Abstract. This chapter extends the linear model introduced in Chapters 1–8 and the binary dependent-variable model in Chapter 9 to the generalized linear model formulation. Generalized linear models (GLMs) represent an important class of nonlinear regression models that have found extensive use in practice. In addition to the normal and Bernoulli distributions, these models include the binomial, Poisson, and Gamma families as distributions for dependent variables.

Section 10.1 begins this chapter with a review of homogeneous GLMs, models that do not incorporate heterogeneity. The Section 10.2 example reinforces this review. Section 10.3 then describes marginal models and generalized estimating equations, a widely applied framework for incorporating heterogeneity. Then, Sections 10.4 and 10.5 allow for heterogeneity by modeling subject-specific quantities as random and fixed effects, respectively. Section 10.6 ties together fixed and random effects under the umbrella of Bayesian inference.