An Introduction to Categorical Data Analysis

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Praise for the First Edition

"This is a superb text from which to teach categorical data analysis, at a variety of levels. . . [t]his book can be very highly recommended."

— Short Book Reviews

"Of great interest to potential readers is the variety of fields that are represented in the examples: health care, financial, government, product marketing, and sports, to name a few."

— Journal of Quality Technology

"Alan Agresti has written another brilliant account of the analysis of categorical data."

— The Statistician

The use of statistical methods for categorical data is ever increasing in today's world. An Introduction to Categorical Data Analysis, Second Edition provides an applied introduction to the most important methods for analyzing categorical data. This new edition summarizes methods that have long played a prominent role in data analysis, such as chi-squared tests, and also places special emphasis on logistic regression and other modeling techniques for univariate and correlated multivariate categorical responses.

This Second Edition features: Two new chapters on the methods for clustered data, with an emphasis on generalized estimating equations (GEE) and random effects models A unified perspective based on generalized linear models An emphasis on logistic regression modeling An appendix that demonstrates the use of SAS® for all methods An entertaining historical perspective on the development of the methods Specialized methods for ordinal data, small samples, multicategory data, and matched pairs More than 100 analyses of real data sets and nearly 300 exercises

Written in an applied, nontechnical style, the book illustratesmethods using a wide variety of real data, including medical clinical trials, drug use by teenagers, basketball shooting, horseshoe crab mating, environmental opinions, correlates of happiness, and much more.

An Introduction to Categorical Data Analysis, Second Edition is an invaluable tool for social, behavioral, and biomedical scientists, as well as researchers in public health, marketing, education, biological and agricultural sciences, and industrial quality control.

Product Details

Preface to the Second Edition xv 1. Introduction 1 1.1 Categorical Response Data 1 1.2 Probability Distributions for Categorical Data 3 1.3 Statistical Inference for a Proportion 6 1.4 More on Statistical Inference for Discrete Data 11 Problems 16 2. Contingency Tables 21 2.1 Probability Structure for Contingency Tables 21 2.2 Comparing Proportions in Two-by-Two Tables 25 2.3 The Odds Ratio 28 2.4 Chi-Squared Tests of Independence 34 2.5 Testing Independence for Ordinal Data 41 2.6 Exact Inference for Small Samples 45 2.7 Association in Three-Way Tables 49 Problems 55 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 Count Data 74 3.4 Statistical Inference and Model Checking 84 3.5 Fitting Generalized Linear Models 88 Problems 90 4. Logistic Regression 99 4.1 Interpreting the Logistic Regression Model 99 4.2 Inference for Logistic Regression 106 4.3 Logistic Regression with Categorical Predictors 110 4.4 Multiple Logistic Regression 115 4.5 Summarizing Effects in Logistic Regression 120 Problems 121 5. Building and Applying Logistic Regression Models 137 5.1 Strategies in Model Selection 137 5.2 Model Checking 144 5.3 Effects of Sparse Data 152 5.4 Conditional Logistic Regression and Exact Inference 157 5.5 Sample Size and Power for Logistic Regression 160 Problems 163 6. Multicategory Logit Models 173 6.1 Logit Models for Nominal Responses 173 6.2 Cumulative Logit Models for Ordinal Responses 180 6.3 Paired-Category Ordinal Logits 189 6.4 Tests of Conditional Independence 193 Problems 196 7. Loglinear Models for Contingency Tables 204 7.1 Loglinear Models for Two-Way and Three-Way Tables 204 7.2 Inference for Loglinear Models 212 7.3 The Loglinear-Logistic Connection 219 7.4 Independence Graphs and Collapsibility 223 7.5 Modeling Ordinal Associations 228 Problems 232 8. Models for Matched Pairs 244 8.1 Comparing Dependent Proportions 245 8.2 Logistic Regression for Matched Pairs 247 8.3 Comparing Margins of Square Contingency Tables 252 8.4 Symmetry and Quasi-Symmetry Models for Square Tables 256 8.5 Analyzing Rater Agreement 260 8.6 Bradley-Terry Model for Paired Preferences 264 Problems 266 9. Modeling Correlated Clustered Responses 276 9.1 Marginal Models Versus Conditional Models 277 9.2 Marginal Modeling: The GEE Approach 279 9.3 Extending GEE: Multinomial Responses 285 9.4 Transitional Modeling Given the Past 288 Problems 290 10. Random Effects: Generalized Linear Mixed Models 297 10.1 Random Effects Modeling of Clustered Categorical Data 297 10.2 Examples of Random Effects Models for Binary Data 302 10.3 Extensions to Multinomial Responses or Multiple Random Effect Terms 310 10.4 Multilevel (Hierarchical) Models 313 10.5 Model Fitting and Inference for GLMMS 316 Problems 318 11. A Historical Tour of Categorical Data Analysis 325 11.1 The Pearson-Yule Association Controversy 325 11.2 R. A. Fisher's Contributions 326 11.3 Logistic Regression 328 11.4 Multiway Contingency Tables and Loglinear Models 329 11.5 Final Comments 331 Appendix A: Software for Categorical Data Analysis 332 Appendix B: Chi-Squared Distribution Values 343 Bibliography 344 Index of Examples 346 Subject Index 350 Brief Solutions to Some Odd-Numbered Problems 357

ALAN AGRESTI, PhD, is Distinguished Professor Emeritus in the Department of Statistics at the University of Florida. He has presented short courses on categorical data methods in thirty countries. Dr. Agresti was named "Statistician of the Year" by the Chicago chapter of the American Statistical Association in 2003. He is the author of two advanced texts, including the bestselling Categorical Data Analysis (Wiley) and is also the coauthor of Statistics: The Art and Science of Learning from Data and Statistical Methods for the Social Sciences.

"Yes, I fully recommend the text as a basis for introductory course, for students, as well as non-specialists in statistics. The wealth of examples provided in the text is, from my point of view, a rich source of motivating ones own studies and work." (Biometrical Journal, Dec 2008) "This text does a good job of achieving its state goal, and we enthusiastically recommend it." (Journal of the American Statistical Association Sept 2008) "This book is very well-written and it is obvious that the author knows the subject inside out." (Journal of Applied Statistics, April 2008) "Provides an applied introduction to the most important methods for analyzing categorical data, such as chi-squared tests and logical regression." (Statistica 2008) "This is an introductory book and as such it is marvelous...essential for a novice..." (MAA Reviews, June 26, 2007)

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