An Introduction to Categorical Data Analysis

1 Wiley Series in Probability and StatisticsALAN AGRESTITHIRD EDITIONAN Introduction TO Categorical data ANALYSISAN Introduction TOCATEGORICAL data ANALYSISWILEY SERIES IN PROBABILITY AND STATISTICSE stablished byWalter A. Shewhart and Samuel S. WilksEditors:David J. Balding, Noel A. C. Cressie, Garrett M. Fitzmaurice,Geof H. Givens, Harvey Goldstein, Geert Molenberghs, David W. Scott,Adrian F. M. Smith, Ruey S. TsayEditors Emeriti:J. Stuart Hunter, Iain M. Johnstone, Joseph B. Kadane,Jozef L. TeugelsTheWiley Series in Probability and Statisticsis well established andauthoritative. It covers many topics of current research interest in bothpure and applied statistics and probability theory. Written by leadingstatisticians and institutions, the titles span both state-of-the-artdevelopments in the field and classical the wide range of current research in statistics, the seriesencompasses applied, methodological and theoretical statistics, rangingfrom applications and new techniques made possible by advances incomputerized practice to rigorous treatment of theoretical series provides essential and invaluable reading for all statisticians,whether in academia, industry, government, or complete list of titles in this series can be found Introduction TOCATEGORICAL DATAANALYSIST hird EditionAlan AgrestiUniversity of Florida, Florida, United StatesThis third edition first published 2019 2019 John Wiley & Sons, History(1e, 1996); John Wiley & Sons, Inc.

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4 | Hoboken, NJ : John Wiley & Sons, 2019. | Series: Wiley series in probability andstatistics | Includes bibliographical references and index. |Identifiers: LCCN 2018026887 (print) | LCCN 2018036674 (ebook) | ISBN 9781119405276 (Adobe PDF) |ISBN 9781119405283 (ePub) | ISBN 9781119405269 (hardcover)Subjects: LCSH: Multivariate : LCC QA278 (ebook) | LCC QA278 .A355 2019 (print) | DDC dc23LC record available at Design: WileyCover Image: in 10 Nimbus by Aptara Inc., New Delhi, IndiaPrinted in the United States of America10987654321 CONTENTSP refaceixAbout the Companion Websitexiii1 Response Distributions for Categorical Inference for a Inference for Discrete Inference for Proportions * for Statistical Inference about Proportions *17 Exercises212 Analyzing Contingency Structure for Contingency Proportions in 2 2 Contingency Odds Tests of Independence for Ordinal Frequentist and Bayesian Inference * in Three-Way Tables52 Exercises56vviCONTENTS3 Generalized Linear of a Generalized Linear Generalized Linear Models for Binary Linear Models for Counts and Statistical Inference and Model Fitting Generalized Linear Models82 Exercises844 Logistic logistic regression Statistical Inference for Logistic logistic regression with Categorical Multiple Logistic Summarizing

5 Effects in Logistic Summarizing Predictive Power: Classification Tables, ROC Curves, andMultiple Correlation110 Exercises1135 Building and Applying logistic regression Strategies in Model Model Infinite Estimates in Logistic Bayesian Inference, Penalized Likelihood, and Conditional Likelihoodfor logistic regression * Alternative Link Functions: Linear Probability andProbit Models * Size and Power for logistic regression *150 Exercises1516 Multicategory Logit Baseline-Category Logit Models for Nominal Logit Models for Ordinal Cumulative Link Models: Model Checking and Extensions * Paired-Category Logit Modeling of Ordinal Responses *184 Exercises1877 Loglinear Models for Contingency Tables and Loglinear Models for Counts in Contingency Statistical Inference for Loglinear The Loglinear Logistic Model Graphs and Ordinal Associations in Contingency Modeling of Count Response Variables *217 Exercises2218 Models for Matched Dependent Proportions for Binary Matched Models and Subject-Specific Models for Matched Proportions for Nominal Matched-Pairs Proportions for Ordinal Matched-Pairs Rater Agreement * Terry Model for Paired Preferences *247 Exercises2499 Marginal Modeling of Correlated, Clustered Models Versus Subject-Specific Modeling.

6 The Generalized Estimating Equations (GEE) Modeling for Clustered Multinomial Modeling, Given the with Missing data *266 Exercises26810 Random Effects: Generalized Linear Mixed Effects Modeling of Clustered Categorical : Random Effects Models for Binary to Multinomial Responses and Multiple Random (Hierarchical) Class Models *291 Exercises29511 Classification and Smoothing * : Linear discriminant : Tree-Based Analysis for Categorical : Generalized Additive for High-Dimensional Categorical data (Largep)313 Exercises321viiiCONTENTS12 A Historical Tour of Categorical data Analysis *325 Appendix: Software for Categorical data Categorical data Categorical data Categorical data Categorical data Analysis346 Brief Solutions to Odd-Numbered Exercises349 Bibliography363 Examples Index365 Subject Index369 PREFACEIn recent years, the use of specialized statistical methods for Categorical data has increaseddramatically, particularly for applications in the biomedical and social sciences.

7 Partly thisreflects the development during the past few decades of sophisticated methods for analyzingcategorical data . It also reflects the increasing methodological sophistication of scientistsand applied statisticians, most of whom now realize that it is unnecessary and ofteninappropriate to use methods for continuous data with Categorical third edition of the book is a substantial revision of the second edition. The mostimportant change is showing how to conduct all the analyses usingRsoftware. As in thefirst two editions, the main focus is presenting the most important methods for analyzingcategorical data . The book summarizes methods that have long played a prominent role,such as chi-squared tests, but gives special emphasis to modeling techniques, in particularto logistic presentation in this book has a low technical level and does not require familiaritywith advanced mathematics such as calculus or matrix algebra.

8 Readers should possess abackground that includes material from a two-semester statistical methods sequence forundergraduate or graduate nonstatistics majors. This background should include estimationand significance testing and exposure to regression book is designed for students taking an introductory course in Categorical dataanalysis, but I also have written it for applied statisticians and practicing scientists involvedin data analyses. I hope that the book will be helpful to analysts dealing with categoricalresponse data in the social, behavioral, and biomedical sciences, as well as in public health,marketing, education, biological and agricultural sciences, and industrial quality basics of Categorical data Analysis are covered in Chapters 1 to 7. Chapter 2 surveysstandard descriptive and inferential methods for contingency tables, such as odds ratios, testsixxPREFACEof independence, and conditional versus marginal associations.

9 I feel that an understandingof methods is enhanced, however, by viewing them in the context of statistical models. Thus,the rest of the text focuses on the modeling of Categorical responses. I prefer to teach categor-ical data methods by unifying their models with ordinary regression models. Chapter 3 doesthis under the umbrella of generalized linear models. That chapter introduces generalizedlinear models for binary data and count data . Chapters 4 and 5 discuss the most impor-tant such model for binary data , logistic regression . Chapter 6 introduces logistic regressionmodels for multicategory responses, both nominal and ordinal. Chapter 7 discusses loglinearmodels for contingency tables and other types of count believe that logistic regression models deserve more attention than loglinear mod-els, because applications more commonly focus on the relationship between a categoricalresponse variable and some explanatory variables (which logistic regression models do)than on the association structure among several response variables (which loglinear modelsdo).

10 Thus, I have given main attention to logistic regression in these chapters and in laterchapters that discuss extensions of this 8 presents methods for matched-pairs data . Chapters 9 and 10 extend thematched-pairs methods to apply to clustered, correlated observations. Chapter 9 does thiswith marginal models, emphasizing the generalized estimating equations (GEE) approach,whereas Chapter 10 uses random effects to model more fully the dependence. Chapter 11is a new chapter, presenting classification and smoothing methods. That chapter also intro-duces regularization methods that are increasingly important with the advent of data setshaving large numbers of explanatory variables. Chapter 12 provides a historical perspectiveof the development of the methods. The text concludes with an appendix showing the useofR, SAS, Stata, and SPSS software for conducting nearly all methods presented in thisbook.