Informative g-Priors for Logistic Regression

Abstract

Eliciting information from experts for use in constructing prior distributions for logistic regression coefficients can be challenging. The task is especially difficult when the model contains many predictor variables, because the expert is asked to provide summary information about the probability of “success” for many subgroups of the population. Often, however, experts are confident only in their assessment of the population as a whole. This paper is about incorporating such overall information easily into a logistic regression data analysis using $g$-priors. We present a version of the $g$-prior such that the prior distribution on the overall population logistic regression probabilities of success can be set to match a beta distribution. A simple data augmentation formulation allows implementation in standard statistical software packages.