[R-meta] Multivariate meta-analysis when "some studies" are multi-outcome

[Viechtbauer, Wolfgang (SP)]

Dear Simon,

Roughly, whatever you put into 'random' accounts for heterogeneity in the true effects (at possibly multiple levels) and can account for possible dependencies in these true effects. Whatever you put into V accounts for the sampling variances in the estimates or more precisely, their sampling errors, and can account for possible dependencies in these sampling errors.

I use the term 'dependencies' in a very vague/broad sense here, since such dependencies (in the true effects and/or the sampling errors) can arise for all kinds of different reasons.

Best,
Wolfgang

>-----Original Message-----
>From: Simon Harmel [mailto:sim.harmel using gmail.com]
>Sent: Wednesday, 17 March, 2021 18:01
>To: Viechtbauer, Wolfgang (SP)
>Cc: Gladys Barragan-Jason; R meta
>Subject: Re: [R-meta] Multivariate meta-analysis when "some studies" are multi-
>outcome
>
>Dear Wolfgang,
>
>I do want to quickly follow-up on the answer you linked
>(https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-July/000896.html).
>
>In `rma.mv(y ~ x1 + x2, V, random = ~ 1 | study/outcome/id, data=data)`, we
>apparently take into account dependence among effect sizes due to multiple
>treatments (`id`), and multiple outcomes (`outcome`) by means of using a level for
>each.
>
>If so, what is the role of `V` when it comes to accounting for effect
>size dependency? Does `V` simply determine the pair-wise structure of effect size
>dependency? If yes, at what level?
>
>Simon