-
Notifications
You must be signed in to change notification settings - Fork 16
/
Ordinal-Logistic-Regression-With-R.html
372 lines (333 loc) · 20.2 KB
/
Ordinal-Logistic-Regression-With-R.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
<!DOCTYPE html>
<html>
<head>
<title>Ordinal Logistic Regression</title>
<meta charset="utf-8">
<meta name="Description" content="R Language Tutorials for Advanced Statistics">
<meta name="Keywords" content="R, Tutorial, Machine learning, Statistics, Data Mining, Analytics, Data science, Linear Regression, Logistic Regression, Time series, Forecasting">
<meta name="Distribution" content="Global">
<meta name="Author" content="Selva Prabhakaran">
<meta name="Robots" content="index, follow">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="shortcut icon" href="/screenshots/iconb-64.png" type="image/x-icon" />
<link href="www/bootstrap.min.css" rel="stylesheet">
<link href="www/highlight.css" rel="stylesheet">
<link href='http://fonts.googleapis.com/css?family=Inconsolata:400,700'
rel='stylesheet' type='text/css'>
<!-- Color Script -->
<style type="text/css">
a {
color: #3675C5;
color: rgb(25, 145, 248);
color: #4582ec;
color: #3F73D8;
}
li {
line-height: 1.65;
}
/* reduce spacing around math formula*/
.MathJax_Display {
margin: 0em 0em;
}
</style>
<!-- Add Google search -->
<script language="Javascript" type="text/javascript">
function my_search_google()
{
var query = document.getElementById("my-google-search").value;
window.open("http://google.com/search?q=" + query
+ "%20site:" + "http://r-statistics.co");
}
</script>
</head>
<body>
<div class="container">
<div class="masthead">
<!--
<ul class="nav nav-pills pull-right">
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">
Table of contents<b class="caret"></b>
</a>
<ul class="dropdown-menu pull-right" role="menu">
<li class="dropdown-header"></li>
<li class="dropdown-header">Tutorial</li>
<li><a href="R-Tutorial.html">R Tutorial</a></li>
<li class="dropdown-header">ggplot2</li>
<li><a href="ggplot2-Tutorial-With-R.html">ggplot2 Short Tutorial</a></li>
<li><a href="Complete-Ggplot2-Tutorial-Part1-With-R-Code.html">ggplot2 Tutorial 1 - Intro</a></li>
<li><a href="Complete-Ggplot2-Tutorial-Part2-Customizing-Theme-With-R-Code.html">ggplot2 Tutorial 2 - Theme</a></li>
<li><a href="Top50-Ggplot2-Visualizations-MasterList-R-Code.html">ggplot2 Tutorial 3 - Masterlist</a></li>
<li><a href="ggplot2-cheatsheet.html">ggplot2 Quickref</a></li>
<li class="dropdown-header">Foundations</li>
<li><a href="Linear-Regression.html">Linear Regression</a></li>
<li><a href="Statistical-Tests-in-R.html">Statistical Tests</a></li>
<li><a href="Missing-Value-Treatment-With-R.html">Missing Value Treatment</a></li>
<li><a href="Outlier-Treatment-With-R.html">Outlier Analysis</a></li>
<li><a href="Variable-Selection-and-Importance-With-R.html">Feature Selection</a></li>
<li><a href="Model-Selection-in-R.html">Model Selection</a></li>
<li><a href="Logistic-Regression-With-R.html">Logistic Regression</a></li>
<li><a href="Environments.html">Advanced Linear Regression</a></li>
<li class="dropdown-header">Advanced Regression Models</li>
<li><a href="adv-regression-models.html">Advanced Regression Models</a></li>
<li class="dropdown-header">Time Series</li>
<li><a href="Time-Series-Analysis-With-R.html">Time Series Analysis</a></li>
<li><a href="Time-Series-Forecasting-With-R.html">Time Series Forecasting </a></li>
<li><a href="Time-Series-Forecasting-With-R-part2.html">More Time Series Forecasting</a></li>
<li class="dropdown-header">High Performance Computing</li>
<li><a href="Parallel-Computing-With-R.html">Parallel computing</a></li>
<li><a href="Strategies-To-Improve-And-Speedup-R-Code.html">Strategies to Speedup R code</a></li>
<li class="dropdown-header">Useful Techniques</li>
<li><a href="Association-Mining-With-R.html">Association Mining</a></li>
<li><a href="Multi-Dimensional-Scaling-With-R.html">Multi Dimensional Scaling</a></li>
<li><a href="Profiling.html">Optimization</a></li>
<li><a href="Information-Value-With-R.html">InformationValue package</a></li>
</ul>
</li>
</ul>
-->
<ul class="nav nav-pills pull-right">
<div class="input-group">
<form onsubmit="my_search_google()">
<input type="text" class="form-control" id="my-google-search" placeholder="Search..">
<form>
</div><!-- /input-group -->
</ul><!-- /.col-lg-6 -->
<h3 class="muted"><a href="/">r-statistics.co</a><small> by Selva Prabhakaran</small></h3>
<hr>
</div>
<div class="row">
<div class="col-xs-12 col-sm-3" id="nav">
<div class="well">
<li>
<ul class="list-unstyled">
<li class="dropdown-header"></li>
<li class="dropdown-header">Tutorial</li>
<li><a href="R-Tutorial.html">R Tutorial</a></li>
<li class="dropdown-header">ggplot2</li>
<li><a href="ggplot2-Tutorial-With-R.html">ggplot2 Short Tutorial</a></li>
<li><a href="Complete-Ggplot2-Tutorial-Part1-With-R-Code.html">ggplot2 Tutorial 1 - Intro</a></li>
<li><a href="Complete-Ggplot2-Tutorial-Part2-Customizing-Theme-With-R-Code.html">ggplot2 Tutorial 2 - Theme</a></li>
<li><a href="Top50-Ggplot2-Visualizations-MasterList-R-Code.html">ggplot2 Tutorial 3 - Masterlist</a></li>
<li><a href="ggplot2-cheatsheet.html">ggplot2 Quickref</a></li>
<li class="dropdown-header">Foundations</li>
<li><a href="Linear-Regression.html">Linear Regression</a></li>
<li><a href="Statistical-Tests-in-R.html">Statistical Tests</a></li>
<li><a href="Missing-Value-Treatment-With-R.html">Missing Value Treatment</a></li>
<li><a href="Outlier-Treatment-With-R.html">Outlier Analysis</a></li>
<li><a href="Variable-Selection-and-Importance-With-R.html">Feature Selection</a></li>
<li><a href="Model-Selection-in-R.html">Model Selection</a></li>
<li><a href="Logistic-Regression-With-R.html">Logistic Regression</a></li>
<li><a href="Environments.html">Advanced Linear Regression</a></li>
<li class="dropdown-header">Advanced Regression Models</li>
<li><a href="adv-regression-models.html">Advanced Regression Models</a></li>
<li class="dropdown-header">Time Series</li>
<li><a href="Time-Series-Analysis-With-R.html">Time Series Analysis</a></li>
<li><a href="Time-Series-Forecasting-With-R.html">Time Series Forecasting </a></li>
<li><a href="Time-Series-Forecasting-With-R-part2.html">More Time Series Forecasting</a></li>
<li class="dropdown-header">High Performance Computing</li>
<li><a href="Parallel-Computing-With-R.html">Parallel computing</a></li>
<li><a href="Strategies-To-Improve-And-Speedup-R-Code.html">Strategies to Speedup R code</a></li>
<li class="dropdown-header">Useful Techniques</li>
<li><a href="Association-Mining-With-R.html">Association Mining</a></li>
<li><a href="Multi-Dimensional-Scaling-With-R.html">Multi Dimensional Scaling</a></li>
<li><a href="Profiling.html">Optimization</a></li>
<li><a href="Information-Value-With-R.html">InformationValue package</a></li>
</ul>
</li>
</div>
<div class="well">
<p>Stay up-to-date. <a href="https://docs.google.com/forms/d/1xkMYkLNFU9U39Dd8S_2JC0p8B5t6_Yq6zUQjanQQJpY/viewform">Subscribe!</a></p>
<p><a href="https://docs.google.com/forms/d/13GrkCFcNa-TOIllQghsz2SIEbc-YqY9eJX02B19l5Ow/viewform">Chat!</a></p>
</div>
<h4>Contents</h4>
<ul class="list-unstyled" id="toc"></ul>
<!--
<hr>
<p><a href="/contribute.html">How to contribute</a></p>
<p><a class="btn btn-primary" href="">Edit this page</a></p>
-->
</div>
<div id="content" class="col-xs-12 col-sm-8 pull-right">
<blockquote>
<p>Ordinal logistic regression can be used to model a ordered factor response.</p>
</blockquote>
<p>The <code>polr()</code> function from the <code>MASS</code> package can be used to build the <em>proportional odds logistic regression</em> and predict the class of multi-class ordered variables. One such use case is described below.</p>
<h2>Example: Predict Cars Evaluation</h2>
<p>Below is a example on how we can use ordered logistic regression to predict the cars evaluation based on <a href="http://archive.ics.uci.edu/ml/datasets/Car+Evaluation">cars evaluation dataset</a>. The cars are evaluated as one amongst <code>very good</code>, <code>good</code>, <code>acceptable</code> or <code>unacceptable</code>. The attributes of the cars available to use to predict this decision are:</p>
<ol style="list-style-type: decimal">
<li>buying : v-high, high, med, low</li>
<li>maint : v-high, high, med, low</li>
<li>doors : 2, 3, 4, 5-more</li>
<li>persons : 2, 4, more</li>
<li>lug_boot : small, med, big</li>
<li>safety : low, med, high</li>
</ol>
<p>Also, it is worthwhile to note that about 70% of the cars are evaluated as <em>unacceptable</em>. The class distribution of the ordered multi class <span class="math inline"><em>Y</em></span> is as follows:</p>
<table>
<thead>
<tr class="header">
<th align="left">class</th>
<th align="left">N</th>
<th align="left">N[%]</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">unacc</td>
<td align="left">1210</td>
<td align="left">(70.023 %)</td>
</tr>
<tr class="even">
<td align="left">acc</td>
<td align="left">384</td>
<td align="left">(22.222 %)</td>
</tr>
<tr class="odd">
<td align="left">good</td>
<td align="left">69</td>
<td align="left">(3.993 %)</td>
</tr>
<tr class="even">
<td align="left">v-good</td>
<td align="left">65</td>
<td align="left">(3.762 %)</td>
</tr>
</tbody>
</table>
<p>Lets being the modeling process by first importing the data and assigning the correct orders to the factor variables.</p>
<h2>Import the data</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">carsdata <-<span class="st"> </span><span class="kw">read.csv</span>(<span class="st">"http://archive.ics.uci.edu/ml/machine-learning-databases/car/car.data"</span>, <span class="dt">header=</span>F, <span class="dt">stringsAsFactors=</span>F) <span class="co"># import string variables as characters.</span>
<span class="kw">colnames</span>(carsdata) <-<span class="st"> </span><span class="kw">c</span>(<span class="st">"buying"</span>, <span class="st">"maint"</span>, <span class="st">"doors"</span>, <span class="st">"persons"</span>, <span class="st">"lug_boot"</span>, <span class="st">"safety"</span>, <span class="st">"class"</span>)</code></pre></div>
<h4>Reorder the levels of factors</h4>
<p>In order logistic regression, the order of the levels in the factor variables matters. So, lets define them explicitly. This is an critical step, otherwise, predictions could go worng easily.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Reorder</span>
carsdata$buying <-<span class="st"> </span><span class="kw">factor</span>(carsdata$buying, <span class="dt">levels=</span><span class="kw">c</span>(<span class="st">"low"</span>, <span class="st">"med"</span>, <span class="st">"high"</span>, <span class="st">"vhigh"</span>), <span class="dt">ordered=</span><span class="ot">TRUE</span>)
carsdata$maint <-<span class="st"> </span><span class="kw">factor</span>(carsdata$maint, <span class="dt">levels=</span><span class="kw">c</span>(<span class="st">"low"</span>, <span class="st">"med"</span>, <span class="st">"high"</span>, <span class="st">"vhigh"</span>), <span class="dt">ordered=</span><span class="ot">TRUE</span>)
carsdata$doors <-<span class="st"> </span><span class="kw">factor</span>(carsdata$doors, <span class="dt">levels=</span><span class="kw">c</span>(<span class="st">"2"</span>, <span class="st">"3"</span>, <span class="st">"4"</span>, <span class="st">"5more"</span>), <span class="dt">ordered=</span><span class="ot">TRUE</span>)
carsdata$persons <-<span class="st"> </span><span class="kw">factor</span>(carsdata$persons, <span class="dt">levels=</span><span class="kw">c</span>(<span class="st">"2"</span>, <span class="st">"4"</span>, <span class="st">"more"</span>), <span class="dt">ordered=</span><span class="ot">TRUE</span>)
carsdata$lug_boot <-<span class="st"> </span><span class="kw">factor</span>(carsdata$lug_boot, <span class="dt">levels=</span><span class="kw">c</span>(<span class="st">"small"</span>, <span class="st">"med"</span>, <span class="st">"big"</span>), <span class="dt">ordered=</span><span class="ot">TRUE</span>)
carsdata$safety <-<span class="st"> </span><span class="kw">factor</span>(carsdata$safety, <span class="dt">levels=</span><span class="kw">c</span>(<span class="st">"low"</span>, <span class="st">"med"</span>, <span class="st">"high"</span>), <span class="dt">ordered=</span><span class="ot">TRUE</span>)
carsdata$class <-<span class="st"> </span><span class="kw">factor</span>(carsdata$class, <span class="dt">levels=</span><span class="kw">c</span>(<span class="st">"unacc"</span>, <span class="st">"acc"</span>, <span class="st">"good"</span>, <span class="st">"vgood"</span>), <span class="dt">ordered=</span><span class="ot">TRUE</span>)</code></pre></div>
<h2>Prepare training and test data</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Prepare Training and Test Data</span>
<span class="kw">set.seed</span>(<span class="dv">100</span>)
trainingRows <-<span class="st"> </span><span class="kw">sample</span>(<span class="dv">1</span>:<span class="kw">nrow</span>(carsdata), <span class="fl">0.7</span> *<span class="st"> </span><span class="kw">nrow</span>(carsdata))
trainingData <-<span class="st"> </span>carsdata[trainingRows, ]
testData <-<span class="st"> </span>carsdata[-trainingRows, ]</code></pre></div>
<h2>Build the ordered logistic regression model</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">### Build ordered logistic regression model
<span class="kw">options</span>(<span class="dt">contrasts =</span> <span class="kw">c</span>(<span class="st">"contr.treatment"</span>, <span class="st">"contr.poly"</span>))
polrMod <-<span class="st"> </span><span class="kw">polr</span>(class ~<span class="st"> </span>safety +<span class="st"> </span>lug_boot +<span class="st"> </span>doors +<span class="st"> </span>buying +<span class="st"> </span>maint, <span class="dt">data=</span>trainingData)
<span class="kw">summary</span>(polrMod)
<span class="co">#> Call:</span>
<span class="co">#> polr(formula = class ~ safety + lug_boot + doors + buying + maint, </span>
<span class="co">#> data = trainingData)</span>
<span class="co">#> </span>
<span class="co">#> Coefficients:</span>
<span class="co">#> Value Std. Error t value</span>
<span class="co">#> safety.L 19.9443 0.06145 324.5411</span>
<span class="co">#> safety.Q -10.6548 0.10088 -105.6189</span>
<span class="co">#> lug_boot.L 1.0119 0.14011 7.2224</span>
<span class="co">#> lug_boot.Q -0.3197 0.13355 -2.3940</span>
<span class="co">#> doors.L 0.5415 0.15573 3.4774</span>
<span class="co">#> doors.Q -0.2787 0.15466 -1.8018</span>
<span class="co">#> doors.C -0.1096 0.15372 -0.7132</span>
<span class="co">#> buying.L -2.0945 0.18137 -11.5480</span>
<span class="co">#> buying.Q -0.1369 0.15659 -0.8746</span>
<span class="co">#> buying.C 0.5219 0.15318 3.4069</span>
<span class="co">#> maint.L -1.8209 0.17533 -10.3856</span>
<span class="co">#> maint.Q -0.4768 0.15811 -3.0153</span>
<span class="co">#> maint.C 0.3319 0.15518 2.1388</span>
<span class="co">#> </span>
<span class="co">#> Intercepts:</span>
<span class="co">#> Value Std. Error t value </span>
<span class="co">#> unacc|acc 9.4557 0.0740 127.8297</span>
<span class="co">#> acc|good 11.8726 0.1345 88.2882</span>
<span class="co">#> good|vgood 13.1331 0.1997 65.7533</span>
<span class="co">#> </span>
<span class="co">#> Residual Deviance: 1300.15 </span>
<span class="co">#> AIC: 1332.15</span></code></pre></div>
<h2>Predict on test data</h2>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">### Predict
predictedClass <-<span class="st"> </span><span class="kw">predict</span>(polrMod, testData) <span class="co"># predict the classes directly</span>
<span class="kw">head</span>(predictedClass)
<span class="co">#> [1] unacc unacc unacc unacc unacc unacc</span>
<span class="co">#> Levels: unacc acc good vgood</span>
predictedScores <-<span class="st"> </span><span class="kw">predict</span>(polrMod, testData, <span class="dt">type=</span><span class="st">"p"</span>) <span class="co"># predict the probabilites</span>
<span class="kw">head</span>(predictedScores)
<span class="co">#> unacc acc good vgood</span>
<span class="co">#> 3 0.9774549 2.049194e-02 1.470224e-03 5.829671e-04</span>
<span class="co">#> 6 0.9347665 5.904708e-02 4.424660e-03 1.761744e-03</span>
<span class="co">#> 12 0.9774549 2.049194e-02 1.470224e-03 5.829671e-04</span>
<span class="co">#> 13 1.0000000 3.574918e-14 2.664535e-15 8.881784e-16</span>
<span class="co">#> 14 0.9762376 2.159594e-02 1.551314e-03 6.151902e-04</span>
<span class="co">#> 18 0.9120030 7.946377e-02 6.099087e-03 2.434191e-03</span>
## Confusion matrix and misclassification error
<span class="kw">table</span>(testData$class, predictedClass) <span class="co"># confusion matrix</span>
<span class="co">#> predictedClass</span>
<span class="co">#> unacc acc good vgood</span>
<span class="co">#> unacc 305 45 0 4</span>
<span class="co">#> acc 60 60 0 0</span>
<span class="co">#> good 0 17 0 0</span>
<span class="co">#> vgood 0 18 0 10</span>
<span class="kw">mean</span>(<span class="kw">as.character</span>(testData$class) !=<span class="st"> </span><span class="kw">as.character</span>(predictedClass)) <span class="co"># misclassification error</span>
<span class="co">#> 0.277</span></code></pre></div>
</div>
</div>
<div class="footer">
<hr>
<p>© 2016-17 Selva Prabhakaran. Powered by <a href="http://jekyllrb.com/">jekyll</a>,
<a href="http://yihui.name/knitr/">knitr</a>, and
<a href="http://johnmacfarlane.net/pandoc/">pandoc</a>.
This work is licensed under the <a href="http://creativecommons.org/licenses/by-nc/3.0/">Creative Commons License.</a>
</p>
</div>
</div> <!-- /container -->
<script src="//code.jquery.com/jquery.js"></script>
<script src="www/bootstrap.min.js"></script>
<script src="www/toc.js"></script>
<!-- MathJax Script -->
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}
});
</script>
<script type="text/javascript"
src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<!-- Google Analytics Code -->
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','//www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-69351797-1', 'auto');
ga('send', 'pageview');
</script>
<style type="text/css">
/* reduce spacing around math formula*/
.MathJax_Display {
margin: 0em 0em;
}
body {
font-family: 'Helvetica Neue', Roboto, Arial, sans-serif;
font-size: 16px;
line-height: 27px;
font-weight: 400;
}
blockquote p {
line-height: 1.75;
color: #717171;
}
.well li{
line-height: 28px;
}
li.dropdown-header {
display: block;
padding: 0px;
font-size: 14px;
}
</style>
</body>
</html>