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.

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3 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. (2e, 2007); John Wiley & Sons, rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, inany form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted bylaw.

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7 | 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

8 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 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.

9 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

10 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: 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.