Bayesian Criterion Based Model Assessment for Categorical Data

Model selection criteria for categorical data pose a challenge to the discreteness of the data structure and the properties attributable to discrete data models. In this presentation, I 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 measure is based on weighting the observations according to their covariate values, which is crucial for categorical data. In addition, the weight component plays the role of penalty term on the dimension of the model. Thus the weight parameter partially controls the magnitude of the penalty term in the criterion and this often! results in better performance compared to the other methods for model comparison. In addition, we show that the weighted quadratic L measure is more attractive than the deviance loss L measure for categorical data. A detailed simulation study is presented to examine the performance of the weighted L measure, and is compared to other established methods such as AIC, BIC and DIC. Finally, a real data set using a bivariate ordinal response model is used to further illustrate the proposed methodology.

This is a joint work with M-H. Chen and J. Ibrahim