Objective Bayes Model Selection in Probit Models

• Activity Number: 612
• Type: Topic Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: ENAR
• Author(s): Luis León-Novelo*+ and George Casella and Elías Moreno
• Companies: University of Florida and University of Florida and University of Granada
• Keywords: Intrinsic Priors ; Bayes Factors ; Model Selection ; Probit Models ; Stochastic Search ; Linear model

Abstract

We describe a variable selection procedure for categorical responses where the candidate models are all probit regression models having a potential set of $k$ covariates. The procedure uses objective intrinsic priors for the model parameters, which do not depend on tuning parameters, and ranks the models for the different subsets of covariates according to their model posterior probabilities. When $k$ is moderate or large, the number of potential models can be very large, and for those cases we derive a new stochastic search algorithm that explores the potential sets of models driven by their model posterior probabilities. The algorithm allows the user to control the dimension of the candidate models, and thus can handle situations when the number of covariates exceed the number of observations. Lastly, we assess, through simulations, the accuracy of the procedure, and apply the variable selector to a gene expression data set, where the response is whether a patient exhibits pneumonia.