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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
1 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)197-220
Number of pages24
JournalTEST
Volume27
Issue number1
Early online date18 May 2017
DOIs
Publication statusPublished - Mar 2018

Keywords

  • Categorical variables
  • Contingency tables
  • Mixtures of g-priors
  • Prior correspondence
  • Posterior correspondence

Fingerprint

Dive into the research topics of 'On the correspondence from Bayesian log-linear modelling to logistic regression modelling with g-priors'. Together they form a unique fingerprint.

Cite this