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An Introduction to Categorical Data Analysis
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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