Introduction to Categorical Data Analysis - GSP Main Site ...

1 Ffirs 2007/1/31 page iii #3An Introduction toCategorical data AnalysisSecond EditionALAN AGRESTID epartment of StatisticsUniversity of FloridaGainesville, Florida ffirs 2007/1/31 pagei #1 ffirs 2007/1/31 pagei #1An Introduction toCategorical data Analysis ffirs 2007/1/31 page ii #2 ffirs 2007/1/31 page iii #3An Introduction toCategorical data AnalysisSecond EditionALAN AGRESTID epartment of StatisticsUniversity of FloridaGainesville, Florida ffirs 2007/1/31 page iv #4 Copyright 2007 by John Wiley & Sons, Inc., All rights by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in CanadaNo part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form orby any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except aspermitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the priorwritten permission of the Publisher, or authorization through payment of the appropriate per-copy fee tothe Copyright Clearance Center, Inc.

2 , 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax(978) 750-4470, or on the web at Requests to the Publisher for permission shouldbe addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ07030, (201) 748-6011, fax (201) 748-6008, or online at of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts inpreparing this book, they make no representations or warranties with respect to the accuracy orcompleteness of the contents of this book and specifically disclaim any implied warranties ofmerchantability or fitness for a particular purpose. No warranty may be created or extended by salesrepresentatives or written sales materials. The advice and strategies contained herein may not be suitablefor your situation.

3 You should consult with a professional where appropriate. Neither the publisher norauthor shall be liable for any loss of profit or any other commercial damages, including but not limited tospecial, incidental, consequential, or other general information on our other products and services or for technical support, please contact ourCustomer Care Department within the United States at (800) 762-2974, outside the United States at (317)572-3993 or fax (317) also publishes its books in a variety of electronic formats. Some content that appears in print maynot be available in electronic formats. For more information about Wiley products, visit our web site of Congress Cataloging-in-Publication DataAgresti, AlanAn Introduction to Categorical data Analysis /Alan bibliographical references and 978-0-471-22618-51.

4 Multivariate Analysis . I. 35 - - dc222006042138 Printed in the United States of ftoc 2007/1/31 pagev #1 ContentsPreface to the Second Editionxv1. Categorical Response data , Response/Explanatory Variable Distinction, Nominal/Ordinal Scale Distinction, Organization of this Book, Probability Distributions for Categorical data , Binomial Distribution, Multinomial Distribution, Statistical Inference for a Proportion, Likelihood Function and Maximum Likelihood Estimation, Significance Test About a Binomial Proportion, Example: Survey Results on Legalizing Abortion, Confidence Intervals for a Binomial Proportion, More on Statistical Inference for Discrete data , Wald, Likelihood-Ratio, and Score Inference, Wald, Score, and Likelihood-Ratio Inference forBinomial Parameter, Small-Sample Binomial Inference, Small-Sample Discrete Inference is Conservative, Inference Based on the MidP-value, Summary, 16 Problems, 162.

5 Contingency Probability Structure for Contingency Tables, Joint, Marginal, and Conditional Probabilities, Example: Belief in Afterlife, 22v ftoc 2007/1/31 page vi # Sensitivity and Specificity in Diagnostic Tests, Independence, Binomial and Multinomial Sampling, Comparing Proportions in Two-by-Two Tables, Difference of Proportions, Example: Aspirin and Heart Attacks, Relative Risk, The Odds Ratio, Properties of the Odds Ratio, Example: Odds Ratio for Aspirin Use and Heart Attacks, Inference for Odds Ratios and Log Odds Ratios, Relationship Between Odds Ratio and Relative Risk, The Odds Ratio Applies in Case Control Studies, Types of Observational Studies, Chi-Squared Tests of Independence, Pearson Statistic and the Chi-Squared Distribution, Likelihood-Ratio Statistic, Tests of Independence, Example: Gender Gap in Political Affiliation, Residuals for Cells in a Contingency Table, Partitioning Chi-Squared, Comments About Chi-Squared Tests, Testing Independence for Ordinal data , Linear Trend Alternative to Independence, Example.

6 Alcohol Use and Infant Malformation, Extra Power with Ordinal Tests, Choice of Scores, Trend Tests forI 2 and 2 JTables, Nominal Ordinal Tables, Exact Inference for Small Samples, Fisher s Exact Test for 2 2 Tables, Example: Fisher s Tea Taster, and Conservatism for ActualP(Type I Error), Small-Sample Confidence Interval for Odds Ratio, Association in Three-Way Tables, Partial Tables, Conditional Versus Marginal Associations: DeathPenalty Example, Simpson s Paradox, Conditional and Marginal Odds Ratios, Conditional Independence Versus Marginal Independence, Homogeneous Association, 54 Problems, 55 ftoc 2007/1/31 page vii #3 CONTENTSvii3. Generalized Linear Components of a Generalized Linear Model, Random Component, Systematic Component, Link Function, Normal GLM, Generalized Linear Models for Binary data , Linear Probability Model, Example: Snoring and Heart Disease, Logistic Regression Model, Probit Regression Model, Binary Regression and Cumulative DistributionFunctions, Generalized Linear Models for Count data , Poisson Regression, Example: Female Horseshoe Crabs and their Satellites, Overdispersion: Greater Variability than Expected, Negative Binomial Regression, Count Regression for Rate data , Example.

7 British Train Accidents over Time, Statistical Inference and Model Checking, Inference about Model Parameters, Example: Snoring and Heart Disease Revisited, The Deviance, Model Comparison Using the Deviance, Residuals Comparing Observations to the Model Fit, Fitting Generalized Linear Models, The Newton Raphson Algorithm Fits GLMs, Wald, Likelihood-Ratio, and Score Inference Use theLikelihood Function, Advantages of GLMs, 90 Problems, 904. Logistic Interpreting the Logistic Regression Model, Linear Approximation Interpretations, Horseshoe Crabs: Viewing and Smoothing a BinaryOutcome, Horseshoe Crabs: Interpreting the Logistic RegressionFit, Odds Ratio Interpretation, 104 ftoc 2007/1/31 page viii # Logistic Regression with Retrospective Studies, Normally DistributedXImplies Logistic RegressionforY, Inference for Logistic Regression, Binary data can be Grouped or Ungrouped, Confidence Intervals for Effects, Significance Testing, Confidence Intervals for Probabilities, Why Use a Model to Estimate Probabilities?

8 , Confidence Intervals for Probabilities: Details, Standard Errors of Model Parameter Estimates, Logistic Regression with Categorical Predictors, Indicator Variables Represent Categories of Predictors, Example: AZT Use and AIDS, ANOVA-Type Model Representation of Factors, The Cochran Mantel Haenszel Test for 2 2 KContingency Tables, Testing the Homogeneity of Odds Ratios, Multiple Logistic Regression, Example: Horseshoe Crabs with Color and WidthPredictors, Model Comparison to Check Whether a Term is Needed, Quantitative Treatment of Ordinal Predictor, Allowing Interaction, Summarizing Effects in Logistic Regression, Probability-Based Interpretations, Standardized Interpretations, 121 Problems, 1215.

9 Building and Applying Logistic Regression Strategies in Model Selection, How Many Predictors Can You Use?, Example: Horseshoe Crabs Revisited, Stepwise Variable Selection Algorithms, Example: Backward Elimination for Horseshoe Crabs, AIC, Model Selection, and the Correct Model, Summarizing Predictive Power: Classification Tables, Summarizing Predictive Power: ROC Curves, Summarizing Predictive Power: A Correlation, Model Checking, Likelihood-Ratio Model Comparison Tests, Goodness of Fit and the Deviance, 145 ftoc 2007/1/31 page ix # Checking Fit: Grouped data , Ungrouped data , andContinuous Predictors, Residuals for Logit Models, Example: Graduate Admissions at University of Florida, Influence Diagnostics for Logistic Regression, Example.

10 Heart Disease and Blood Pressure, Effects of Sparse data , Infinite Effect Estimate: Quantitative Predictor, Infinite Effect Estimate: Categorical Predictors, Example: Clinical Trial with Sparse data , Effect of Small Samples onX2andG2 Tests, Conditional Logistic Regression and Exact Inference, Conditional Maximum Likelihood Inference, Small-Sample Tests for Contingency Tables, Example: Promotion Discrimination, Small-Sample Confidence Intervals for LogisticParameters and Odds Ratios, Limitations of Small-Sample Exact Methods, Sample Size and Power for Logistic Regression, Sample Size for Comparing Two Proportions, Sample Size in Logistic Regression, Sample Size in Multiple Logistic Regression, 162 Problems, 1636.