Explanation for default priors: rm-ANOVAs in JASP
Hi there,
Apologies if someone already asked this question and I missed it.
I have used JASP (v. 0.19.3) for a Bayesian repeated measures ANOVA with its default settings. My comparisons are against a null model. Upon reporting the ANOVA in the paper, one of the reviewers asked me to justify the choice of the multivariate Cauchy prior. Based on different blogposts and papers I found on the internet, I came up with the following big picture explanation:
JASPS uses the multivariate Cauchy distribution as the prior for two complementary reasons. First, it places the greatest prior probability on small-to-moderate effect sizes (a reasonable default assumption in most psychological research) while still assigning meaningful probability to larger effects, unlike a normal prior whose tails diminish too rapidly to do so (Rouder et al., 2012). Second, and more formally, the Cauchy prior satisfies the property of consistency in information: as evidence in the data accumulates, the Bayes factor responds appropriately and without bound, rather than plateauing or behaving incorrectly under strong data (Rouder et al., 2012). This property holds for the Cauchy but not for lighter-tailed alternatives (Rouder et al., 2012).
Does this make sense? Am I missing anything?
Any help or comments are appreciated!
Cheers,
Melinda
(I have used as a reference this Rouder et al., 2012 paper: https://www.sciencedirect.com/science/article/pii/S0022249612000806#aep-acknowledgment-id18)
Comments
Yes makes sense. I would add this reference:
@ARTICLE{LiangEtAl2008,
AUTHOR = {Liang, F. and Paulo, R. and Molina, G. and Clyde, M. A. and Berger, J. O.},
TITLE = {Mixtures of $g$ Priors for {B}ayesian Variable Selection},
JOURNAL = {Journal of the American Statistical Association},
YEAR = {2008},
volume = {103},
pages = {410--423},
}
Thanks a lot for the quick reply. I'll make sure to also add the suggested reference! Cheers, Melinda