A valuable new edition of a standard reference
The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. An Introduction to Categorical Data Analysis, Third Edition summarizes these methods and shows readers how to use them using software. Readers will find a unified generalized linear models approach that connects logistic regression and loglinear models for discrete data with normal regression for continuous data.
Adding to the value in the new edition is:
• Illustrations of the use of R software to perform all the analyses in the book
• A new chapter on alternative methods for categorical data, including smoothing and regularization methods (such as the lasso), classification methods such as linear discriminant analysis and classification trees, and cluster analysis
• New sections in many chapters introducing the Bayesian approach for the methods of that chapter
• More than 70 analyses of data sets to illustrate application of the methods, and about 200 exercises, many containing other data sets
• An appendix showing how to use SAS, Stata, and SPSS, and an appendix with short solutions to most odd-numbered exercises
Written in an applied, nontechnical style, this book illustrates the methods using a wide variety of real data, including medical clinical trials, environmental questions, drug use by teenagers, horseshoe crab mating, basketball shooting, correlates of happiness, and much more.
An Introduction to Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and biostatisticians as well as methodologists in the social and behavioral sciences, medicine and public health, marketing, education, and the biological and agricultural sciences.

Agresti, Alan

Wiley & Sons, Incorporated, John

Wiley Global Research (STMS)

American Geophysical Union

Wiley-Blackwell

Wiley series in probability and statistics, Third edition, Hoboken, NJ, 2019

John Wiley & Sons, Inc. Textbook Subscription, Hoboken, NJ, 2019

United States, United States of America

Hoboken, N.J, 2018

3, 20181011

4.3 LOGISTIC REGRESSION WITH CATEGORICAL PREDICTORS -- 4.3.1 Indicator Variables Represent Categories of Predictors -- 4.3.2 Example: Survey about Marijuana Use -- 4.3.3 ANOVA-Type Model Representation of Factors -- 4.3.4 Tests of Conditional Independence and of Homogeneity for Three-Way Contingency Tables -- 4.4 MULTIPLE LOGISTIC REGRESSION -- 4.4.1 Example: Horseshoe Crabs with Color and Width Predictors -- 4.4.2 Model Comparison to Check Whether a Term is Needed -- 4.4.3 Example: Treating Color as Quantitative or Binary -- 4.4.4 Allowing Interaction between Explanatory Variables -- 4.4.5 Effects Depend on Other Explanatory Variables in Model -- 4.5 SUMMARIZING EFFECTS IN LOGISTIC REGRESSION -- 4.5.1 Probability-Based Interpretations -- 4.5.2 Marginal Effects and Their Average -- 4.5.3 Standardized Interpretations -- 4.6 SUMMARIZING PREDICTIVE POWER: CLASSIFICATION TABLES, ROC CURVES, AND MULTIPLE CORRELATION -- 4.6.1 Summarizing Predictive Power: Classification Tables -- 4.6.2 Summarizing Predictive Power: ROC Curves -- 4.6.3 Summarizing Predictive Power: Multiple Correlation -- EXERCISES -- 5 Building and Applying Logistic Regression Models -- 5.1 STRATEGIES IN MODEL SELECTION -- 5.1.1 How Many Explanatory Variables Can the Model Handle? -- 5.1.2 Example: Horseshoe Crab Satellites Revisited -- 5.1.3 Stepwise Variable Selection Algorithms -- 5.1.4 Purposeful Selection of Explanatory Variables -- 5.1.5 Example: Variable Selection for Horseshoe Crabs -- 5.1.6 AIC and the Bias/Variance Tradeoff -- 5.2 MODEL CHECKING -- 5.2.1 Goodness of Fit: Model Comparison Using the Deviance -- 5.2.2 Example: Goodness of Fit for Marijuana Use Survey -- 5.2.3 Goodness of Fit: Grouped versus Ungrouped Data and Continuous Predictors -- 5.2.4 Residuals for Logistic Models with Categorical Predictors -- 5.2.5 Example: Graduate Admissions at University of Florida

5.2.6 Standardized versus Pearson and Deviance Residuals -- 5.2.7 Influence Diagnostics for Logistic Regression -- 5.2.8 Example: Heart Disease and Blood Pressure -- 5.3 INFINITE ESTIMATES IN LOGISTIC REGRESSION -- 5.3.1 Complete and Quasi-Complete Separation: Perfect Discrimination -- 5.3.2 Example: Infinite Estimate for Toy Example -- 5.3.3 Sparse Data and Infinite Effects with Categorical Predictors -- 5.3.4 Example: Risk Factors for Endometrial Cancer Grade -- 5.4 BAYESIAN INFERENCE, PENALIZED LIKELIHOOD, AND CONDITIONAL LIKELIHOOD FOR LOGISTIC REGRESSION -- 5.4.1 Bayesian Modeling: Specification of Prior Distributions -- 5.4.2 Example: Risk Factors for Endometrial Cancer Revisited -- 5.4.3 Penalized Likelihood Reduces Bias in Logistic Regression -- 5.4.4 Example: Risk Factors for Endometrial Cancer Revisited -- 5.4.5 Conditional Likelihood and Conditional Logistic Regression -- 5.4.6 Conditional Logistic Regression and Exact Tests for Contingency Tables -- 5.5 ALTERNATIVE LINK FUNCTIONS: LINEAR PROBABILITY AND PROBIT MODELS -- 5.5.1 Linear Probability Model -- 5.5.2 Example: Political Ideology and Belief in Evolution -- 5.5.3 Probit Model and Normal Latent Variable Model -- 5.5.4 Example: Snoring and Heart Disease Revisited -- 5.5.5 Latent Variable Models Imply Binary Regression Models -- 5.5.6 CDFs and Shapes of Curves for Binary Regression Models -- 5.6 SAMPLE SIZE AND POWER FOR LOGISTIC REGRESSION -- 5.6.1 Sample Size for Comparing Two Proportions -- 5.6.2 Sample Size in Logistic Regression Modeling -- 5.6.3 Example: Modeling the Probability of Heart Disease -- Exercises -- 6 Multicategory Logit Models -- 6.1 BASELINE-CATEGORY LOGIT MODELS FOR NOMINAL RESPONSES -- 6.1.1 Baseline-Category Logits -- 6.1.2 Example: What Do Alligators Eat? -- 6.1.3 Estimating Response Probabilities -- 6.1.4 Checking Multinomial Model Goodness of Fit

Intro -- An Introduction to Categorical Data Analysis -- Contents -- Preface -- About the Companion Website -- 1 Introduction -- 1.1 CATEGORICAL RESPONSE DATA -- 1.1.1 Response Variable and Explanatory Variables -- 1.1.2 Binary-Nominal-Ordinal Scale Distinction -- 1.1.3 Organization of this Book -- 1.2 PROBABILITY DISTRIBUTIONS FOR CATEGORICAL DATA -- 1.2.1 Binomial Distribution -- 1.2.2 Multinomial Distribution -- 1.3 STATISTICAL INFERENCE FOR A PROPORTION -- 1.3.1 Likelihood Function and Maximum Likelihood Estimation -- 1.3.2 Significance Test About a Binomial Parameter -- 1.3.3 Example: Surveyed Opinions About Legalized Abortion -- 1.3.4 Confidence Intervals for a Binomial Parameter -- 1.3.5 Better Confidence Intervals for a Binomial Proportion -- 1.4 STATISTICAL INFERENCE FOR DISCRETE DATA -- 1.4.1 Wald, Likelihood-Ratio, and Score Tests -- 1.4.2 Example: Wald, Score, and Likelihood-Ratio Binomial Tests -- 1.4.3 Small-Sample Binomial Inference and the Mid P-Value -- 1.5 BAYESIAN INFERENCE FOR PROPORTIONS -- 1.5.1 The Bayesian Approach to Statistical Inference -- 1.5.2 Bayesian Binomial Inference: Beta Prior Distributions -- 1.5.3 Example: Opinions about Legalized Abortion, Revisited -- 1.5.4 Other Prior Distributions -- 1.6 USING R SOFTWARE FOR STATISTICAL INFERENCE ABOUT PROPORTIONS -- 1.6.1 Reading Data Files and Installing Packages -- 1.6.2 Using R for Statistical Inference about Proportions -- 1.6.3 Summary: Choosing an Inference Method -- Exercises -- 2 Analyzing Contingency Tables -- 2.1 PROBABILITY STRUCTURE FOR CONTINGENCY TABLES -- 2.1.1 Joint, Marginal, and Conditional Probabilities -- 2.1.2 Example: Sensitivity and Specificity -- 2.1.3 Statistical Independence of Two Categorical Variables -- 2.1.4 Binomial and Multinomial Sampling -- 2.2 COMPARING PROPORTIONS IN 2×2 CONTINGENCY TABLES -- 2.2.1 Difference of Proportions

2.2.2 Example: Aspirin and Incidence of Heart Attacks -- 2.2.3 Ratio of Proportions (Relative Risk) -- 2.2.4 Using R for Comparing Proportions in 2×2 Tables -- 2.3 THE ODDS RATIO -- 2.3.1 Properties of the Odds Ratio -- 2.3.2 Example: Odds Ratio for Aspirin Use and Heart Attacks -- 2.3.3 Inference for Odds Ratios and Log Odds Ratios -- 2.3.4 Relationship Between Odds Ratio and Relative Risk -- 2.3.5 Example: The Odds Ratio Applies in Case-Control Studies -- 2.3.6 Types of Studies: Observational Versus Experimental -- 2.4 CHI-SQUARED TESTS OF INDEPENDENCE -- 2.4.1 Pearson Statistic and the Chi-Squared Distribution -- 2.4.2 Likelihood-Ratio Statistic -- 2.4.3 Testing Independence in Two-Way Contingency Tables -- 2.4.4 Example: Gender Gap in Political Party Affiliation -- 2.4.5 Residuals for Cells in a Contingency Table -- 2.4.6 Partitioning Chi-Squared Statistics -- 2.4.7 Limitations of Chi-Squared Tests -- 2.5 TESTING INDEPENDENCE FOR ORDINAL VARIABLES -- 2.5.1 Linear Trend Alternative to Independence -- 2.5.2 Example: Alcohol Use and Infant Malformation -- 2.5.3 Ordinal Tests Usually Have Greater Power -- 2.5.4 Choice of Scores -- 2.5.5 Trend Tests for r×2 and 2×c and Nominal-Ordinal Tables -- 2.6 EXACT FREQUENTIST AND BAYESIAN INFERENCE -- 2.6.1 Fisher's Exact Test for 2×2 Tables -- 2.6.2 Example: Fisher's Tea Tasting Colleague -- 2.6.3 Conservatism for Actual (Type I Error) -- Mid -Values -- 2.6.4 Small-Sample Confidence Intervals for Odds Ratio -- 2.6.5 Bayesian Estimation for Association Measures -- 2.6.6 Example: Bayesian Inference in a Small Clinical Trial -- 2.7 ASSOCIATION IN THREE-WAY TABLES -- 2.7.1 Partial Tables -- 2.7.2 Example: Death Penalty Verdicts and Race -- 2.7.3 Simpson's Paradox -- 2.7.4 Conditional and Marginal Odds Ratios -- 2.7.5 Homogeneous Association -- Exercises -- 3 Generalized Linear Models

3.1 COMPONENTS OF A GENERALIZED LINEAR MODEL -- 3.1.1 Random Component -- 3.1.2 Linear Predictor -- 3.1.3 Link Function -- 3.1.4 Ordinary Linear Model: GLM with Normal Random Component -- GENERALIZED LINEAR MODELS FOR BINARY DATA -- 3.2.1 Linear Probability Model -- 3.2.2 Logistic Regression Model -- 3.2.3 Example: Snoring and Heart Disease -- 3.2.4 Using R to Fit Generalized Linear Models for Binary Data -- 3.2.5 Data Files: Ungrouped or Grouped Binary Data -- 3.3 GENERALIZED LINEAR MODELS FOR COUNTS AND RATES -- 3.3.1 Poisson Distribution for Counts -- 3.3.2 Poisson Loglinear Model -- 3.3.3 Example: Female Horseshoe Crabs and their Satellites -- 3.3.4 Overdispersion: Greater Variability than Expected -- 3.4 STATISTICAL INFERENCE AND MODEL CHECKING -- 3.4.1 Wald, Likelihood-Ratio, and Score Inference Use the Likelihood Function -- 3.4.2 Example: Political Ideology and Belief in Evolution -- 3.4.3 The Deviance of a GLM -- 3.4.4 Model Comparison Using the Deviance -- 3.4.5 Residuals Comparing Observations to the Model Fit -- 3.5 FITTING GENERALIZED LINEAR MODELS -- 3.5.1 The Fisher Scoring Algorithm Fits GLMs -- 3.5.2 Bayesian Methods for Generalized Linear Models -- 3.5.3 GLMs: A Unified Approach to Statistical Analysis -- Exercises -- 4 Logistic Regression -- 4.1 THE LOGISTIC REGRESSION MODEL -- 4.1.1 The Logistic Regression Model -- 4.1.2 Odds Ratio and Linear Approximation Interpretations -- 4.1.3 Example: Whether a Female Horseshoe Crab Has Satellites -- 4.1.4 Logistic Regression with Retrospective Studies -- 4.1.5 Normally Distributed X Implies Logistic Regression for Y -- 4.2 STATISTICAL INFERENCE FOR LOGISTIC REGRESSION -- 4.2.1 Confidence Intervals for Effects -- 4.2.2 Significance Testing -- 4.2.3 Fitted Values and Confidence Intervals for Probabilities -- 4.2.4 Why Use a Model to Estimate Probabilities?

2023-01-28