[R-meta] Sigma in Bayesian Multi-Level Meta-Analytic Models (brms)

[Yefeng Yang]

Dear Hanna and Wolfgang,

Just jump in. I have a following-up question regarding Wolfgang's comment about 'yi | se(sei, sigma=TRUE) ~ ...'

If setting 'sigma=TRUE' is equivalent to add an estimate level random effect and if in the random part of the model I do not have (1 | estimate) (which means there is no redundant effect level random effect), whether "bf(y ~ X + (1 | study), sigma ~ 1 + X)" is equivalent to a location-scale meta-analysis?

All the best,
Yefeng

________________________________
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> on behalf of Viechtbauer, Wolfgang (NP) via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org>
Sent: Thursday, January 9, 2025 23:43
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Cc: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>
Subject: Re: [R-meta] Sigma in Bayesian Multi-Level Meta-Analytic Models (brms)

Dear Hanna,

Correct, when you use something like 'yi | se(sei) ~ ...' in brms, then the known standard errors replace the sigma parameter, which is just set to 0 (and given as such in the output). So sigma here is not an estimate but simply a fixed value. See help(brmsformula).

It is possible to use 'yi | se(sei, sigma=TRUE) ~ ...', where sigma will be estimated. However, this just adds a regular error term to the model, which would be redundant with an estimate level random effect (i.e., (1 | estimate)), which should be part of the model anyway.

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of Hanna M��tze via R-sig-meta-analysis
> Sent: Thursday, January 9, 2025 11:19
> To: r-sig-meta-analysis using r-project.org
> Cc: Hanna M��tze <muetzeh using uni-bremen.de>
> Subject: [R-meta] Sigma in Bayesian Multi-Level Meta-Analytic Models (brms)
>
> Dear all,
>
> I conducted a Bayesian 3-level meta-analysis with |brms| and noticed
> that �� is consistently estimated as 0, even in 2-level and 4-level
> models. I observed the same behavior in this tutorial:
> https://mvuorre.github.io/posts/2016-09-29-bayesian-meta-analysis/#ref-
> mcelreathStatisticalRethinkingBayesian2020.
> How should I interpret this result?
>
> How should I interpret this result? Am I correct in assuming that
> Bayesian models do not estimate the sampling error because it is assumed
> to be known based on the sample size? Unfortunately, I could not find
> references supporting this interpretation and would appreciate any
> clarification or guidance.
>
> Thank you for your time and help!
>
> Best regards,
> Hanna M��tze
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