Categorical Data Analysis

Preface xiii 1 Introduction: Distributions and Inference for Categorical Data 1 1.1 Categorical Response Data, 1 1.2 Distributions for Categorical Data, 5 1.3 Statistical Inference for Categorical Data, 8 1.4 Statistical Inference for Binomial Parameters, 13 1.5 Statistical Inference for Multinomial Parameters, 17 1.6 Bayesian Inference for Binomial and Multinomial Parameters, 22 Notes, 27 Exercises, 28 2 Describing Contingency Tables 37 2.1 Probability Structure for Contingency Tables, 37 2.2 Comparing Two Proportions, 43 2.3 Conditional Association in Stratified 2 × 2 Tables, 47 2.4 Measuring Association in I × J Tables, 54 Notes, 60 Exercises, 60 3 Inference for Two-Way Contingency Tables 69 3.1 Confidence Intervals for Association Parameters, 69 3.2 Testing Independence in Two-way Contingency Tables, 75 3.3 Following-up Chi-Squared Tests, 80 3.4 Two-Way Tables with Ordered Classifications, 86 3.5 Small-Sample Inference for Contingency Tables, 90 3.6 Bayesian Inference for Two-way Contingency Tables, 96 3.7 Extensions for Multiway Tables and Nontabulated Responses, 100 Notes, 101 Exercises, 103 4 Introduction to Generalized Linear Models 113 4.1 The Generalized Linear Model, 113 4.2 Generalized Linear Models for Binary Data, 117 4.3 Generalized Linear Models for Counts and Rates, 122 4.4 Moments and Likelihood for Generalized Linear Models, 130 4.5 Inference and Model Checking for Generalized Linear Models, 136 4.6 Fitting Generalized Linear Models, 143 4.7 Quasi-Likelihood and Generalized Linear Models, 149 Notes, 152 Exercises, 153 5 Logistic Regression 163 5.1 Interpreting Parameters in Logistic Regression, 163 5.2 Inference for Logistic Regression, 169 5.3 Logistic Models with Categorical Predictors, 175 5.4 Multiple Logistic Regression, 182 5.5 Fitting Logistic Regression Models, 192 Notes, 195 Exercises, 196 6 Building, Checking, and Applying Logistic Regression Models 207 6.1 Strategies in Model Selection, 207 6.2 Logistic Regression Diagnostics, 215 6.3 Summarizing the Predictive Power of a Model, 221 6.4 Mantel-Haenszel and Related Methods for Multiple 2 × 2 Tables, 225 6.5 Detecting and Dealing with Infinite Estimates, 233 6.6 Sample Size and Power Considerations, 237 Notes, 241 Exercises, 243 7 Alternative Modeling of Binary Response Data 251 7.1 Probit and Complementary Log-log Models, 251 7.2 Bayesian Inference for Binary Regression, 257 7.3 Conditional Logistic Regression, 265 7.4 Smoothing: Kernels, Penalized Likelihood, Generalized Additive Models, 270 7.5 Issues in Analyzing High-Dimensional Categorical Data, 278 Notes, 285 Exercises, 287 8 Models for Multinomial Responses 293 8.1 Nominal Responses: Baseline-Category Logit Models, 293 8.2 Ordinal Responses: Cumulative Logit Models, 301 8.3 Ordinal Responses: Alternative Models, 308 8.4 Testing Conditional Independence in I × J × K Tables, 314 8.5 Discrete-Choice Models, 320 8.6 Bayesian Modeling of Multinomial Responses, 323 Notes, 326 Exercises, 329 9 Loglinear Models for Contingency Tables 339 9.1 Loglinear Models for Two-way Tables, 339 9.2 Loglinear Models for Independence and Interaction in Three-way Tables, 342 9.3 Inference for Loglinear Models, 348 9.4 Loglinear Models for Higher Dimensions, 350 9.5 Loglinear--Logistic Model Connection, 353 9.6 Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions, 356 9.7 Loglinear Model Fitting: Iterative Methods and Their Application, 364 Notes, 368 Exercises, 369 10 Building and Extending Loglinear Models 377 10.1 Conditional Independence Graphs and Collapsibility, 377 10.2 Model Selection and Comparison, 380 10.3 Residuals for Detecting Cell-Specific Lack of Fit, 385 10.4 Modeling Ordinal Associations, 386 10.5 Generalized Loglinear and Association Models, Correlation Models, and Correspondence Analysis, 393 10.6 Empty Cells and Sparseness in Modeling Contingency Tables, 398 10.7 Bayesian Loglinear Modeling, 401 Notes, 404 Exercises, 407 11 Models for Matched Pairs 413 11.1 Comparing Dependent Proportions, 414 11.2 Conditional Logistic Regression for Binary Matched Pairs, 418 11.3 Marginal Models for Square Contingency Tables, 424 11.4 Symmetry, Quasi-Symmetry, and Quasi-Independence, 426 11.5 Measuring Agreement Between Observers, 432 11.6 Bradley-Terry Model for Paired Preferences, 436 11.7 Marginal Models and Quasi-Symmetry Models for Matched Sets, 439 Notes, 443 Exercises, 445 12 Clustered Categorical Data: Marginal and Transitional Models 455 12.1 Marginal Modeling: Maximum Likelihood Approach, 456 12.2 Marginal Modeling: Generalized Estimating Equations (GEEs) Approach, 462 12.3 Quasi-Likelihood and Its GEE Multivariate Extension: Details, 465 12.4 Transitional Models: Markov Chain and Time Series Models, 473 Notes, 478 Exercises, 479 13 Clustered Categorical Data: Random Effects Models 489 13.1 Random Effects Modeling of Clustered Categorical Data, 489 13.2 Binary Responses: Logistic-Normal Model, 494 13.3 Examples of Random Effects Models for Binary Data, 498 13.4 Random Effects Models for Multinomial Data, 511 13.5 Multilevel Modeling, 515 13.6 GLMM Fitting, Inference, and Prediction, 519 13.7 Bayesian Multivariate Categorical Modeling, 523 Notes, 525 Exercises, 527 14 Other Mixture Models for Discrete Data 535 14.1 Latent Class Models, 535 14.2 Nonparametric Random Effects Models, 542 14.3 Beta-Binomial Models, 548 14.4 Negative Binomial Regression, 552 14.5 Poisson Regression with Random Effects, 555 Notes, 557 Exercises, 558 15 Non-Model-Based Classification and Clustering 565 15.1 Classification: Linear Discriminant Analysis, 565 15.2 Classification: Tree-Structured Prediction, 570 15.3 Cluster Analysis for Categorical Data, 576 Notes, 581 Exercises, 582 16 Large- and Small-Sample Theory for Multinomial Models 587 16.1 Delta Method, 587 16.2 Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities, 592 16.3 Asymptotic Distributions of Residuals and Goodness-of-fit Statistics, 594 16.4 Asymptotic Distributions for Logit/Loglinear Models, 599 16.5 Small-Sample Significance Tests for Contingency Tables, 601 16.6 Small-Sample Confidence Intervals for Categorical Data, 603 16.7 Alternative Estimation Theory for Parametric Models, 610 Notes, 615 Exercises, 616 17 Historical Tour of Categorical Data Analysis 623 17.1 Pearson-Yule Association Controversy, 623 17.2 R. A. Fisher's Contributions, 625 17.3 Logistic Regression, 627 17.4 Multiway Contingency Tables and Loglinear Models, 629 17.5 Bayesian Methods for Categorical Data, 633 17.6 A Look Forward, and Backward, 634 Appendix A Statistical Software for Categorical Data Analysis 637 Appendix B Chi-Squared Distribution Values 641 References 643 Author Index 689 Example Index 701 Subject Index 705 Appendix C Software Details for Text Examples (text website)