ABSTRACT
Binomial regression uses predictor variables to estimate the probability that some event will happen. Section 1 introduces three examples and discusses the sampling model. The first example examines the relationships between O-ring failures on space shuttles and launch temperatures. The second example looks at domestic and international students enrolled in graduate school. This is really a two independent binomials problem as discussed in Subsection 5.1.3 but here is discussed using the terminology of logistic regression. The final example involves survival of patients at a trauma center. The three examples are carried throughout the chapter. Section 2 presupposes that the priors are known and examines the posterior analysis. Section 3 considers two aspects of model checking: Box’s significance test using the marginal distribution of the data and Bayes factors for examining alternative modeling strategies. Much of the heavy lifting occurs in Section 4, which discusses the choice of prior distributions. Section 5 examines random effects models for logistic regression. This chapter owes much to Bedrick, Christensen, and Johnson [BCJ] (1996, 1997) and to an unpublished early version of the 1997 article also discussed in Christensen (1997, Chapter 13).
