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

[Viechtbauer, Wolfgang (SP)]

Whether this makes sense or not depends on how we believe covariances among the sampling errors are arising. Two estimates from the same study based on the same sample of subjects (e.g., based on two different response variables) probably have correlated sampling errors. Two estimates from the same study, one for female, the other for male participants, not (the underlying true effects may still be correlated). So, the 'cluster' variable should be specified accordingly (i.e., same levels for the two estimates in the first case, different levels for the two estimates in the second case; i.e., 1, 1, 2, 3).

>-----Original Message-----
>From: Simon Harmel [mailto:sim.harmel using gmail.com]
>Sent: Thursday, 18 March, 2021 12:53
>To: Viechtbauer, Wolfgang (SP)
>Cc: R meta
>Subject: Re: [R-meta] Multivariate meta-analysis when "some studies" are multi-
>outcome
>
>Dear Wolfgang,
>
>Many thanks for your response. The reason I asked which level of dependence does V
>matrix account for was that I realized (at least when using
>'impute_covariance_matrix()' function) that always the highest cluster level
>(e.g., study_id rather than outcome_id or es_id) is used to construct the V
>matrix.
>
>So, is there a reason for that?
>
>Many thanks
>
>On Thu, Mar 18, 2021, 6:38 AM Viechtbauer, Wolfgang (SP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>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