Variable Selection or Variable Assessment?

Abstract

Variable-selection regression methods are oriented towards selecting a single model as the vehicle for further inferences. The appropriate inference about variables not included is unclear - the conclusion that they have no effect may be misleading. In many situations, the objective of the statistical method should be to assess the relative importance of every variable. The term variable assessment we think is more descriptive of this objective. We develop a method for variable assessment that makes use of Bayesian model-selection methodology. The marginal posterior probability that a variable is needed in the model is a measure of its importance. Using the Gibbs sampler for computation greatly reduces CPU requirements and also allows us to extend the model to one that allows for outliers. A simulation demonstrates that the method has good statistical properties.