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

[Viechtbauer, Wolfgang (NP)]

> -----Original Message-----
> From: Yefeng Yang <yefeng.yang1 using unsw.edu.au>
> Sent: Friday, January 10, 2025 05:24
> To: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer using maastrichtuniversity.nl>; R
> Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
> Subject: Re: [R-meta] Sigma in Bayesian Multi-Level Meta-Analytic Models (brms)
>
> Dear Wolfgang,
>
> Thank you for your confirmation and clarification. I have a further question. It
> is clear to me that for a dataset with dependent effect sizes, bf(yi | se(sei,
> sigma=TRUE) ~ X + (1 | study), sigma ~ X) will model location and estimate level
> scale parameter (or we call it effect size level in the context of meta-
> analysis) as a function of X.
>
> But for a dataset with independent effect sizes (where between-study level is
> equal to estimate level), what sort of scale parameter will be modelled by bf(yi
> | se(sei, sigma=TRUE) ~ X + (1 | study), sigma ~ X)? (1 | study) already
> accounts for all random effects and there is nothing left for  'sigma ~ X'.

That was my point earlier in the thread. Do NOT use sigma=TRUE and also add an estimate level random effect at the same time, since it is redundant.

> Another question is that a dataset with dependent effect sizes, if I want to
> model between-study variance (rather than estimate level) as a function of 'X',
> what the syntax will be?

Don't know off the top of my head if this is possible with brms().

> Happy to see your comment on these.
>
> Thanks,
> Yefeng
>
> ________________________________________
> From: Viechtbauer, Wolfgang (NP)
> <mailto:wolfgang.viechtbauer using maastrichtuniversity.nl>
> Sent: Friday, January 10, 2025 3:59
> To: Yefeng Yang <mailto:yefeng.yang1 using unsw.edu.au>; R Special Interest Group for
> Meta-Analysis <mailto:r-sig-meta-analysis using r-project.org>
> Subject: RE: [R-meta] Sigma in Bayesian Multi-Level Meta-Analytic Models (brms)
>
> Dear Yefeng,
>
> Yes, that is correct. To be precise, it should be:
>
> bf(yi | se(sei, sigma=TRUE) ~ X, sigma ~ X)
>
> Note that brms() parameterizes the scale part as log(tau) and not as log(tau^2)
> as is done in rma(), so the coefficients will be about half of the size (and of
> course can differ due to the priors).
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: Yefeng Yang <mailto:yefeng.yang1 using unsw.edu.au>
> > Sent: Thursday, January 9, 2025 14:50
> > To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-
> > project.org>
> > Cc: Viechtbauer, Wolfgang (NP)
> <mailto:wolfgang.viechtbauer using maastrichtuniversity.nl>
> > Subject: Re: [R-meta] Sigma in Bayesian Multi-Level Meta-Analytic Models
> (brms)
> >
> > 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 <mailto:r-sig-meta-analysis-bounces using r-project.org>
> on
> > behalf of Viechtbauer, Wolfgang (NP) via R-sig-meta-analysis <mailto:r-sig-
> meta-
> > mailto:analysis using r-project.org>
> > Sent: Thursday, January 9, 2025 23:43
> > To: R Special Interest Group for Meta-Analysis <mailto:r-sig-meta-analysis using r-
> > project.org>
> > Cc: Viechtbauer, Wolfgang (NP)
> > <mailto: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 <mailto: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: mailto:r-sig-meta-analysis using r-project.org
> > > Cc: Hanna Mütze <mailto: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