| Preface | |
| 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 | 9 |
| 1.4 | Statistical Inference for Binomial Parameters | 14 |
| 1.5 | Statistical Inference for Multinomial Parameters | 21 |
| 2 | Describing Contingency Tables | 36 |
| 2.1 | Probability Structure for 'Contingency Tables | 36 |
| 2.2 | Comparing Two Proportions | 43 |
| 2.3 | Partial Association in Stratified 2 X 2 Tables | 47 |
| 2.4 | Extensions for I X J Tables | 54 |
| 3 | Inference for Contingency Tables | 70 |
| 3.1 | Confidence Intervals for Association Parameters | 70 |
| 3.2 | Testing Independence in Two-Way Contingency Tables | 78 |
| 3.3 | Following-Up Chi-Squared Tests | 80 |
| 3.4 | Two-Way Tables with Ordered Classifications | 86 |
| 3.5 | Small-Sample Tests of Independence | 91 |
| 3.6 | Small-Sample Confidence Intervals for 2 X 2 Tables | 98 |
| 3.7 | Extensions for Multiway Tables and Nontabulated Responses | 101 |
| 4 | Introduction to Generalized Linear Models | 115 |
| 4.1 | Generalized Linear Model | 116 |
| 4.2 | Generalized Linear Models for Binary Data | 120 |
| 4.3 | Generalized Linear Models for Counts | 125 |
| 4.4 | Moments and Likelihood for Generalized Linear Models | 132 |
| 4.5 | Inference for Generalized Linear Models | 139 |
| 4.6 | Fitting Generalized Linear Models | 143 |
| 4.7 | Quasi-likelihood and Generalized Linear Models | 149 |
| 4.8 | Generalized Additive Models | 153 |
| 5 | Logistic Regression | 165 |
| 5.1 | Interpreting Parameters in Logistic Regression | 166 |
| 5.2 | Inference for Logistic Regression | 172 |
| 5.3 | Logit Models with Categorical Predictors | 177 |
| 5.4 | Multiple Logistic Regression | 182 |
| 5.5 | Fitting Logistic Regression Models | 192 |
| 6 | Building and Applying Logistic Regression Models | 211 |
| 6.1 | Strategies in Model Selection | 211 |
| 6.2 | Logistic Regression Diagnostics | 219 |
| 6.3 | Inference About Conditional Associations in 2 X 2 X K Tables | 230 |
| 6.4 | Using Models to Improve Inferential Power | 236 |
| 6.5 | Sample Size and Power Considerations | 240 |
| 6.6 | Probit and Complementary Log-Log Models | 245 |
| 6.7 | Conditional Logistic Regression and Exact Distributions | 250 |
| 7 | Logit Models for Multinomial Responses | 267 |
| 7.1 | Nominal Responses: Baseline-Category Logit Models | 267 |
| 7.2 | Ordinal Responses: Cumulative Logit Models | 274 |
| 7.3 | Ordinal Responses: Cumulative Link Models | 282 |
| 7.4 | Alternative Models for Ordinal Responses | 286 |
| 7.5 | Testing Conditional Independence in I X J X K Tables | 293 |
| 7.6 | Discrete-Choice Multinomial Logit Models | 298 |
| 8 | Loglinear Models for Contingency Tables | 314 |
| 8.1 | Loglinear Models for Two-Way Tables | 314 |
| 8.2 | Loglinear Models for Independence and Interaction in Three-Way Tables | 318 |
| 8.3 | Inference for Loglinear Models | 324 |
| 8.4 | Loglinear Models for Higher Dimensions | 326 |
| 8.5 | The Loglinear-Logit Model Connection | 330 |
| 8.6 | Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions | 333 |
| 8.7 | Loglinear Model Fitting: Iterative Methods and their Application | 342 |
| 9 | Building and Extending Loglinear/Logit Models | 357 |
| 9.1 | Association Graphs and Collapsibility | 357 |
| 9.2 | Model Selection and Comparison | 360 |
| 9.3 | Diagnostics for Checking Models | 366 |
| 9.4 | Modeling Ordinal Associations | 367 |
| 9.5 | Association Models | 373 |
| 9.6 | Association Models, Correlation Models, and Correspondence Analysis | 379 |
| 9.7 | Poisson Regression for Rates | 385 |
| 9.8 | Empty Cells and Sparseness in Modeling Contingency Tables | 391 |
| 10 | Models for Matched Pairs | 409 |
| 10.1 | Comparing Dependent Proportions | 410 |
| 10.2 | Conditional Logistic Regression for Binary Matched Pairs | 414 |
| 10.3 | Marginal Models for Square Contingency Tables | 420 |
| 10.4 | Symmetry, Quasi-symmetry, and Quasi-independence | 423 |
| 10.5 | Measuring Agreement Between Observers | 431 |
| 10.6 | Bradley-Terry Model for Paired Preferences | 436 |
| 10.7 | Marginal Models and Quasi-symmetry Models for Matched Sets | 439 |
| 11 | Analyzing Repeated Categorical Response Data | 455 |
| 11.1 | Comparing Marginal Distributions: Multiple Responses | 456 |
| 11.2 | Marginal Modeling: Maximum Likelihood Approach | 459 |
| 11.3 | Marginal Modeling: Generalized Estimating Equations Approach | 466 |
| 11.4 | Quasi-likelihood and Its GEE Multivariate Extension: Details | 470 |
| 11.5 | Markov Chains: Transitional Modeling | 476 |
| 12 | Random Effects: Generalized Linear Mixed Models for Categorical Responses | 491 |
| 12.1 | Random Effects Modeling of Clustered Categorical Data | 492 |
| 12.2 | Binary Responses: Logistic-Normal Model | 496 |
| 12.3 | Examples of Random Effects Models for Binary Data | 502 |
| 12.4 | Random Effects Models for Multinomial Data | 513 |
| 12.5 | Multivariate Random Effects Models for Binary Data | 516 |
| 12.6 | GLMM Fitting, Inference, and Prediction | 520 |
| 13 | Other Mixture Models for Categorical Data | 538 |
| 13.1 | Latent Class Models | 538 |
| 13.2 | Nonparametric Random Effects Models | 545 |
| 13.3 | Beta-Binomial Models | 553 |
| 13.4 | Negative Binomial Regression | 559 |
| 13.5 | Poisson Regression with Random Effects | 563 |
| 14 | Asymptotic Theory for Parametric Models | 576 |
| 14.1 | Delta Method | 577 |
| 14.2 | Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities | 582 |
| 14.3 | Asymptotic Distributions of Residuals and Goodness-of-Fit Statistics | 587 |
| 14.4 | Asymptotic Distributions for Logit/Loglinear Models | 592 |
| 15 | Alternative Estimation Theory for Parametric Models | 600 |
| 15.1 | Weighted Least Squares for Categorical Data | 600 |
| 15.2 | Bayesian Inference for Categorical Data | 604 |
| 15.3 | Other Methods of Estimation | 611 |
| 16 | Historical Tour of Categorical Data Analysis | 619 |
| 16.1 | Pearson-Yule Association Controversy | 619 |
| 16.2 | R. A. Fisher's Contributions | 622 |
| 16.3 | Logistic Regression | 624 |
| 16.4 | Multiway Contingency Tables and Loglinear Models | 625 |
| 16.5 | Recent (and Future?) Developments | 629 |
| App. A | Using Computer Software to Analyze Categorical Data | 632 |
| App. B | Chi-Squared Distribution Values | 654 |
| References | 655 |
| Examples Index | 689 |
| Author Index | 693 |
| Subject Index | 701 |