High-Dimensional Variable Selection for Logistic Regression

• Activity Number: 541
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Naveen Naidu Narisetty*+ and Xuming He and Juan Shen
• Companies: University of Michigan and University of Michigan and University of Michigan
• Keywords: Logistic regression ; variable selection ; high dimensions ; Bayesian model

Abstract

Logistic regression is one of the most commonly used models for data with binary response. Many of the variable selection methods for logistic regression face theoretical and computational challenges when a high dimensional variable is present. We propose a new method that makes use of the normal scale mixture representation of the logistic distribution and places priors on the regression coefficients, similar to the well-known spike and slab priors but with well-controlled prior variances. Such prior distributions achieve appropriate shrinkage of the coefficients while allowing computationally efficient Gibbs sampling of the posterior. The proposed method is strongly consistent for model selection even when the number of covariates is much larger than the sample size. Through simulation studies, we demonstrate the fine performance of the method in comparison with some of the state of the art methods in the literature.