Bayesian Analysis of Binary Regression Using Symmetric and Asymmetric Links

Binary response regression is a useful technique for analyzing categorical data. Popular binary models use special link functions such as the logit or the probit link. In this article, the inverse link function H is modeled to be a scale mixture of cumulative distribution functions. Two different models for H are proposed: (i) H is a finite normal scale mixture with a Dirichlet distribution prior on the mixing distribution; and (ii) H is a scale mixture of truncated normal distributions with the mixing distribution having a Dirichlet prior. The second model allows symmetric as well as asymmetric links. Bayesian analyses of these models using data augmentation and Gibbs sampling are described. Model diagnostics by cross validation of the conditional predictive distributions are proposed. These analyses are illustrated in the Beetle mortality data and the Challenger o-ring distress data.