BAYESIAN ANALYSIS OF A RANDOM LINK FUNCTION IN BINARY RESPONSE REGRESSION by

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. We assume that the inverse link function H is a random member of the class of normal scale mixture cdfs. We propose three di erent models for this random H : (i) H is a nite scale mixture with a Dirichlet distribution prior on the mixing distribution; (ii) H is a general scale mixture, the mixing distribution has a Dirichlet process prior; and (iii) H is a scale mixture of truncated normal distributions with the mixing distribution having a Dirichlet prior. We describe Bayesian analyses of these models using data augmentation and Gibbs sampling. Model diagnostics by cross validation of the conditional predictive distributions are proposed. These analyses are illustrated in two examples. Our proposed models match the performances of Bayesian probit and t link models in the rst example whereas they outperform probit and t link models in the second example.