Alan Agresti
Categorical Data Analysis (eBook, ePUB)
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Alan Agresti
Categorical Data Analysis (eBook, ePUB)
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Praise for the Second Edition
"A must-have book for anyone expecting to do research and/or applications in categorical data analysis." — Statistics in Medicine
"It is a total delight reading this book." — Pharmaceutical Research
"If you do any analysis of categorical data, this is an essential desktop reference." — Technometrics
The use of statistical methods for analyzing categorical data has increased dramatically, particularly in the biomedical, social sciences, and financial industries. Responding to new developments, this book offers a comprehensive treatment of the most…mehr
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Praise for the Second Edition
"A must-have book for anyone expecting to do research and/or applications in categorical data analysis."
—Statistics in Medicine
"It is a total delight reading this book."
—Pharmaceutical Research
"If you do any analysis of categorical data, this is an essential desktop reference."
—Technometrics
The use of statistical methods for analyzing categorical data has increased dramatically, particularly in the biomedical, social sciences, and financial industries. Responding to new developments, this book offers a comprehensive treatment of the most important methods for categorical data analysis.
Categorical Data Analysis, Third Edition summarizes the latest methods for univariate and correlated multivariate categorical responses. Readers will find a unified generalized linear models approach that connects logistic regression and Poisson and negative binomial loglinear models for discrete data with normal regression for continuous data. This edition also features:
Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and methodologists, such as biostatisticians and researchers in the social and behavioral sciences, medicine and public health, marketing, education, finance, biological and agricultural sciences, and industrial quality control.
"A must-have book for anyone expecting to do research and/or applications in categorical data analysis."
—Statistics in Medicine
"It is a total delight reading this book."
—Pharmaceutical Research
"If you do any analysis of categorical data, this is an essential desktop reference."
—Technometrics
The use of statistical methods for analyzing categorical data has increased dramatically, particularly in the biomedical, social sciences, and financial industries. Responding to new developments, this book offers a comprehensive treatment of the most important methods for categorical data analysis.
Categorical Data Analysis, Third Edition summarizes the latest methods for univariate and correlated multivariate categorical responses. Readers will find a unified generalized linear models approach that connects logistic regression and Poisson and negative binomial loglinear models for discrete data with normal regression for continuous data. This edition also features:
- An emphasis on logistic and probit regression methods for binary, ordinal, and nominal responses for independent observations and for clustered data with marginal models and random effects models
- Two new chapters on alternative methods for binary response data, including smoothing and regularization methods, classification methods such as linear discriminant analysis and classification trees, and cluster analysis
- New sections introducing the Bayesian approach for methods in that chapter
- More than 100 analyses of data sets and over 600 exercises
- Notes at the end of each chapter that provide references to recent research and topics not covered in the text, linked to a bibliography of more than 1,200 sources
- A supplementary website showing how to use R and SAS; for all examples in the text, with information also about SPSS and Stata and with exercise solutions
Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and methodologists, such as biostatisticians and researchers in the social and behavioral sciences, medicine and public health, marketing, education, finance, biological and agricultural sciences, and industrial quality control.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons
- Erscheinungstermin: 8. April 2013
- Englisch
- ISBN-13: 9781118710944
- Artikelnr.: 38260468
- Verlag: John Wiley & Sons
- Erscheinungstermin: 8. April 2013
- Englisch
- ISBN-13: 9781118710944
- Artikelnr.: 38260468
ALAN AGRESTI is Distinguished Professor Emeritus in the Department of Statistics at the University of Florida. He has presented short courses on categorical data methods in thirty countries. He is the author of five other books, including An Introduction to Categorical Data Analysis, Second Edition and Analysis of Ordinal Categorical Data, Second Edition, both published by Wiley.
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)
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)
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)
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)
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)
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)
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)
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)