Description
A valuable new edition of a standard reference
The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. An Introduction to Categorical Data Analysis, Third Edition summarizes these methods and shows readers how to use them using software. Readers will find a unified generalized linear models approach that connects logistic regression and loglinear models for discrete data with normal regression for continuous data.
Adding to the value in the new edition is:
• Illustrations of the use of R software to perform all the analyses in the book
• A new chapter on alternative methods for categorical data, including smoothing and regularization methods (such as the lasso), classification methods such as linear discriminant analysis and classification trees, and cluster analysis
• New sections in many chapters introducing the Bayesian approach for the methods of that chapter
• More than 70 analyses of data sets to illustrate application of the methods, and about 200 exercises, many containing other data sets
• An appendix showing how to use SAS, Stata, and SPSS, and an appendix with short solutions to most odd-numbered exercises
Written in an applied, nontechnical style, this book illustrates the methods using a wide variety of real data, including medical clinical trials, environmental questions, drug use by teenagers, horseshoe crab mating, basketball shooting, correlates of happiness, and much more.
An Introduction to Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and biostatisticians as well as methodologists in the social and behavioral sciences, medicine and public health, marketing, education, and the biological and agricultural sciences.
Table of Contents
Preface ix
About the Companion Website xiii
1 Introduction 1
1.1 Categorical Response Data 1
1.2 Probability Distributions for Categorical Data 3
1.3 Statistical Inference for a Proportion 5
1.4 Statistical Inference for Discrete Data 10
1.5 Bayesian Inference for Proportions * 13
1.6 Using R Software for Statistical Inference about Proportions * 17
Exercises 21
2 Analyzing Contingency Tables 25
2.1 Probability Structure for Contingency Tables 26
2.2 Comparing Proportions in 2 × 2 Contingency Tables 29
2.3 The Odds Ratio 31
2.4 Chi-Squared Tests of Independence 36
2.5 Testing Independence for Ordinal Variables 42
2.6 Exact Frequentist and Bayesian Inference * 46
2.7 Association in Three-Way Tables 52
Exercises 56
3 Generalized Linear Models 65
3.1 Components of a Generalized Linear Model 66
3.2 Generalized Linear Models for Binary Data 68
3.3 Generalized Linear Models for Counts and Rates 72
3.4 Statistical Inference and Model Checking 76
3.5 Fitting Generalized Linear Models 82
Exercises 84
4 Logistic Regression 89
4.1 The Logistic Regression Model 89
4.2 Statistical Inference for Logistic Regression 94
4.3 Logistic Regression with Categorical Predictors 98
4.4 Multiple Logistic Regression 102
4.5 Summarizing Effects in Logistic Regression 107
4.6 Summarizing Predictive Power: Classification Tables, ROC Curves, and Multiple Correlation 110
Exercises 113
5 Building and Applying Logistic Regression Models 123
5.1 Strategies in Model Selection 123
5.2 Model Checking 130
5.3 Infinite Estimates in Logistic Regression 136
5.4 Bayesian Inference, Penalized Likelihood, and Conditional Likelihood for Logistic Regression * 140
5.5 Alternative Link Functions: Linear Probability and Probit Models * 145
5.6 Sample Size and Power for Logistic Regression * 150
Exercises 151
6 Multicategory Logit Models 159
6.1 Baseline-Category Logit Models for Nominal Responses 159
6.2 Cumulative Logit Models for Ordinal Responses 167
6.3 Cumulative Link Models: Model Checking and Extensions * 176
6.4 Paired-Category Logit Modeling of Ordinal Responses * 184
Exercises 187
7 Loglinear Models for Contingency Tables and Counts 193
7.1 Loglinear Models for Counts in Contingency Tables 194
7.2 Statistical Inference for Loglinear Models 200
7.3 The Loglinear – Logistic Model Connection 207
7.4 Independence Graphs and Collapsibility 210
7.5 Modeling Ordinal Associations in Contingency Tables 214
7.6 Loglinear Modeling of Count Response Variables * 217
Exercises 221
8 Models for Matched Pairs 227
8.1 Comparing Dependent Proportions for Binary Matched Pairs 228
8.2 Marginal Models and Subject-Specific Models for Matched Pairs 230
8.3 Comparing Proportions for Nominal Matched-Pairs Responses 235
8.4 Comparing Proportions for Ordinal Matched-Pairs Responses 239
8.5 Analyzing Rater Agreement * 243
8.6 Bradley–Terry Model for Paired Preferences * 247
Exercises 249
9 Marginal Modeling of Correlated, Clustered Responses 253
9.1 Marginal Models Versus Subject-Specific Models 254
9.2 Marginal Modeling: The Generalized Estimating Equations (GEE) Approach 255
9.3 Marginal Modeling for Clustered Multinomial Responses 260
9.4 Transitional Modeling, Given the Past 263
9.5 Dealing with Missing Data * 266
Exercises 268
10 Random Effects: Generalized Linear Mixed Models 273
10.1 Random Effects Modeling of Clustered Categorical Data 273
10.2 Examples: Random Effects Models for Binary Data 278
10.3 Extensions to Multinomial Responses and Multiple Random Effect Terms 284
10.4 Multilevel (Hierarchical) Models 288
10.5 Latent Class Models * 291
Exercises 295
11 Classification and Smoothing * 299
11.1 Classification: Linear Discriminant Analysis 300
11.2 Classification: Tree-Based Prediction 302
11.3 Cluster Analysis for Categorical Responses 306
11.4 Smoothing: Generalized Additive Models 310
11.5 Regularization for High-Dimensional Categorical Data (Large p) 313
Exercises 321
12 A Historical Tour of Categorical Data Analysis * 325
Appendix: Software for Categorical Data Analysis 331
A.1 R for Categorical Data Analysis 331
A.2 SAS for Categorical Data Analysis 332
A.3 Stata for Categorical Data Analysis 342
A.4 SPSS for Categorical Data Analysis 346
Brief Solutions to Odd-Numbered Exercises 349
Bibliography 363
Examples Index 365
Subject Index 369
