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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.
Categorical Data analysis WILEY SERIES IN PROBABILITY AND STATISTICS Established by WALTER A sheWHART and samuel s WIlks Editors: David /. Balding Noel A C Cressie, Garrett M. Fitzmauric Harvey Goldstein, lain M. Johnstone, Geert Molenberghs, David w. Scott, Adrian F M. Smith, Ruey S Tsay, Sanford Weisberg Editors Emeriti: Vic Barnett, Stuart Hunter, Joseph b. Kadane, Jozef L. Teugels A complete list of the titles in this series appears at the end of this volume Categorical Data Analysis Third edition ALAN AGRESTI Department of Statistics University of Florida Gainesville. Florida EiWILEY-INTERSCIENCE A JoHn WILEY SONS INC. PUBLICATION Cover Image: (back ground) Peter Firus/iStockphoto, (line art) courtesy of the author Copyright@ 2013 by John Wiley Sons All rights reserved Published by John Wiley Sons, Inc, Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per -copy fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive Danvers MA 01923. 978-750-8400. fax 978-750-4470. or on the web at www.copyright.comRequeststothePublisherforpermissionshouldbeaddressedtothePermissions Department, John Wiley Sons, Inc 1 1 1 River Street, Hoboken, NJ 07030, 201-748-6011, fax 201-748-6008 oronlineat Limit of Liability/Disclaimer of warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Cu Care Department within the United States at 800-762-2974, outside the United States at 317-572-3993 ortomer fax3l7572-4002 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be Library of Congress Cataloging-in-Publication data Agresti, Alan Categorical data analysis /alan a grest. -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.A3532013 519.5′35-dc23 2012009792 Printed in the United States of America 098765432 To Jacki Contents Preface XIII I Introduction: Distributions and Inference for Categorical Data 1. 1 Categorical Response data, I 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. I Probability Structure for Contingency Tables, 37 2.2 Comparing Two Proportions, 43 2,3 Conditional Association in Stratified 2 x 2 Tables. 47 2. 4 Measuring Association in /x J Tables, 54 Notes. 60 Exercises. 60 3 Inference for Two-Way Contingency Tables 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 VIll CONTENTS 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 2x 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

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