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

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  • Michail Papathomas

    (University of St Andrews)

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.

Suggested Citation

  • Michail Papathomas, 2018. "On the correspondence from Bayesian log-linear modelling to logistic regression modelling with g-priors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 197-220, March.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:1:d:10.1007_s11749-017-0540-8
    DOI: 10.1007/s11749-017-0540-8
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    References listed on IDEAS

    as
    1. M. Papathomas & P. Dellaportas & V. G. S. Vasdekis, 2011. "A novel reversible jump algorithm for generalized linear models," Biometrika, Biometrika Trust, vol. 98(1), pages 231-236.
    2. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
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