Journal
BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY
Volume 72, Issue 2, Pages 316-333Publisher
WILEY
DOI: 10.1111/bmsp.12150
Keywords
Hypothesis test; Bayesian model selection; marginal likelihood; variable selection; Jeffreys-Zellner-Siow prior; general linear model
Categories
Funding
- research training group Statistical Modeling in Psychology - German Research Foundation (DFG) [GRK 2277]
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The Savage-Dickey density ratio is a simple method for computing the Bayes factor for an equality constraint on one or more parameters of a statistical model. In regression analysis, this includes the important scenario of testing whether one or more of the covariates have an effect on the dependent variable. However, the Savage-Dickey ratio only provides the correct Bayes factor if the prior distribution of the nuisance parameters under the nested model is identical to the conditional prior under the full model given the equality constraint. This condition is violated for multiple regression models with a Jeffreys-Zellner-Siow prior, which is often used as a default prior in psychology. Besides linear regression models, the limitation of the Savage-Dickey ratio is especially relevant when analytical solutions for the Bayes factor are not available. This is the case for generalized linear models, non-linear models, or cognitive process models with regression extensions. As a remedy, the correct Bayes factor can be computed using a generalized version of the Savage-Dickey density ratio.
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