Variable Selection and Covariance Selection in Multivariate Regression Models

• Activity Number: 89
• Type: Contributed
• Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Christopher K. Carter*+ and Ed Cripps and Robert Kohn
• Companies: Commonwealth Scientific and Industrial Research Organization and University of New South Wales and University of New South Wales
• Keywords: cross-sectional regression ; longitudinal data ; model averaging ; Markov chain

Abstract

This article provides a general framework for Bayesian variable selection and covariance selection in a multivariate regression model with Gaussian errors. By variable selection we mean allowing certain regression coefficients to be zero. By covariance selection we mean allowing certain elements of the inverse covariance matrix to be zero. We estimate all the model parameters by model averaging using a Markov chain Monte Carlo simulation method. The methodology is illustrated by applying it to four real datasets. The effectiveness of variable selection and covariance selection in estimating the multivariate regression model is assessed by using four loss functions and four simulated datasets. Each of the simulated datasets is based on parameter estimates obtained from a corresponding real dataset.