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

[Viechtbauer, Wolfgang (NP)]

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 Mütze via R-sig-meta-analysis
> Sent: Thursday, January 9, 2025 11:19
> To: r-sig-meta-analysis using r-project.org
> Cc: Hanna Mütze <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 σ 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 Mütze