Bayesian predictive simultaneous variable and transformation selection in the linear model

Abstract

Variable selection and transformation selection are two commonly encountered problems in the linear model. It is often of interest to combine these two procedures in an analysis. Due to recent developments in computing technology, such a procedure is now feasible. In 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 backward elimination procedure for variables and transformations 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.