Bootstrap model selection in generalized linear models

Model selection is a central component of data analysis. Though there are a variety of methods for likelihood-based estimation methods, there are relatively few for non-likelihood-based generalized linear models (GLMs), such as in the quasi-likelihood and generalized estimating equation (GEE) approaches. In this paper, we develop basic and bias-corrected bootstrap approaches to estimate the predictive mean squared error (PMSE) of a model and use the PMSE for model selection. Simulation studies show that the bias-corrected bootstrap estimate works well when quasi-likelihood or GEE is used to fit either overdispersed or correlated response GLMs. For correlated response data, when the marginal distribution assumption is (almost) correct, Akaike's information criterion (AIC) and Bayesian information criterion (BIC) calculated under the working independence model also perform well. For illustration, the methods are applied to data sets from evolutionary biology and teratology.