RBA - Bayes factor

Dear experts,

we have been using Gang Chen's et al Region Based analysis program for a while now in our neuroimaging analyses and are very pleased with the ease of use, the nice plots (and great results)! We have however increasingly getting questions from co-authors and reviewers whether it is also possible to derive Bayes factors from the analyses to not only infer the likelihood of the alternative but also the null hypothesis as I don't think that you can claim that there is credible evidence for the null hypothesis when the P+ value is close to 0.50 (or am I wrong )? I know that there are R packages out there with which you can calculate a Bayes factor for a single outcome variable but those cannot take into account the interdependency between the ROIs as RBA does.
long story short: Is it possible to calculate/derive a Bayes factor per ROI from the RBA (*.Rdata) output?

many thanks and best wishes, Chris

Welcome on board, Chris!

It's great to hear that the RBA program has been beneficial in your analytical journey. The approach implemented in RBA involves using a single model that incorporates all brain regions. The Bayes factor concept is typically used for comparing two models. Therefore, I find it challenging to apply the Bayes factor in this context. Do you have any specific suggestions on how to implement it in this scenario?

Gang Chen

thanks Gang!
Specifics on how to implement it are unfortunately beyond me but I've for example previously used the BayesFactor R package ( CRAN: Package BayesFactor) to compute the BF for two-group comparisons (for single outcomes). Do I understand you correctly that even if between-subjects factor (e.g. group) is specified as EOI, RBA can only draw the positive posterior distributions and no BF because it estimates the difference in one model? If so, is there another way to make claims about the credibility of the null hypothesis (i.e. no difference between groups) using the RBA output?

thanks, Chris


The R pacakge BayesFactor you mentioned does not appear to support any Bayesian modeling methods such as brms.

is there another way to make claims about the credibility of the null hypothesis (i.e. no difference between groups) using the RBA output?

One possible approach is to adopt a ROPE (Region of Practical Equivalence) test that can be used to determine whether the difference between two groups is practically small. Specifically, you define the range around the null value that represents practical equivalence. For example, if differences smaller than ±0.3 are considered negligible, the ROPE could be set to [−0.3,0.3]. If a large proportion (e.g., 95% or more) of the posterior distribution falls within the ROPE, you can conclude that the difference between the two groups is practically equivalent to zero.

See this paper for more discussion about ROPE: Kruschke, J. K., & Liddell, T. M. (2018). The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Psychonomic Bulletin & Review, 25, 178–206. doi:10.3758/s13423-016-1221-4

Gang Chen

thanks for the tip, Gang. I will have a look at the paper and test.