Computer Intensive Statistical Model Building

Abstract

We consider resampling techniques in multiple linear regression where the objective is to identify a subset of the full set of explanatory variables that best captures the behaviour of the dependent variable, but using as few explanatory variables as possible. The total number of possible subsets or models grows exponentially with the number of explanatory variables, so a full examination of all possible models rapidly becomes intractable. The standard approach to this problem is to use a sequential selection procedure which avoids having to examine all subsets. When the number of explanatory variables is large there is a possible concern that good models might be missed. It is also important to examine whether the selected “best” model is the only good choice or whether other models might be equally satisfactory. We show how bootstrap resampling can handle both concerns in a simple way. In particular resampling enables a tractably small subset of good possible models to be selected as well as providing a method for comparing these models systematically. We describe the methodology and provide two numerical examples.