Raftery, Adrian E. Approximate Bayes factors and accounting for model uncertainty in generalised linear models. (English) Zbl 0864.62049 Biometrika 83, No. 2, 251-266 (1996). Summary: 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 application 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. Cited in 1 ReviewCited in 85 Documents MSC: 62J12 Generalized linear models (logistic models) 62F15 Bayesian inference 65C99 Probabilistic methods, stochastic differential equations Keywords:Bayesian model averaging; logistic regression; log-linear model; odds ratio; approximate Bayes factors; Laplace method for integrals; reference set of proper priors; overdispersion; link functions; error distributions; variance functions; model uncertainty; relative risks Software:LISP-STAT PDFBibTeX XMLCite \textit{A. E. Raftery}, Biometrika 83, No. 2, 251--266 (1996; Zbl 0864.62049) Full Text: DOI Link