Introduction to Categorical Data Analysis

CHAPTER 3
Generalized Linear Models
Chapter 2 presented methods for analyzing contingency tables. Those methods help
us investigate effects of explanatory variables on categorical response variables. The
rest of this book uses models as the basis of such analyses. In fact, the methods of
Chapter 2 also result from analyzing effects in certain models, but models can handle
more complicated situations, such as analyzing simultaneously the effects of several
explanatory variables.
A good-fitting model has several benefits. The structural form of the model
describes the patterns of association and interaction. The sizes of the model parameters
determine the strength and importance of the effects. Inferences about the parameters
evaluate which explanatory variables affect the response variable Y , while controlling
effects of possible confounding variables. Finally, the model’s predicted values
smooth the data and provide improved estimates of the mean of Y at possible
explanatory variable values.
The models this book presents are generalized linear models. This broad class of
models includes ordinary regression and ANOVA models for continuous responses
as well as models for discrete responses. This chapter introduces generalized linear
models for categorical and other discrete response data. The acronym GLM is
shorthand for generalized linear model.
Section 3.1 defines GLMs. Section 3.2 introduces GLMs for binary responses. An
important special case is the logistic regression model, which Chapters 4–6 present in
detail. Section 3.3 introduces GLMs for responses for an outcome that is a count. An
important special case is the loglinear model, the subject of Chapter 7. Section 3.4
discusses inference and model checking for GLMs, and Section 3.5 discusses ML
fitting.
An Introduction to Categorical Data Analysis, Second Edition. By Alan Agresti
Copyright © 2007 John Wiley & Sons, Inc.
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