@article {Heck:2019:0007-1102:316,
title = "A caveat on the SavageDickey density ratio: The case of computing Bayes factors for regression parameters",
journal = "British Journal of Mathematical and Statistical Psychology",
parent_itemid = "infobike://bpl/bmsp",
publishercode ="bp",
year = "2019",
volume = "72",
number = "2",
publication date ="2019-05-01T00:00:00",
pages = "316-333",
itemtype = "ARTICLE",
issn = "0007-1102",
eissn = "2044-8317",
url = "https://www.ingentaconnect.com/content/bpl/bmsp/2019/00000072/00000002/art00006",
doi = "doi:10.1111/bmsp.12150",
keyword = "Bayesian model selection, marginal likelihood, general linear model, Jeffreysâ€“Zellnerâ€“Siow prior, Hypothesis test, variable selection",
author = "Heck, Daniel W.",
abstract = "The SavageDickey 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 SavageDickey 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 JeffreysZellnerSiow prior, which is often used as a default prior in psychology. Besides linear regression models, the limitation of the SavageDickey ratio is especially relevant when analytical solutions for the Bayes
factor are not available. This is the case for generalized linear models, nonlinear models, or cognitive process models with regression extensions. As a remedy, the correct Bayes factor can be computed using a generalized version of the SavageDickey density ratio.",
}