# [R-meta] Simple Bayesian meta-analysis in R

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Sun Oct 6 00:03:58 CEST 2019

```Dear Gaspar,

Yes, your model code is correct.

I don't know how to extract a Bayes factor here, but you can in essence examine the equivalence by looking at the coefficient corresponding to the 'version' dummy variable (this should be called something like 'beta_version' in the output). This coefficient represents the *difference* between the two versions, so if it is 0, then there is no difference. Obviously, that difference will never be exactly 0, so you can look at the 2.5% and 97.5% percentiles of the posterior distribution of that coefficient. You can be 95% certain that the difference falls within these bounds.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Gaspar Lukacs
Sent: Friday, 27 September, 2019 17:45
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Simple Bayesian meta-analysis in R

Hi,

I'd like to conduct a Bayesian meta-analysis in R in order to support
equivalence between the effects of two design types (within each study).
E.g., Bayes factors would be perfect.

The metaBMA package seems to imply that I can get simple Bayes factors for
a moderator in a meta-analysis. (Most other Bayesian packages don't seem to
allow moderators.) But I don't find any info about how exactly to use it
and/or how to interpret the output.

Here is a simple example:

bayes_model = metaBMA::meta_random(
y = cohens_d~version,
SE = sed,
labels = study,
data = met_bf
)

"cohens_d" is the effect in each study, separately for each of the two
levels of "version", and I would simply want to know whether there is
substantial support for the equivalence between the "version" factors. Is
this model correct? And in any case, how can I get Bayes factors out of it
(or any direct proof of equivalence)?

A more detailed description of the question is here (where I was suggested
this mailing list):
https://stats.stackexchange.com/questions/428654/simple-bayesian-meta-analysis-in-r

I'd much appreciate any help.

Best,
Gaspar

```