On the correspondence between Bayesian log-linear and logistic regression models with g-priors
Michail Papathomas · arXiv (Cornell University) · 2014
Consider a set of categorical variables where at least one of them is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the outcome. We prove that assigning a g-prior to the parameters of the log-linear model designates a g-prior on the parameters of the corresponding logistic regression. Consequently, it is valid to translate inferences from fitting a log-linear model to inferences within the logistic regression framework, with regard to the presence of main effects and interaction terms.