Bayesian Criterion-Based Model Assessment for Categorical Data

• Activity Number: 320
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Ming-Hui Chen*+ and Dipak K. Dey and Joseph G. Ibrahim
• Companies: University of Connecticut and University of Connecticut and University of North Carolina
• Keywords: binary data ; L measure ; loss function ; model selection ; multivariate categorical response ; weighted L measure

Abstract

We propose a general Bayesian criterion for model assessment for categorical data called the weighted L measure, which is constructed from the posterior predictive distribution of the data. The weighted L measure is based on weighting the observations according to the sampling variance of their future response vector. The weight component in the weighted L measure plays the role of a penalty term in the criterion, in which a greater weight to covariate values implies a greater penalty term on the dimension of the model. Thus the weight parameter in the weighted L measure partially controls the magnitude of the penalty term in the criterion and this often results in better performance compared to other methods for model selection. In addition, we present several theoretical properties of the weighted L measure for a wide variety of discrete data models, including binary regression models, ordinal regression models, multivariate categorical response models, and discrete choice models. A detailed simulation study and a real dataset are presented to examine the performance of the weighted L measure.