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

[Simon Harmel]

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
>

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