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Categorical Data Analysis, 3rd Edition

ISBN: 978-0-470-46363-5
744 pages
December 2012
Categorical Data Analysis, 3rd Edition (0470463635) cover image

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:

  • 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.

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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)

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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.

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