Categorical Data Analysis, Third Edition

A classic in its own right, this book continues to provide an introduction to modern generalized linear models for categorical variables. The text emphasizes methods that are most commonly used in practical application, such as classical inferences for two- and three-way contingency tables, logistic regression, loglinear models, models for multinomial (nominal and ordinal) responses, and methods for repeated measurement and other forms of clustered, correlated response data. Chapter headings remain essentially with the exception of a new one on Bayesian inference for parametric models. Other major changes include an expansion of clustered data, new research on analysis of data sets with robust variables, extensive discussions of ordinal data, more on interpretation, and additional exercises throughout the book. R and SAS are now showcased as the software of choice. An author web site with solutions, commentaries, software programs, and data sets is available.

ALAN AGRESTI 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. He is the author of five other books, including An Introduction to Categorical Data Analysis, Second Edition and Analysis of Ordinal Categorical Data, Second Edition, both published by Wiley.

Preface


1. Introduction: Distributions and Inference for Categorical Data 1


1.1 Categorical Response Data, 1


1.2 Distributions for Categorical Data


1.3 Statistical Inference for Categorical Data


1.4 Statistical Inference for Binomial Parameters


1.5 Statistical Inference for Multinomial Parameters


1.6 Bayesian Inference for Binomial and Multinomial Parameters


Notes


Exercises


2. Describing Contingency Tables


2.1 Probability Structure for Contingency Tables


2.2 Comparing Two Proportions


2.3 Conditional Association in Stratified 2x2 Tables


2.4 Measuring Association in I x J Tables


Notes


Exercises


3. Inference for Two-Way Contingency Tables


3.1 Confidence Intervals for Association Parameters


3.2 Testing Independence in Two-Way Contingency Tables


3.3 Following-Up Chi-Squared Tests


3.4 Two-Way Tables with Ordered Classifications


3.5 Small-Sample Inference for Contingency Tables


3.6 Bayesian Inference for Two-Way Contingency Tables


3.7 Extensions for Multiway Tables and Nontabulated Responses


Notes


Exercises


4. Introduction to Generalized Linear Models


4.1 The Generalized Linear Model


4.2 Generalized Linear Models for Binary Data


4.3 Generalized Linear Models for Counts and Rates


4.4 Moments and Likelihood for Generalized Linear Models


4.5 Inference and Model Checking for Generalized Linear Models


4.6 Fitting Generalized Linear Models


4.7 Quasi-Likelihood and Generalized Linear Models


Notes


Exercises


5. Logistic Regression


5.1 Interpreting Parameters in Logistic Regression


5.2 Inference for Logistic Regression


5.3 Logistic Models with Categorical Predictors


5.4 Multiple Logistic Regression


5.5 Fitting Logistic Regression Models


Notes


Exercises


6. Building, Checking, and Applying Logistic Regression Models


6.1 Strategies in Model Selection


6.2 Logistic Regression Diagnostics


6.3 Summarizing the Predictive Power of a Model


6.3 Mantel-Haenszel and Related Methods for Multiple 2x2 Tables


6.4 Detecting and Dealing with Infinite Estimates


6.5 Sample Size and Power Considerations


Notes


Exercises


7. Alternative Modeling of Binary Response Data


7.1 Probit and Complementary Log-Log Models


7.2 Bayesian Inference for Binary Regression


7.3 Conditional Logistic Regression


7.4 Smoothing: Kernels, Penalized Likelihood, Generalized Additive Models


7.5 Issues in Analyzing High-Dimensional Categorical Data


Notes


Exercises


8. Models for Multinomial Responses


8.1 Nominal Responses: Baseline-Category Logit Models


8.2 Ordinal Responses: Cumulative Logit Models


8.3 Ordinal Responses: Alternative Models


8.4 Testing Conditional Independence in I ? J ? K Tables


8.5 Discrete-Choice Models


8.6 Bayesian Modeling of Multinomial Responses


Notes


Exercises


9. Loglinear Models for Contingency Tables


9.1 Loglinear Models for Two-Way Tables


9.2 Loglinear Models for Independence and Interaction in Three-Way Tables


9.3 Inference for Loglinear Models


9.4 Loglinear Models for Higher Dimensions


9.5 The Loglinear?Logistic Model Connection


9.6 Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions


9.7 Loglinear Model Fitting: Iterative Methods and their Application


Notes


Exercises


10. Building and Extending Loglinear Models


10.1 Conditional Independence Graphs and Collapsibility


10.2 Model Selection and Comparison


10.3 Residuals for Detecting Cell-Specific Lack of Fit


10.4 Modeling Ordinal Associations


10.5 Generalized Loglinear and Association Models, Correlation Models, and Correspondence Analysis


10.6 Empty Cells and Sparseness in Modeling Contingency Tables


10.7 Bayesian Loglinear Modeling


Notes


Exercises


11. Models for Matched Pairs


11.1 Comparing Dependent Proportions


11.2 Conditional Logistic Regression for Binary Matched Pairs


11.3 Marginal Models for Square Contingency Tables


11.4 Symmetry, Quasi-symmetry, and Quasi-independence


11.5 Measuring Agreement Between Observers


11.6 Bradley-Terry Model for Paired Preferences


11.7 Marginal Models and Quasi-symmetry Models for Matched Sets


Notes


Exercises


12. Clustered Categorical Data: Marginal and Transitional Models


12.1 Marginal Modeling: Maximum Likelihood Approach


12.2 Marginal Modeling: Generalized Estimating Equations Approach


12.3 Quasi-likelihood and Its GEE Multivariate Extension: Details


12.4 Transitional Models: Markov Chain and Time Series Models


Notes


Exercises


13. Clustered Categorical Data: Random Effects Models


13.1 Random Effects Modeling of Clustered Categorical Data


13.2 Binary Responses: The Logistic-Normal Model


13.3 Examples of Random Effects Models for Binary Data


13.4 Random Effects Models for Multinomial Data


13.5 Multilevel Models


13.6 GLMM Fitting, Inference, and Prediction


13.7 Bayesian Multivariate Categorical Modeling


Notes


Exercises


14. Other Mixture Models for Discrete Data


14.1 Latent Class Models


14.2 Nonparametric Random Effects Models


14.3 Beta-Binomial Models


14.4 Negative Binomial Regression


14.5 Poisson Regression with Random Effects


Notes


Exercises


15. Non-Model-Based Classification and Clustering


15.2 Classification: Linear Discriminant Analysis


15.3 Classification: Tree-Structured Prediction


15.4 Cluster Analysis for Categorical Data


Notes


Exercises


16. Large- and Small-Sample Theory for Parametric Models


16.1 Delta Method


16.2 Asymptotic Distributions of Estimators of Model Parameters and Cell


Probabilities


16.3 Asymptotic Distributions of Residuals and Goodness-of-Fit Statistics


16.4 Asymptotic Distributions for Logit/Loglinear Models


16.5 Small-Sample Significance Tests for Contingency Tables


16.6 Small-Sample Confidence Intervals for Categorical Data


16.7 Alternative Estimation Theory for Parametric Models


Notes


Exercises


17. Historical Tour of Categorical Data Analysis


17.1 Pearson-Yule Association Controversy


17.2 R. A. Fisher’s Contributions


17.3 Logistic Regression


17.4 Multiway Contingency Tables and Loglinear Models


17.5 Bayesian Methods for Categorical Data


17.6 A Look Forward, and Backward


Appendix A. Statistical Software for Categorical Data Analysis


Appendix B. Chi-Squared Distribution Values


References


Author Index


Example Index


Subject Index