[R-meta] weight in rmv metafor

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Thu Jun 11 15:33:02 CEST 2020

Dear Norman,

To give a simple example: When (some of the) studies contribute multiple estimates, the dataset has a multilevel structure (with estimates nested within studies). A common way to deal with this is to fit a multilevel model with random effects for studies and estimates within studies. Like this:


However, multiple estimates from the same study are actually often computed based on the same sample of subjects. In that case, the sampling errors are also correlated. The multilevel model does not capture this. For this, one would ideally want to fit a model that also allows for correlated sampling errors. Like this:


However, computing the covariances between the sampling errors within a study is difficult and requires information that is often not available.

We can ignore those correlations and use the multilevel model as a working model that is an approximation to the model that also accounts for correlated sampling errors. After fitting the multilevel model with rma.mv(), one can then use cluster robust inference methods to 'fix things up'.

Quite a bit of this has been discussed at length in previous posts on this mailing list. You might want to search the archives for some of these posts.


>-----Original Message-----
>From: Norman DAURELLE [mailto:norman.daurelle using agroparistech.fr]
>Sent: Thursday, 11 June, 2020 15:05
>To: Viechtbauer, Wolfgang (SP)
>Cc: r-sig-meta-analysis
>Subject: Re: [R-meta] weight in rmv metafor
>Thank you.
>I am not sure I understand exactly what you mean by " if the working model
>is only an approximation and doesn't cover all dependencies ".
>Could you please explain it ?
>For now I used the rma() function to synthesize the available literature
>existing on the blackleg - oil seed rape disease-yield relationship, using
>slopes as effect-sizes.
>the models that gave me the slopes I used in the meta-analysis are all Y = a
>+ bX, simple linear regressions with Y being the yield and X being the
>diseqse severity.
>So my slopes, b, are all negative, and I have obtained a "summary" effect
>size through the rma() function.
>But I indeed have two studies that for now contribute to most of the effect-
>sizes that are included in my meta-analysis.
>So why exactly is it necessary to use the rma.mv() function ?
>What exactly does the "multivariate" qualificative refer to ?
>Thank you,
>De: "Wolfgang Viechtbauer" <wolfgang.viechtbauer using maastrichtuniversity.nl>
>À: "Norman DAURELLE" <norman.daurelle using agroparistech.fr>, "r-sig-meta-
>analysis" <r-sig-meta-analysis using r-project.org>
>Envoyé: Jeudi 11 Juin 2020 22:34:55
>Objet: RE: [R-meta] weight in rmv metafor
>Dear Norman,
>If you only used rma(), then this is not correct. rma.mv() with an
>appropriately specified model (plus clubSandwich::coef_test() if the working
>model is only an approximation and doesn't cover all dependencies) would be
>more appropriate.
>>-----Original Message-----
>>From: Norman DAURELLE [mailto:norman.daurelle using agroparistech.fr]
>>Sent: Thursday, 11 June, 2020 14:13
>>To: r-sig-meta-analysis
>>Cc: Viechtbauer, Wolfgang (SP)
>>Subject: Re: [R-meta] weight in rmv metafor
>>Hi all,
>>I read this discussion and one question came to my mind : I also had some
>>studies that contributed multiple effect sizes in the meta-analysis that I
>>recently ran thanks to Dr Viechtbauer's advice.
>>For now I only used the rma function, but should I have used rma.mv because
>>of these stuides that had multiple effect sizes ?
>>Thank you !
>>De: "James Pustejovsky" <jepusto using gmail.com>
>>À: "Wolfgang Viechtbauer" <wolfgang.viechtbauer using maastrichtuniversity.nl>
>>Cc: "r-sig-meta-analysis" <r-sig-meta-analysis using r-project.org>, "Huang Wu"
>><huang.wu using wmich.edu>
>>Envoyé: Mercredi 10 Juin 2020 05:08:09
>>Objet: Re: [R-meta] weight in rmv metafor
>>Hi Huang,
>>I've written up some notes that add a bit of further intuition to the
>>discussion that Wolfgang provided. The main case that I focus on is a model
>>that is just a meta-analysis (i.e., no predictors) and that includes random
>>effects to capture both between-study and within-study heterogeneity. I
>>also say a little bit about meta-regression models with only study-level
>>On Sun, Jun 7, 2020 at 4:11 PM Viechtbauer, Wolfgang (SP) <
>>wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>>> Of course the weights "impact the estimated fixed effects". But whether
>>> studies with multiple effect sizes tend to receive more weight depends on
>>> various factors, including the variances of the random effects and the
>>> sampling error (co)variances.
>>> A more detailed discussion around the way weighting works in rma.mv
>>> models can be found here:
>>> http://www.metafor-project.org/doku.php/tips:weights_in_rma.mv_models
>>> Note that weights(res, type="rowsum") currently only works in the 'devel'
>>> version of metafor, so follow
>>> https://wviechtb.github.io/metafor/#installation if you want to reproduce
>>> this part as well.
>>> I hope this clarifies things.
>>> Best,
>>> Wolfgang

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