this article we propose three criteria that can be used to address model selection. These emphasize observables rather than parameters and are based on a certain Bayesian predictive density. They have a unifying basis that is simple and interpretable,are free of asymptotic de#nitions,and allow the incorporation of prior information. Moreover,two of these criteria are readily calibrated.

this paper, we propose two variable and transformation selection procedures on the predictor variables in the linear model. The first procedure is a simultaneous variable and transformation selection procedure. For data sets with many predictors, a stepwise variable selection procedure is also presented. The procedures are based on Bayesian model selection criteria introduced by Ibrahim and Laud (1994) and Laud and Ibrahim (1995). Several examples are given to illustrate the methodology.

We argue for the adoption of a predictive approach to model specification. Specifically, we derive the difference between means and the ratio of determinants of covariance matrices when a subset of explanatory variables is included or excluded from a regression. For several special cases these measures are shown to be related to widely used tools for studying model specification. Results for a set of simulated data and for two economic applications are presented as examples. Thanks to Professor Siddhartha Chib for comments. An earlier version of this paper was presented at the Midwest Econometrics Group meeting at Notre Dame in September 1991. 1 1