Categorical Data Analysis Book

	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