Approximate Bayes factors and accounting for model uncertainty in generalised linear models

Abstract

Ways of obtaining approximate Bayes factors for generalised linear models are described, based on the Laplace method for integrals. We propose a new approximation which uses only the output of standard computer programs for estimating generalised linear models, this appears to be quite accurate. A reference set of proper priors is suggested, both to represent the situation where there is not much prior information, and to assess the sensitivity of the results to the prior distribution. The methods can be used when the dispersion parameter is unknown, when there is overdispersion, to compare link functions, and to compare error distributions and variance functions. The methods can be used to implement the Bayesian approach to accounting for model uncertainty. We describe an applciation to inference about relative risks in the presence of control factors where model uncertainty is large and important. Software to implement the methods is available at no cost from StatLib.