  Bayesian model selection poses two main challenges: the specification of
parameter priors for all models, and the computation of the resulting Bayes
factors between models. There is now a large literature on automatic and
objective parameter priors in the linear model. One important class are
$g$-priors, which were recently extended from linear to generalized linear
models (GLMs). We show that the resulting Bayes factors can be approximated by
test-based Bayes factors (Johnson [Scand. J. Stat. 35 (2008) 354-368]) using
the deviance statistics of the models. To estimate the hyperparameter $g$, we
propose empirical and fully Bayes approaches and link the former to minimum
Bayes factors and shrinkage estimates from the literature. Furthermore, we
describe how to approximate the corresponding posterior distribution of the
regression coefficients based on the standard GLM output. We illustrate the
approach with the development of a clinical prediction model for 30-day
survival in the GUSTO-I trial using logistic regression.
