Introduction to Categorical Data Analysis

ALAN AGRESTI is Distinguished Professor Emeritus at the University of Florida. He has presented short courses on categorical data methods in 35 countries. He is the author of seven books, including the bestselling Categorical Data Analysis (Wiley), Foundations of Linear and Generalized Linear Models (Wiley), Statistics: The Art and Science of Learning from Data (Pearson), and Statistical Methods for the Social Sciences (Pearson).

• Preface ixAbout the Companion Website xiii1 Introduction 11.1 Categorical Response Data 11.2 Probability Distributions for Categorical Data 31.3 Statistical Inference for a Proportion 51.4 Statistical Inference for Discrete Data 101.5 Bayesian Inference for Proportions * 131.6 Using R Software for Statistical Inference about Proportions * 17Exercises 212 Analyzing Contingency Tables 252.1 Probability Structure for Contingency Tables 262.2 Comparing Proportions in 2 × 2 Contingency Tables 292.3 The Odds Ratio 312.4 Chi-Squared Tests of Independence 362.5 Testing Independence for Ordinal Variables 422.6 Exact Frequentist and Bayesian Inference * 462.7 Association in Three-Way Tables 52Exercises 563 Generalized Linear Models 653.1 Components of a Generalized Linear Model 663.2 Generalized Linear Models for Binary Data 683.3 Generalized Linear Models for Counts and Rates 723.4 Statistical Inference and Model Checking 763.5 Fitting Generalized Linear Models 82Exercises 844 Logistic Regression 894.1 The Logistic Regression Model 894.2 Statistical Inference for Logistic Regression 944.3 Logistic Regression with Categorical Predictors 984.4 Multiple Logistic Regression 1024.5 Summarizing Effects in Logistic Regression 1074.6 Summarizing Predictive Power: Classification Tables, ROC Curves, and Multiple Correlation 110Exercises 1135 Building and Applying Logistic Regression Models 1235.1 Strategies in Model Selection 1235.2 Model Checking 1305.3 Infinite Estimates in Logistic Regression 1365.4 Bayesian Inference, Penalized Likelihood, and Conditional Likelihood for Logistic Regression * 1405.5 Alternative Link Functions: Linear Probability and Probit Models * 1455.6 Sample Size and Power for Logistic Regression * 150Exercises 1516 Multicategory Logit Models 1596.1 Baseline-Category Logit Models for Nominal Responses 1596.2 Cumulative Logit Models for Ordinal Responses 1676.3 Cumulative Link Models: Model Checking and Extensions * 1766.4 Paired-Category Logit Modeling of Ordinal Responses * 184Exercises 1877 Loglinear Models for Contingency Tables and Counts 1937.1 Loglinear Models for Counts in Contingency Tables 1947.2 Statistical Inference for Loglinear Models 2007.3 The Loglinear – Logistic Model Connection 2077.4 Independence Graphs and Collapsibility 2107.5 Modeling Ordinal Associations in Contingency Tables 2147.6 Loglinear Modeling of Count Response Variables * 217Exercises 2218 Models for Matched Pairs 2278.1 Comparing Dependent Proportions for Binary Matched Pairs 2288.2 Marginal Models and Subject-Specific Models for Matched Pairs 2308.3 Comparing Proportions for Nominal Matched-Pairs Responses 2358.4 Comparing Proportions for Ordinal Matched-Pairs Responses 2398.5 Analyzing Rater Agreement * 2438.6 Bradley–Terry Model for Paired Preferences * 247Exercises 2499 Marginal Modeling of Correlated, Clustered Responses 2539.1 Marginal Models Versus Subject-Specific Models 2549.2 Marginal Modeling: The Generalized Estimating Equations (GEE) Approach 2559.3 Marginal Modeling for Clustered Multinomial Responses 2609.4 Transitional Modeling, Given the Past 2639.5 Dealing with Missing Data * 266Exercises 26810 Random Effects: Generalized Linear Mixed Models 27310.1 Random Effects Modeling of Clustered Categorical Data 27310.2 Examples: Random Effects Models for Binary Data 27810.3 Extensions to Multinomial Responses and Multiple Random Effect Terms 28410.4 Multilevel (Hierarchical) Models 28810.5 Latent Class Models * 291Exercises 29511 Classification and Smoothing * 29911.1 Classification: Linear Discriminant Analysis 30011.2 Classification: Tree-Based Prediction 30211.3 Cluster Analysis for Categorical Responses 30611.4 Smoothing: Generalized Additive Models 31011.5 Regularization for High-Dimensional Categorical Data (Large p) 313Exercises 32112 A Historical Tour of Categorical Data Analysis * 325Appendix: Software for Categorical Data Analysis 331A.1 R for Categorical Data Analysis 331A.2 SAS for Categorical Data Analysis 332A.3 Stata for Categorical Data Analysis 342A.4 SPSS for Categorical Data Analysis 346Brief Solutions to Odd-Numbered Exercises 349Bibliography 363Examples Index 365Subject Index 369