The Generalized Linear Model

Abstract

With generalized linear model (GLM) two important issues surface: the distribution of the response and the model that relates the mean response to the regression variables. This chapter first deals with GLMs in the general framework along with illustrations as to how it applies in the special cases of the binomial and Poisson cases. An important unifying concept underlying the GLM is the exponential family of distributions. The chapter emphasizes the use of maximum likelihood estimation for the parameter vector β in the GLM. Exponential and gamma distributions are the two important response distributions. The chapter explains modeling both a process mean and process variance using GLM, and discusses two different approaches: when there is true replication, and when there is no replication, in which case the residuals can be used as the basis for modeling the variance. The chapter also discusses the quality of asymptotic results. Controlled Vocabulary Terms binomial distribution; gamma distribution; maximum likelihood estimation; mean; Poisson distribution; residual analysis