An Introduction to Categorical Data Analysis

Chapter 1: Introduction

• • 1.1 Categorical Response Data
• • 1.2 Probability Distributions for Categorical Data
• • 1.3 Statistical Inference for a Proportion
• • 1.4 Statistical Inference for Discrete Data
• • 1.5 Bayesian Inference for Proportions *
• • 1.6 Using R Software for Statistical Inference about Proportions *
• • Exercises

Chapter 2: Analyzing Contingency Tables

• • 2.1 Probability Structure for Contingency Tables
• • 2.2 Comparing Proportions in 2 × 2 Contingency Tables
• • 2.3 The Odds Ratio
• • 2.4 Chi-Squared Tests of Independence
• • 2.5 Testing Independence for Ordinal Variables
• • 2.6 Exact Frequentist and Bayesian Inference *
• • 2.7 Association in Three-Way Tables
• • Exercises

Chapter 3: Generalized Linear Models

• • 3.1 Components of a Generalized Linear Model
• • 3.2 Generalized Linear Models for Binary Data
• • 3.3 Generalized Linear Models for Counts and Rates
• • 3.4 Statistical Inference and Model Checking
• • 3.5 Fitting Generalized Linear Models
• • Exercises

Chapter 4: Logistic Regression

• • 4.1 The Logistic Regression Model
• • 4.2 Statistical Inference for Logistic Regression
• • 4.3 Logistic Regression with Categorical Predictors
• • 4.4 Multiple Logistic Regression
• • 4.5 Summarizing Effects in Logistic Regression
• • 4.6 Summarizing Predictive Power: Classification Tables, ROC Curves, and Multiple Correlation
• • Exercises

Chapter 5: Building and Applying Logistic Regression Models

• • 5.1 Strategies in Model Selection
• • 5.2 Model Checking
• • 5.3 Infinite Estimates in Logistic Regression
• • 5.4 Bayesian Inference, Penalized Likelihood, and Conditional Likelihood for Logistic Regression *
• • 5.5 Alternative Link Functions: Linear Probability and Probit Models *
• • 5.6 Sample Size and Power for Logistic Regression *
• • Exercises

Chapter 6: Multicategory Logit Models

• • 6.1 Baseline-Category Logit Models for Nominal Responses
• • 6.2 Cumulative Logit Models for Ordinal Responses
• • 6.3 Cumulative Link Models: Model Checking and Extensions *
• • 6.4 Paired-Category Logit Modeling of Ordinal Responses *
• • Exercises

Chapter 7: Loglinear Models for Contingency Tables and Counts

• • 7.1 Loglinear Models for Counts in Contingency Tables
• • 7.2 Statistical Inference for Loglinear Models
• • 7.3 The Loglinear – Logistic Model Connection
• • 7.4 Independence Graphs and Collapsibility
• • 7.5 Modeling Ordinal Associations in Contingency Tables
• • 7.6 Loglinear Modeling of Count Response Variables *
• • Exercises

Chapter 8: Models for Matched Pairs

• • 8.1 Comparing Dependent Proportions for Binary Matched Pairs
• • 8.2 Marginal Models and Subject-Specific Models for Matched Pairs
• • 8.3 Comparing Proportions for Nominal Matched-Pairs Responses
• • 8.4 Comparing Proportions for Ordinal Matched-Pairs Responses
• • 8.5 Analyzing Rater Agreement *
• • 8.6 Bradley–Terry Model for Paired Preferences *
• • Exercises

Chapter 9: Marginal Modeling of Correlated, Clustered Responses

• • 9.1 Marginal Models Versus Subject-Specific Models
• • 9.2 Marginal Modeling: The Generalized Estimating Equations (GEE) Approach
• • 9.3 Marginal Modeling for Clustered Multinomial Responses
• • 9.4 Transitional Modeling, Given the Past
• • 9.5 Dealing with Missing Data *
• • Exercises

Chapter 10: Random Effects: Generalized Linear Mixed Models

• • 10.1 Random Effects Modeling of Clustered Categorical Data
• • 10.2 Examples: Random Effects Models for Binary Data
• • 10.3 Extensions to Multinomial Responses and Multiple Random Effect Terms
• • 10.4 Multilevel (Hierarchical) Models
• • 10.5 Latent Class Models *
• • Exercises

Chapter 11: Classification and Smoothing *

• • 11.1 Classification: Linear Discriminant Analysis
• • 11.2 Classification: Tree-Based Prediction
• • 11.3 Cluster Analysis for Categorical Responses
• • 11.4 Smoothing: Generalized Additive Models
• • 11.5 Regularization for High-Dimensional Categorical Data (Large p)
• • Exercises

Chapter 12: A Historical Tour of Categorical Data Analysis *

Chapter Appendix: Software for Categorical Data Analysis

• • A.1 R for Categorical Data Analysis
• • A.2 SAS for Categorical Data Analysis
• • A.3 Stata for Categorical Data Analysis
• • A.4 SPSS for Categorical Data Analysis