Categorical Data Analysis for the Behavioral and Social Sciences

296 Pages·2010·14.8 MB·English

by  Razia Azen

Categorical Data
Analysis for the
Behavioral and
Social Sciences

Categorical Data
Analysis for the
Behavioral and
Social Sciences
Razia Azen
University of Wisconsin-Milwaukee
Cindy M. Walker
University of Wisconsin-Milwaukee
Routledge Routledge
Taylor & Francis Group Taylor & Francis Group
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Library of Congress Cataloging-in-Publication Data
Azen, Razia, 1969-
Categorical data analysis for the behavioral and social sciences / Razia Azen, Cindy M. Walker.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-84872-836-3
1. Social sciences--Statistical methods. I. Walker, Cindy M., 1965- II. Title.
HA29.A94 2011
519.5’35--dc22 2010014461
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Dedication
To our students: past, present, and future

Contents
Preface..............................................................................................................................................xi
Chapter 1 Introduction and overview....................................................................................1
1.1 What is categorical data analysis?......................................................................................1
1.2 Scales of measurement.........................................................................................................2
1.3 A brief history of categorical methods..............................................................................3
1.4 Organization of this book...................................................................................................4
1.5 Summary...............................................................................................................................5
Chapter 2 Probability distributions........................................................................................7
2.1 Probability distributions for categorical variables...........................................................7
2.2 Frequency distribution tables for discrete variables.......................................................8
2.3 The hypergeometric distribution.......................................................................................9
2.4 The Bernoulli distribution.................................................................................................12
2.5 The binomial distribution.................................................................................................12
2.6 The multinomial distribution...........................................................................................14
2.7 The Poisson distribution....................................................................................................16
2.8 Summary.............................................................................................................................19
Chapter 3 Proportions, estimation, and goodness-of-fit..................................................21
3.1 Maximum likelihood estimation: a single proportion..................................................21
3.2 Hypothesis testing for a single proportion.....................................................................23
3.3 Confidence intervals for a single proportion..................................................................29
3.4 Goodness-of-fit: comparing distributions for a single discrete variable....................30
3.5 Computer output: single proportion example................................................................32
3.6 Computer output: goodness-of-fit example....................................................................38
3.7 Summary.............................................................................................................................41
Chapter 4 Association between two categorical variables...............................................45
4.1 Contingency tables for two categorical variables..........................................................45
4.2 Independence......................................................................................................................46
4.3 Odds ratio............................................................................................................................47
4.4 Testing the association between two categorical variables..........................................54
4.5 Applications: inter-rater agreement.................................................................................61
4.6 Computer output: test of independence..........................................................................63
4.7 Computer output: inter-rater agreement.........................................................................69
4.8 Complete example..............................................................................................................72
4.9 Summary.............................................................................................................................73
vii
viii Contents
Chapter 5 Association between three categorical variables............................................79
5.1 Contingency tables for three categorical variables........................................................80
5.2 Marginal and conditional independence........................................................................84
5.3 Inferential statistics for three-way tables........................................................................87
5.4 Computer output: test of association...............................................................................94
5.5 Computer output: inferential tests for three-way tables...............................................97
5.6 Complete example............................................................................................................103
5.7 Summary...........................................................................................................................111
Chapter 6 Modeling and the generalized linear model..................................................117
6.1 Components of a GLM.....................................................................................................118
6.2 Parameter estimation.......................................................................................................126
6.3 Model fit.............................................................................................................................128
6.4 Parameter inference.........................................................................................................132
6.5 Summary...........................................................................................................................134
Chapter 7 Log-linear models................................................................................................137
7.1 Coding of variables and notation in log-linear models..............................................138
7.2 Log-linear models for two-way contingency tables....................................................140
7.3 Log-linear models for three-way contingency tables..................................................143
7.4 Inference for log-linear models: model fit.....................................................................154
7.5 Log-linear models for higher tables...............................................................................156
7.6 Computer output: fitting log-linear models..................................................................162
7.7 Complete example............................................................................................................169
7.8 Summary...........................................................................................................................177
Chapter 8 Logistic regression with continuous predictors............................................181
8.1 The logistic regression model.........................................................................................182
8.2 Parameter interpretation.................................................................................................184
8.3 Inference.............................................................................................................................188
8.4 Model fit, residuals, and diagnostics of fit....................................................................194
8.5 Complete example and computing................................................................................198
8.6 Summary...........................................................................................................................210
Chapter 9 Logistic regression with categorical predictors.............................................215
9.1 Coding categorical predictors.........................................................................................215
9.2 Parameter interpretation.................................................................................................218
9.3 Inferential procedures......................................................................................................219
9.4 Model testing.....................................................................................................................220
9.5 Interactions........................................................................................................................221
9.6 The relationship between logistic regression and log-linear models.......................223
9.7 Computing.........................................................................................................................226
9.8 Complete example of logistic regression using both categorical
and continuous predictors..............................................................................................235
9.9 Summary...........................................................................................................................239
Chapter 10 Logistic regression for multicategory outcomes............................................243
10.1 The multicategory logistic regression model...............................................................243
10.2 Parameter testing and interpretation............................................................................249
Contents ix
10.3 Multicategory logistic regression with ordinal outcome variables...........................250
10.4 Computing and complete example using a nominal outcome variable...................253
10.5 Computing and complete example using an ordinal outcome variable..................262
10.6 Summary...........................................................................................................................272
References....................................................................................................................................275
Appendix......................................................................................................................................277
Index.............................................................................................................................................279