Categorical data analysis

**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. Content: Preface 1. Introduction: Distributions and Inference for Categorical Data 1 1.1 Categorical Response Data, 1 1.2 Distributions for Categorical Data 1.3 Statistical Inference for Categorical Data 1.4 Statistical Inference for Binomial Parameters 1.5 Statistical Inference for Multinomial Parameters 1.6 Bayesian Inference for Binomial and Multinomial Parameters Notes Exercises 2. Describing Contingency Tables 2.1 Probability Structure for Contingency Tables 2.2 Comparing Two Proportions 2.3 Conditional Association in Stratified 2x2 Tables 2.4 Measuring Association in I x J Tables Notes Exercises 3. Inference for Two-Way Contingency Tables 3.1 Confidence Intervals for Association Parameters 3.2 Testing Independence in Two-Way Contingency Tables 3.3 Following-Up Chi-Squared Tests 3.4 Two-Way Tables with Ordered Classifications 3.5 Small-Sample Inference for Contingency Tables 3.6 Bayesian Inference for Two-Way Contingency Tables 3.7 Extensions for Multiway Tables and Nontabulated Responses Notes Exercises 4. Introduction to Generalized Linear Models 4.1 The Generalized Linear Model 4.2 Generalized Linear Models for Binary Data 4.3 Generalized Linear Models for Counts and Rates 4.4 Moments and Likelihood for Generalized Linear Models 4.5 Inference and Model Checking for Generalized Linear Models 4.6 Fitting Generalized Linear Models 4.7 Quasi-Likelihood and Generalized Linear Models Notes Exercises 5. Logistic Regression 5.1 Interpreting Parameters in Logistic Regression 5.2 Inference for Logistic Regression 5.3 Logistic Models with Categorical Predictors 5.4 Multiple Logistic Regression 5.5 Fitting Logistic Regression Models Notes Exercises 6. Building, Checking, and Applying Logistic Regression Models 6.1 Strategies in Model Selection 6.2 Logistic Regression Diagnostics 6.3 Summarizing the Predictive Power of a Model 6.3 Mantel-Haenszel and Related Methods for Multiple 2x2 Tables 6.4 Detecting and Dealing with Infinite Estimates 6.5 Sample Size and Power Considerations Notes Exercises 7. Alternative Modeling of Binary Response Data 7.1 Probit and Complementary Log-Log Models 7.2 Bayesian Inference for Binary Regression 7.3 Conditional Logistic Regression 7.4 Smoothing: Kernels, Penalized Likelihood, Generalized Additive Models 7.5 Issues in Analyzing High-Dimensional Categorical Data Notes Exercises 8. Models for Multinomial Responses 8.1 Nominal Responses: Baseline-Category Logit Models 8.2 Ordinal Responses: Cumulative Logit Models 8.3 Ordinal Responses: Alternative Models 8.4 Testing Conditional Independence in I? J? K Tables 8.5 Discrete-Choice Models 8.6 Bayesian Modeling of Multinomial Responses Notes Exercises 9. Loglinear Models for Contingency Tables 9.1 Loglinear Models for Two-Way Tables 9.2 Loglinear Models for Independence and Interaction in Three-Way Tables 9.3 Inference for Loglinear Models 9.4 Loglinear Models for Higher Dimensions 9.5 The Loglinear?Logistic Model Connection 9.6 Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions 9.7 Loglinear Model Fitting: Iterative Methods and their Application Notes Exercises 10. Building and Extending Loglinear Models 10.1 Conditional Independence Graphs and Collapsibility 10.2 Model Selection and Comparison 10.3 Residuals for Detecting Cell-Specific Lack of Fit 10.4 Modeling Ordinal Associations 10.5 Generalized Loglinear and Association Models, Correlation Models, and Correspondence Analysis 10.6 Empty Cells and Sparseness in Modeling Contingency Tables 10.7 Bayesian Loglinear Modeling Notes Exercises 11. Models for Matched Pairs 11.1 Comparing Dependent Proportions 11.2 Conditional Logistic Regression for Binary Matched Pairs 11.3 Marginal Models for Square Contingency Tables 11.4 Symmetry, Quasi-symmetry, and Quasi-independence 11.5 Measuring Agreement Between Observers 11.6 Bradley-Terry Model for Paired Preferences 11.7 Marginal Models and Quasi-symmetry Models for Matched Sets Notes Exercises 12. Clustered Categorical Data: Marginal and Transitional Models 12.1 Marginal Modeling: Maximum Likelihood Approach 12.2 Marginal Modeling: Generalized Estimating Equations Approach 12.3 Quasi-likelihood and Its GEE Multivariate Extension: Details 12.4 Transitional Models: Markov Chain and Time Series Models Notes Exercises 13. Clustered Categorical Data: Random Effects Models 13.1 Random Effects Modeling of Clustered Categorical Data 13.2 Binary Responses: The Logistic-Normal Model 13.3 Examples of Random Effects Models for Binary Data 13.4 Random Effects Models for Multinomial Data 13.5 Multilevel Models 13.6 GLMM Fitting, Inference, and Prediction 13.7 Bayesian Multivariate Categorical Modeling Notes Exercises 14. Other Mixture Models for Discrete Data 14.1 Latent Class Models 14.2 Nonparametric Random Effects Models 14.3 Beta-Binomial Models 14.4 Negative Binomial Regression 14.5 Poisson Regression with Random Effects Notes Exercises 15. Non-Model-Based Classification and Clustering 15.2 Classification: Linear Discriminant Analysis 15.3 Classification: Tree-Structured Prediction 15.4 Cluster Analysis for Categorical Data Notes Exercises 16. Large- and Small-Sample Theory for Parametric Models 16.1 Delta Method 16.2 Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities 16.3 Asymptotic Distributions of Residuals and Goodness-of-Fit Statistics 16.4 Asymptotic Distributions for Logit/Loglinear Models 16.5 Small-Sample Significance Tests for Contingency Tables 16.6 Small-Sample Confidence Intervals for Categorical Data 16.7 Alternative Estimation Theory for Parametric Models Notes Exercises 17. Historical Tour of Categorical Data Analysis 17.1 Pearson-Yule Association Controversy 17.2 R.A. Fisher's Contributions 17.3 Logistic Regression 17.4 Multiway Contingency Tables and Loglinear Models 17.5 Bayesian Methods for Categorical Data 17.6 A Look Forward, and Backward Appendix A. Statistical Software for Categorical Data Analysis Appendix B. Chi-Squared Distribution Values References Author Index Example Index Subject Index. Abstract: 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. Read more... Machine generated contents note: Preface 1. Introduction: Distributions and Inference for Categorical Data 1 1.1 Categorical Response Data, 1 1.2 Distributions for Categorical Data 1.3 Statistical Inference for Categorical Data 1.4 Statistical Inference for Binomial Parameters 1.5 Statistical Inference for Multinomial Parameters 1.6 Bayesian Inference for Binomial and Multinomial Parameters Notes Exercises 2. Describing Contingency Tables 2.1 Probability Structure for Contingency Tables 2.2 Comparing Two Proportions 2.3 Conditional Association in Stratified 2x2 Tables 2.4 Measuring Association in I x J Tables Notes Exercises 3. Inference for Two-Way Contingency Tables 3.1 Confidence Intervals for Association Parameters 3.2 Testing Independence in Two-Way Contingency Tables 3.3 Following-Up Chi-Squared Tests 3.4 Two-Way Tables with Ordered Classifications 3.5 Small-Sample Inference for Contingency Tables 3.6 Bayesian Inference for Two-Way Contingency Tables 3.7 Extensions for Multiway Tables and Nontabulated Responses Notes Exercises 4. Introduction to Generalized Linear Models 4.1 The Generalized Linear Model 4.2 Generalized Linear Models for Binary Data 4.3 Generalized Linear Models for Counts and Rates 4.4 Moments and Likelihood for Generalized Linear Models 4.5 Inference and Model Checking for Generalized Linear Models 4.6 Fitting Generalized Linear Models 4.7 Quasi-Likelihood and Generalized Linear Models Notes Exercises 5. Logistic Regression 5.1 Interpreting Parameters in Logistic Regression 5.2 Inference for Logistic Regression 5.3 Logistic Models with Categorical Predictors 5.4 Multiple Logistic Regression 5.5 Fitting Logistic Regression Models Notes Exercises 6. Building, Checking, and Applying Logistic Regression Models 6.1 Strategies in Model Selection 6.2 Logistic Regression Diagnostics 6.3 Summarizing the Predictive Power of a Model 6.3 Mantel-Haenszel and Related Methods for Multiple 2x2 Tables 6.4 Detecting and Dealing with Infinite Estimates 6.5 Sample Size and Power Considerations Notes Exercises 7. Alternative Modeling of Binary Response Data 7.1 Probit and Complementary Log-Log Models 7.2 Bayesian Inference for Binary Regression 7.3 Conditional Logistic Regression 7.4 Smoothing: Kernels, Penalized Likelihood, Generalized Additive Models 7.5 Issues in Analyzing High-Dimensional Categorical Data Notes Exercises 8. Models for Multinomial Responses 8.1 Nominal Responses: Baseline-Category Logit Models 8.2 Ordinal Responses: Cumulative Logit Models 8.3 Ordinal Responses: Alternative Models 8.4 Testing Conditional Independence in I ? J ? K Tables 8.5 Discrete-Choice Models 8.6 Bayesian Modeling of Multinomial Responses Notes Exercises 9. Loglinear Models for Contingency Tables 9.1 Loglinear Models for Two-Way Tables 9.2 Loglinear Models for Independence and Interaction in Three-Way Tables 9.3 Inference for Loglinear Models 9.4 Loglinear Models for Higher Dimensions 9.5 The Loglinear?Logistic Model Connection 9.6 Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions 9.7 Loglinear Model Fitting: Iterative Methods and their Application Notes Exercises 10. Building and Extending Loglinear Models 10.1 Conditional Independence Graphs and Collapsibility 10.2 Model Selection and Comparison 10.3 Residuals for Detecting Cell-Specific Lack of Fit 10.4 Modeling Ordinal Associations 10.5 Generalized Loglinear and Association Models, Correlation Models, and Correspondence Analysis 10.6 Empty Cells and Sparseness in Modeling Contingency Tables 10.7 Bayesian Loglinear Modeling Notes Exercises 11. Models for Matched Pairs 11.1 Comparing Dependent Proportions 11.2 Conditional Logistic Regression for Binary Matched Pairs 11.3 Marginal Models for Square Contingency Tables 11.4 Symmetry, Quasi-symmetry, and Quasi-independence 11.5 Measuring Agreement Between Observers 11.6 Bradley-Terry Model for Paired Preferences 11.7 Marginal Models and Quasi-symmetry Models for Matched Sets Notes Exercises 12. Clustered Categorical Data: Marginal and Transitional Models 12.1 Marginal Modeling: Maximum Likelihood Approach 12.2 Marginal Modeling: Generalized Estimating Equations Approach 12.3 Quasi-likelihood and Its GEE Multivariate Extension: Details 12.4 Transitional Models: Markov Chain and Time Series Models Notes Exercises 13. Clustered Categorical Data: Random Effects Models 13.1 Random Effects Modeling of Clustered Categorical Data 13.2 Binary Responses: The Logistic-Normal Model 13.3 Examples of Random Effects Models for Binary Data 13.4 Random Effects Models for Multinomial Data 13.5 Multilevel Models 13.6 GLMM Fitting, Inference, and Prediction 13.7 Bayesian Multivariate Categorical Modeling Notes Exercises 14. Other Mixture Models for Discrete Data 14.1 Latent Class Models 14.2 Nonparametric Random Effects Models 14.3 Beta-Binomial Models 14.4 Negative Binomial Regression 14.5 Poisson Regression with Random Effects Notes Exercises 15. Non-Model-Based Classification and Clustering 15.2 Classification: Linear Discriminant Analysis 15.3 Classification: Tree-Structured Prediction 15.4 Cluster Analysis for Categorical Data Notes Exercises 16. Large- and Small-Sample Theory for Parametric Models 16.1 Delta Method 16.2 Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities 16.3 Asymptotic Distributions of Residuals and Goodness-of-Fit Statistics 16.4 Asymptotic Distributions for Logit/Loglinear Models 16.5 Small-Sample Significance Tests for Contingency Tables 16.6 Small-Sample Confidence Intervals for Categorical Data 16.7 Alternative Estimation Theory for Parametric Models Notes Exercises 17. Historical Tour of Categorical Data Analysis 17.1 Pearson-Yule Association Controversy 17.2 R. A. Fisher's Contributions 17.3 Logistic Regression 17.4 Multiway Contingency Tables and Loglinear Models 17.5 Bayesian Methods for Categorical Data 17.6 A Look Forward, and Backward Appendix A. Statistical Software for Categorical Data Analysis Appendix B. Chi-Squared Distribution Values References Author Index Example Index Subject Index. 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. A Classic In Its Own Right, This Book Continues To Provide An Introduction To Modern Generalized Linear Models For Categorical Variables. The Text Emphasizes Methods That Are Most Commonly Used In Practical Application, Such As Classical Inferences For Two- And Three-way Contingency Tables, Logistic Regression, Loglinear Models, Models For Multinomial (nominal And Ordinal) Responses, And Methods For Repeated Measurement And Other Forms Of Clustered, Correlated Response Data. Chapter Headings Remain Essentially With The Exception Of A New One On Bayesian Inference For Parametric Models. Other Major Changes Include An Expansion Of Clustered Data, New Research On Analysis Of Data Sets With Robust Variables, Extensive Discussions Of Ordinal Data, More On Interpretation, And Additional Exercises Throughout The Book. R And Sas Are Now Showcased As The Software Of Choice. An Author Web Site With Solutions, Commentaries, Software Programs, And Data Sets Is Available-- Machine Generated Contents Note: Preface 1. Introduction: Distributions And Inference For Categorical Data 1 1.1 Categorical Response Data, 1 1.2 Distributions For Categorical Data 1.3 Statistical Inference For Categorical Data 1.4 Statistical Inference For Binomial Parameters 1.5 Statistical Inference For Multinomial Parameters 1.6 Bayesian Inference For Binomial And Multinomial Parameters Notes Exercises 2. Describing Contingency Tables 2.1 Probability Structure For Contingency Tables 2.2 Comparing Two Proportions 2.3 Conditional Association In Stratified 2x2 Tables 2.4 Measuring Association In I X J Tables Notes Exercises 3.^ Alan Agresti. Includes Bibliographical References And Index. "A classic in its own right, this book continues to provide an introduction to modern generalized linear models for categorical variables. The text emphasizes methods that are most commonly used in practical application, such as classical inferences for two- and three-way contingency tables, logistic regression, loglinear models, models for multinomial (nominal and ordinal) responses, and methods for repeated measurement and other forms of clustered, correlated response data. Chapter headings remain essentially with the exception of a new one on Bayesian inference for parametric models. Other major changes include an expansion of clustered data, new research on analysis of data sets with robust variables, extensive discussions of ordinal data, more on interpretation, and additional exercises throughout the book. R and SAS are now showcased as the software of choice. An author web site with solutions, commentaries, software programs, and data sets is available"-- Provided by publisher