Objective Bayesian Variable Selection for Logistic Regression Models with Jeffreys' Prior

• Activity Number: 461
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2007 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ming-Hui Chen*+ and Joseph G. Ibrahim and Sung Duk Kim
• Companies: University of Connecticut and The University of North Carolina at Chapel Hill and University of Connecticut
• Keywords: BIC ; Importance sampling ; Normalizing constant ; Posterior probability ; Tail behavior ; Variable selection

Abstract

We study several theoretical properties of Jeffreys' prior for logistic regression models with a focus on its applications to variable selection problems. We show that Jeffreys' prior is symmetric and unimodal about 0 and always has lighter tails than a t distribution and heavier tails than a normal distribution. We also develop an efficient importance sampling algorithm for calculating the prior and posterior normalizing constants based on Jeffreys' prior. Moreover, we show that the prior and posterior normalizing constants under Jeffreys' prior are scale invariant in the covariates. A closed form for Jeffreys' prior is obtained for saturated logistic regression models with binary covariates. Detailed simulation studies are presented to demonstrate its properties and performance and a real dataset is also analyzed to further illustrate the proposed methodology.