Categorical Data Analysis E-Book

Alan Agresti

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2013

Beschreibung

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.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Dedication

Preface

Chapter 1: Introduction: Distributions and Inference for Categorical Data

1.1 Categorical Response Data

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

Chapter 2: Describing Contingency Tables

2.1 Probability Structure for Contingency Tables

2.2 Comparing Two Proportions

2.3 Conditional Association in Stratified 2 × 2 Tables

2.4 Measuring Association in I × J Tables

Notes

Exercises

Chapter 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

Chapter 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

Chapter 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

Chapter 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

6.4 Mantel–Haenszel and Related Methods for Multiple 2 × 2 Tables

6.5 Detecting and Dealing with Infinite Estimates

6.6 Sample Size and Power Considerations

Notes

Exercises

Chapter 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

Chapter 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

Chapter 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 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

Chapter 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

Chapter 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

Chapter 12: Clustered Categorical Data: Marginal and Transitional Models

12.1 Marginal Modeling: Maximum Likelihood Approach

12.2 Marginal Modeling: Generalized Estimating Equations (GEEs) Approach

12.3 Quasi-Likelihood and Its GEE Multivariate Extension: Details

12.4 Transitional Models: Markov Chain and Time Series Models

Notes

Exercises

Chapter 13: Clustered Categorical Data: Random Effects Models

13.1 Random Effects Modeling of Clustered Categorical Data

13.2 Binary Responses: Logistic-Normal Model

13.3 Examples of Random Effects Models for Binary Data

13.4 Random Effects Models for Multinomial Data

13.5 Multilevel Modeling

13.6 GLMM Fitting, Inference, and Prediction

13.7 Bayesian Multivariate Categorical Modeling

Notes

Exercises

Chapter 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

Chapter 15: Non-Model-Based Classification and Clustering

15.1 Classification: Linear Discriminant Analysis

15.2 Classification: Tree-Structured Prediction

15.3 Cluster Analysis for Categorical Data

Notes

Exercises

Chapter 16: Large- and Small-Sample Theory for Multinomial 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

Chapter 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

A.1 SAS

A.2 R And S-Plus

A.3 Stata

A.4 SPSS

A.5 Statxact and Logxact

A.6 Other Software

Appendix B: Chi-Squared Distribution Values

References

Author Index

Example Index

Subject Index

Categorical Data Analysis

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Library of Congress Cataloging-in-Publication Data

Agresti, Alan. Categorical data analysis / Alan Agresti. – 3rd ed. p. cm. – (Wiley series in probability and statistics; 792)Includes bibliographical references and index. ISBN 978-0-470-46363-5 (hardback) 1. Multivariate analysis. I. Title. QA278.A353 2013 519.5′35–dc23 2012009792

To Jacki

Preface

The explosion in the development of methods for analyzing categorical data that began in the 1960s has continued apace in recent years. This book provides an overview of these methods, as well as older, now standard, methods. It gives special emphasis to generalized linear modeling techniques, which extend linear model methods for continuous variables, and their extensions for multivariate responses.

OUTLINE OF TOPICS

Chapters 1–10 present the core methods for categorical response variables. Chapters 1–3 cover distributions for categorical responses and traditional methods for two-way contingency tables. Chapters 4–8 introduce logistic regression and related models such as the probit model for binary and multicategory response variables. Chapters 9 and 10 cover loglinear models for contingency tables.

In the past quarter century, a major area of new research has been the development of methods for repeated measurement and other forms of clustered categorical data. Chapters 11–14 present these methods, including marginal models and generalized linear mixed models with random effects. Chapter 15 introduces non-model-based methods for classification and clustering. Chapter 16 presents theoretical foundations as well as alternatives to the maximum likelihood paradigm that this text adopts. Chapter 17 is devoted to a historical overview of the development of the methods. It examines contributions of noted statisticians, such as Pearson and Fisher, whose pioneering efforts—and sometimes vocal debates—broke the ground for this evolution.

Appendices illustrate the use of statistical software for analyzing categorical data. The website for the text, vww.stat.ufl.edu/~aa/cda/cda.html, contains an appendix with detailed examples of the use of software (especially R, SAS, and Stata) for performing the analyses in this book, solutions to many of the exercises, extra exercises, and corrections.

CHANGES IN THIS EDITION

Given the explosion of research in the past 50 years on categorical data methods, it is an increasing challenge to write a comprehensive book covering all the commonly used methods. The second edition of this book already exceeded 700 pages. In including much new material without letting the book grow much, I have necessarily had to make compromises in depth and use relatively simple examples. I try to present a broad overview, while presenting bibliographic notes with many references in which the reader can find more details. In attempting to make the book relatively comprehensive while presenting substantive new material, every chapter of the first two editions has been extensively rewritten. The major changes are:

A new Chapter 7 presents alternative methods for binary response data, including some regularization methods that are becoming popular in this age of massive data sets with enormous numbers of variables.

A new Chapter 15 introduces non-model-based methods of classification, such as linear discriminant analysis and classification trees, and cluster analysis.

Many chapters now include a section describing the Bayesian approach for the methods of that chapter. We also have added material (e.g., Sections 6.5 and 7.4) about ways that frequentist methods can deal with awkward situations such as infinite maximum likelihood estimates.

The use of various software for categorical data methods is discussed at a much expanded website for the text,

www.stat.ufl.edu/~aa/cda/cda.html

. Examples are shown of the use of R, SAS, and Stata for most of the examples in the text, and there is discussion also about SPSS, StatXact, and other software. That website also contains many of the text’s data sets, some of which have only excerpts shown in the text itself, as well as solutions for many exercises and corrections of errors found in early printings of the book. I recommend that you refer to this appendix (or specialized software manuals) while reading the text, perhaps printing the pages about the software you prefer, as an aid to implementing the methods. This material was placed at the website partly because the text is already so long without it and also because it is then easier to keep the presentation up-to-date.

In this text, I interpret categorical data analysis to refer to methods for categorical response variables. For most methods, explanatory variables can be categorical or quantitative, as in ordinary regression. Thus, the focus is intended to be more general than contingency table analysis, although for simplicity of data presentation, most examples use contingency tables. These examples are simplistic, but should help you focus on understanding the methods themselves and make it easier for you to replicate results with your favorite software.

Other special features of the text include:

More than 100 analyses of data sets.

About 600 exercises, some directed toward theory and methods and some toward applications and data analysis.

Notes at the end of each chapter that provide references for recent research and many topics not covered in the text, linked to a bibliography of more than 1200 sources.

INTENDED AUDIENCE AND USE AS A TEXTBOOK

I intend this book to be accessible to the diverse mix of students who take graduate-level courses in categorical data analysis. But I have also written it with practicing statisticians and biostatisticians in mind. I hope it enables them to catch up with recent advances and learn about methods that sometimes receive inadequate attention in the traditional statistics curriculum.

The development of new methods has influenced—and been influenced by—the increasing availability of data sets with categorical responses in the social, behavioral, and biomedical sciences, as well as in public health, genetics, ecology, education, marketing and the financial industry, and industrial quality control. And so, although this book is directed mainly to statisticians and biostatisticians, I also aim for it to be helpful to methodologists in these fields.

Readers should possess a background that includes regression and analysis of variance models, as well as maximum likelihood methods of statistical theory. Those not having much theory background should be able to follow most methodological discussions. Those with mainly applied interests can skip most of Chapter 4 on the theory of generalized linear models and proceed to other chapters. However, the book has a distinctly higher technical level and is more thorough and complete than my lower-level text, An Introduction to Categorical Data Analysis, Second Edition (Wiley, 2007).

Today, because of the ubiquity of categorical data in applications, most statistics and biostatistics departments offer courses on categorical data analysis or on generalized linear models with strong emphasis on methods for discrete data. This book can be used as a text for such courses. The material in Chapters 1–6 forms the heart of most courses. There is too much material in this book for a single course, but a one-term course can be based on the following outline:

Basic contingency table analysis, covering Chapters 1–3, perhaps skipping some tangential sections such as 1.5.7, 1.6, 2.4, 3.4–3.7.

Logistic regression and related methods for binary data, covering Chapters 4–6, perhaps skipping some tangential sections such as 4.4–4.7 and 6.4–6.6.

Multinomial response models, covering at least Sections 8.1 and 8.2.

Matched pairs and clustered data, covering at least Sections 11.1–11.2.

Courses with biostatistical orientation may want to include bits from Chapters 12 and 13 on marginal and random effects models. Courses with social science emphasis may want to include some topics on loglinear modeling from Chapters 9 and 10. Some courses may want to select specialized topics from Chapter 7, such as probit modeling, conditional logistic regression, Bayesian binary data modeling, smoothing, and issues in the analysis of high-dimensional data.

ACKNOWLEDGMENTS

I thank those who commented on parts of the manuscript or provided help of some type. Special thanks to Anna Gottard, David Hoaglin, Maria Kateri, Bernhard Klingenberg, Keli Liu, and Euijung Ryu, who gave insightful comments on some chapters and made many helpful suggestions, and Brett Presnell for his advice and resources about R software and his comments about some of the material. Thanks to people who made suggestions about new material for this edition, including Jonathan Bischof, James Booth, Brian Caffo, Tianxi Cai, Brent Coull, Nicholas Cox, Ralitza Gueorguieva, Debashis Ghosh, John Henretta, David Hitchcock, Galin Jones, Robert Kushler, Xihong Lin, Jun Liu, Gianfranco Lovison, Giovanni Marchetti, David Olive, Art Owen, Alessandra Petrucci, Michael Radelet, Gerard Scallan, Maura Stokes, Anestis Touloumis, and Ming Yang. Thanks to those who commented on aspects of the second edition, including pointing out errors or typos, such as Pat Altham, Roberto Bertolusso, Nicholas Cox, David Firth, Rene Gonin, David Hoaglin, Harry Khamis, Bernhard Klingenberg, Robert Kushler, Gianfranco Lovison, Theo Nijsse, Richard Reyment, Misha Salganik, William Santo, Laura Thompson, Michael Vock, and Zhongming Yang. Thanks also to Laura Thompson for preparing her very helpful manual on using R and S-Plus for examples in the second edition. Thanks to the many who reviewed material or suggested examples for the first two editions, mentioned in the Prefaces of those editions. Thanks also to Wiley Executive Editor Steve Quigley and Associate Editor Jacqueline Palmieri for their steadfast encouragement and facilitation of this project. Finally, thanks to my wife Jacki Levine for continuing support of all kinds.

ALAN AGRESTI

Gainesville, Florida and Brookline, MassachusettsFebruary 2012

CHAPTER 1

Introduction: Distributions and Inference for Categorical Data

From helping to assess the value of new medical treatments to evaluating the factors that affect our opinions and behaviors, analysts today are finding myriad uses for categorical data methods. In this book we introduce these methods and the theory behind them.

Statistical methods for categorical responses were late in gaining the level of sophistication achieved early in the twentieth century by methods for continuous responses. Despite influential work around 1900 by the British statistician Karl Pearson, relatively Utile development of models for categorical responses occurred until the 1960s. In this book we describe the early fundamental work that still has importance today but place primary emphasis on more recent modeling approaches.