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

Michail Papathomas ()
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Michail Papathomas: University of St Andrews

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 1, No 10, 197-220

Abstract: Abstract 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.

Keywords: Categorical variables; Contingency tables; Mixtures of g-priors; Prior correspondence; Posterior correspondence; 62F15 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11749-017-0540-8

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