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A caveat on the Savage–Dickey density ratio: The case of computing Bayes factors for regression parameters
Author(s) -
Heck Daniel W.
Publication year - 2019
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/bmsp.12150
Subject(s) - bayes factor , mathematics , econometrics , statistics , bayes' theorem , covariate , regression analysis , linear regression , conditional probability distribution , constraint (computer aided design) , linear model , prior probability , regression , bayesian probability , geometry
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.