Model Selection: An Integral Part of Inference

Abstract

We argue that model selection uncertainty should be fully incorporated into statistical inference whenever estimation is sensitive to model choice and that choice is made with reference to the data. We consider different philosophies for achieving this goal and suggest strategies for data analysis. We illustrate our methods through three examples. The first is a Poisson regression of bird counts in which a choice is to be made between inclusion of one or both of two covariates. The second is a line transect data set for which different models yield substantially different estimates of abundance. The third is a simulated example in which truth is known.