Bayes Anova output calculations

Perseus78

Hello

Please see http://callistoscraters.com/node/101

This was created with the app Jasp. I just cant replicate how the BF10 Factors are computed out of above classical Anova. The guides on other websites dont seem to address this and I have tried everything. I tried to calculate the BF10 usi g the BIC, but I get different results.

Could you please tell me, for example, how BF10 of 1.074 was calculated? Number of subjects was: 112. Basically I need the formulas for all the output numbers - I need to report them in my paper if I want to apply Bayes statistics.

Thank you very much.

EJ

Hi Perseus,

The Bayesian ANOVA is not computed from the classical ANOVA. Instead, the Bayesian ANOVA is obtained by applying the "Jeffreys Zellner Siow" framework developed in regression and the t-test to the case of ANOVA. An introductory treatment is here: Rouder, J. N., Morey, R. D., Verhagen, A. J., Swagman, A. R., & Wagenmakers, E.-J. (in press). Bayesian analysis of factorial designs. Psychological Methods. http://www.ejwagenmakers.com/inpress/RouderEtAlinpressANOVAPM.pdf

Note that the go-to reference is a 2012 JMP paper by Rouder and colleagues. It is relatively technical material though.

Cheers,
E.J.

Perseus78

Hi E.J. - thank you for responding!

I thought the BF10 is calculated (approximated) via the BIC - according to the procedure here: http://truebra.in/?p=673#comment-115

Do you know of a corresponding way of calculating Bayes Factors from BICs for models in a two-way between-subjects Anova?

Thanks again.

EJ

Hi Perseus,

Yes, BIC is an approximation to the Bayes factor, and you can use the transformations shown in the blog to make that more clear. But there is no "single" Bayes factor -- the JZS approach can be viewed as just a somewhat more intelligent approach.

But in general, whenever you have a BIC, you can apply the transformations and get a "BIC-based Bayes factor" (see the Mike Masson papers). I believe there are R packages that provide BIC for ANOVA-style objects. Nevertheless, with a JZS BF in hand, I am not sure why you would want to opt for the less sophisticated approach.

Cheers,
E.J.

Perseus78

Hello E.J. - I guess the BIC-based approach is appealing because it is rather simple to calculate. My problem is that when I apply the procedure outlined in the blog, I don't get the BF10 that Jasp is getting. But then, I suppose I rather have to contact the author of the blog :-)
Thanks for your replies.

EJ

Hi Perseus

You won't get the BF10 from JASP. The BF10 from JASP is based on a specific set of priors; the implicit BF10 from the BIC is based on a different set of priors!

Cheers,
E.J.

ptq1

Hi

I am new to this forum and I think I have just been through the process of trying to get values for BF10 that align across JASP and standard ANOVA following the advice of Wagenmakers (2007) Glover and Dixon (2004) and Jarosz and WIley (2014). I turned to this forum as the values do not correspond.

I am now not sure what to conclude - have the methods I cite now been superseded?

With thanks in anticipation,

Philip

Philip Quinlan

EJ

Hi Philip,

JASP implements the JZS approach from Rouder et al., 2012, as implemented in the BayesFactor package. This is a more subtle approach than the BIC, although they are trying to estimate the same quantity.

Cheers,

E.J.