Bayesian Robust Multivariate Linear Regression with Incomplete Data

The multivariate t distribution and other normal/independent multivariate distributions, such as the multivariate slash distribution and the multivariate contaminated distribution, are used for robust regression with complete or incomplete data. Most previous work focused on the method of maximum likelihood estimation for linear regression using normal/independent distributions. This article considers Bayesian estimation of multivariate linear regression models using normal/independent distributions with fully observed predictor variables and possible missing values from outcome variables. A monotone data augmentation algorithm for posterior simulation of the parameters and missing data imputation is presented. The posterior distributions of functions of the parameters can be obtained using Monte Carlo methods. The monotone data augmentation algorithm can also be used for creating multiple imputations for incomplete data sets. An illustrative example of using the multivariate t is also included.