Bayesian model selection for generalized linear models using non-local priors

Abstract

Variable selection is currently an important research topic under both frequentist and Bayesian framework. While most developments in Bayesian model selection literature are based on a local prior on regression parameters, a nonlocal prior for model selection can be also used. In this article, we extend nonlocal prior approach to logistic regression and to generalized linear models. Laplace approximation is used in implementation to avoid integration in the likelihood. A convergence rate is derived under some regularity conditions. The selection based on a nonlocal prior eliminates unnecessary variables and recommends a simple model. The method is validated by simulation study and illustrated by a real data example.