Data Augmentation Strategies for the Bayesian Spatial Probit Regression Model

• Activity Number: 161
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Candace Berrett*+ and Catherine Calder
• Companies: The Ohio State University and The Ohio State University
• Keywords: Spatial statistics ; Latent variable methods ; Categorical data ; MCMC

Abstract

Widely recognized data augmentation methods for the Bayesian probit regression model readily allow commonly used covariance structures in the normal linear model to be adapted to the generalized linear model setting, e.g., the Bayesian spatial probit regression model. However, the variance parameter in this model is not identifiable. This problem can be overcome either by fixing the value of the variance parameter or by specifying proper priors and reporting inferences on the properly normalized regression coefficients. Within the data augmentation MCMC class of algorithms, these approaches can be viewed as conditional and marginal augmentation, respectively, where the non-identifiable variance serves as a working parameter. We compare various versions of these algorithms for the Bayesian spatial probit regression model using a simulation study and an analysis of land cover data.