ABSTRACT
This chapter reviews generalized linear models from a Bayesian perspective. We discuss noninformative prior distributions, conjugate prior distributions, and, most important, hierarchical models, focusing on the normal specification for the generalized linear model coefficients. We present a computational method based on approximating the generalized linear model by a normal linear model at the mode and then obtaining exact simulations, if necessary, using the Metropolis algorithm. Finally, we discuss the class of loglinear models, a subclass of Poisson generalized linear models that is commonly used for missing data imputation and discrete multivariate outcomes. We show how to simulate from the posterior distribution of the loglinear model with noninformative and conjugate prior distributions using a stochastic version of the iterative proportional fitting algorithm. This chapter is not intended to be exhaustive, but rather to provide enough guidance so that the reader can combine generalized linear models with the ideas of hierarchical models, posterior simulation, prediction, model checking, and sensitivity analysis that we have already presented for Bayesian methods in general, and linear models in particular. Our computational strategy is based on extending available tools of maximum likelihood for fitting generalized linear models to the Bayesian case.
