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.
Within the Bayesian framework, the g-prior and mixtures of g-priors are commonly
assigned to the parameters of a generalized linear model. We prove that assigning
a g-prior (or a mixture of g-priors) to the parameters of a certain log-linear model
designates a g-prior (or a mixture of g-priors) on the parameters of the corresponding
logistic regression. By deriving an asymptotic result, and with numerical illustrations,
we demonstrate that when a g-prior is adopted, this correspondence extends to the
posterior distribution of the model parameters. Thus, 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.

EB00000004348K

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• On the correspondence from Bayesian log-linear modelling to logistic regression modelling with g-priors