  In this work we apply the methodology of integral priors to handle Bayesian
model selection in binomial regression models with a general link function.
These models are very often used to investigate associations and risks in
epidemiological studies where one goal is to exhibit whether or not an exposure
is a risk factor for developing a certain disease; the purpose of the current
paper is to test the effect of specific exposure factors. We formulate the
problem as a Bayesian model selection case and solve it using objective Bayes
factors. To construct the reference prior distributions on the regression
coefficients of the binomial regression models, we rely on the methodology of
integral priors that is nearly automatic as it only requires the specification
of estimation reference priors and it does not depend on tuning parameters or
on hyperparameters within these priors.
