Bayesian Variable Selection for Generalized Linear Models Using the Power-Conditional-Expected-Posterior Prior

Abstract

The power-conditional-expected-posterior (PCEP) prior developed for variable selection in normal regression models combines ideas from the power-prior and expected-posterior prior, relying on the concept of random imaginary data, and provides a consistent variable selection method which leads to parsimonious selection. In this paper, the PCEP methodology is extended to generalized linear models (GLMs). We define the PCEP prior in the GLM setting, explain the connections to other default model-selection priors, and present various posterior representations which can be used for model-specific posterior inference or for variable selection. The method is implemented for a logistic regression example with Bernoulli data. Results indicate that the PCEP prior leads to parsimonious selection for logistic regression models, similarly to the case of normal regression. Current limitations in generalizing the applicability of PCEP and possible solutions are discussed.