Introduction to Linear Regression Analysis, 5th Edition

CHAPTER 13

GENERALIZED LINEAR MODELS

13.1 INTRODUCTION

In Chapter 5, we developed and illustrated data transformation as an approach to fitting regression models when the assumptions of a normally distributed response variable with constant variance are not appropriate. Transformation of the response variable is often a very effective way to deal with both response nonnormality and inequality of variance. Weighted least squares is also a potentially useful way to handle the non-constant variance problem. In this chapter, we present an alternative approach to data transformation when the “usual” assumptions of normality and constant variance are not satisfied. This approach is based on the generalized linear model (GLM).

The GLM is a unification of both linear and nonlinear regression models that also allows the incorporation of nonnormal response distributions. In a GLM, the response variable distribution must only be a member of the exponential family, which includes the normal, Poisson, binomial, exponential, and gamma distributions as members. Furthermore, the normal-error linear model is just a special case of the GLM, so in many ways, the GLM can be thought of as a unifying approach to many aspects of empirical modeling and data analysis.

We begin our presentation of these models by considering the case of logistic regression. This is a situation where the response variable has only two possible outcomes, generically called success and failure and denoted by 0 and 1. Notice ...