An Introduction to Categorical Data Analysis

Abstract

The presentation in this book has a low technical level and does not require familiarity with advanced mathematics such as calculus or matrix algebra. Readers should possess a background that includes material from a two-semester statistical methods sequence for undergraduate or graduate nonstatistics majors. This background should include estimation and significance testing and exposure to regression modeling. This book is designed for students taking an introductory course in categorical data analysis, but I also have written it for applied statisticians and practicing scientists involved in data analyses. I hope that the book will be helpful to analysts dealing with categorical response data in the social, behavioral, and biomedical sciences, as well as in public health, marketing, education, biological and agricultural sciences, and industrial quality control. The basics of categorical data analysis are covered in Chapters 1 to 7. Chapter 2 surveys standard descriptive and inferential methods for contingency tables, such as odds ratios, tests of independence, and conditional versus marginal associations. I feel that an understanding ofmethods is enhanced, however, by viewing them in the context of statistical models. Thus, the rest of the text focuses on the modeling ofcategorical responses. I prefer to teach categor- ical data methods by unifying their models with ordinary regression models. Chapter 3 does this under the umbrella of generalized linear models. That chapter introduces generalized linear 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 regression models for multicategory responses, both nominal and ordinal. Chapter 7 discusses loglinear models for contingency tables and other types of count data. I believe that logistic regression models deserve more attention than loglinear mod- els, because applications more commonly focus on the relationship between a categorical response variable and some explanatory variables (which logistic regression models do) than on the association structure among several response variables (which loglinear models do). Thus, I have given main attention to logistic regression in these chapters and in later chapters that discuss extensions of this model. Chapter 8 presents methods for matched-pairs data. Chapters 9 and 10 extend the matched-pairs methods to apply to clustered, correlated observations. Chapter 9 does this with marginal models, emphasizing the generalized estimating equations (GEE) approach, whereas Chapter 10 uses random effects to model more fully the dependence. Chapter 11 is a new chapter, presenting classification and smoothing methods. That chapter also intro- duces regularization methods that are increasingly important with the advent of data sets having large numbers of explanatory variables. Chapter 12 provides a historical perspective of the development of the methods. The text concludes with an appendix showing the use of R, SAS, Stata, and SPSS software for conducting nearly all methods presented in this book. Many of the chapters now also show how to use the Bayesian approach to conduct the analyses The material in Chapters 1 to 7 forms the heart of an introductory course in categorical data analysis. Sections that can be skipped if desired, to provide more time for other topics, include Sections 1.5, 2.5–2.7, 3.3 and 3.5, 5.4–5.6, 6.3–6.4, and 7.4–7.6. Instructors can choose sections from Chapters 8 to 12 to supplement the topics of primary importance. Sections and subsections labeled with an asterisk can be skipped for those wanting a briefer survey of the methods. This book has lower technical level thanmy bookCategoricalData Analysis (3rd edition, Wiley 2013). I hope that it will appeal to readers who prefer a more applied focus than that book provides. For instance, this book does not attempt to derive likelihood equations, prove asymptotic distributions, or cite current research work.