">coplot</span>(ABUND <span class="sc">~</span> LOGAREA <span class="sc">|</span> FGRAZE,</span>
<span id="cb12-4"><a href="#cb12-4" tabindex="-1"></a> <span class="at">data =</span> loyn,</span>
<span id="cb12-5"><a href="#cb12-5" tabindex="-1"></a> <span class="at">panel =</span> <span class="cf">function</span>(x, y, ...) {</span>
<span id="cb12-6"><a href="#cb12-6" tabindex="-1"></a> tmp <span class="ot"><-</span> <span class="fu">lm</span>(y <span class="sc">~</span> x, <span class="at">na.action =</span> na.omit)</span>
<span id="cb12-7"><a href="#cb12-7" tabindex="-1"></a> <span class="fu">abline</span>(tmp)</span>
<span id="cb12-8"><a href="#cb12-8" tabindex="-1"></a> <span class="fu">points</span>(x, y) })</span></code></pre></div>
<p><img src="graphical_data_exploration_exercise_solutions_files/figure-html/Q11b-1.png" width="672" /></p>
<p> </p>
<p><sup>1</sup> Loyn, R. (1987). Effects of patch area and habitat on
bird abundances, species numbers and tree health in fragmented Victoria
forests. Nature conservation: the role of remnants of native vegetation.
65-77.</p>
<p><sup>2</sup> Quinn, G. P., and Michael J. Keough. 2002. Experimental
design and data analysis for biologists. Cambridge, UK: Cambridge
University Press.</p>
<p><sup>3</sup> Zuur, A.F., Ieno, E.N. and Elphick, C.S. (2010), A
protocol for data exploration to avoid common statistical problems.
Methods in Ecology and Evolution, 1: 3-14. <a
href="doi:10.1111/j.2041-210X.2009.00001.x"
class="uri">doi:10.1111/j.2041-210X.2009.00001.x</a></p>
<p> </p>
<p>End of Graphical data exploration using R Exercise</p>
</div>
</div>
<script>
// add bootstrap table styles to pandoc tables
function bootstrapStylePandocTables() {
$('tr.odd').parent('tbody').parent('table').addClass('table table-condensed');
}
$(document).ready(function () {
bootstrapStylePandocTables();
});
</script>
<!-- tabsets -->
<script>
$(document).ready(function () {
window.buildTabsets("TOC");
});
$(document).ready(function () {
$('.tabset-dropdown > .nav-tabs > li').click(function () {
$(this).parent().toggleClass('nav-tabs-open');
});
});
</script>
<!-- code folding -->
<script>
$(document).ready(function () {
window.initializeCodeFolding("hide" === "show");
});
</script>
<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
(function () {
var script = document.createElement("script");
script.type = "text/javascript";
script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
document.getElementsByTagName("head")[0].appendChild(script);
})();
</script>
</body>
</html>