[R-meta] multivariate meta-analysis assuming the correlation

[Reza Norouzian]

Dear Filippo,

The rho argument in the rma.mv() function has to do with with correlation
between the *true* effects specified via the first ~ inner | outer term in
the `random` argument (a modeling assumption). Except for certain cases,
one may use the rho argument for model comparison purposes.

The (block diagonal) var-covariance matrix input via the V argument carries
the var-covariance between the *observed* effect size estimates due to the
overlapping participant information in the individual studies included in
the meta-analysis (a data reality).

So, these are two different types of correlation. If, for each study, you
construct the V matrix the way you showed, then you have assumed that the
correlation among observed effects is constant in all studies leading to a
compound symmetry structure for the var-covariance matrix for observed
effect size estimates in each study.

Kind regards,
Reza

On Sat, Nov 6, 2021 at 2:17 PM Filippo Gambarota <
filippo.gambarota using gmail.com> wrote:

> Hi,
> I'm trying to do a multivariate meta-analysis without knowing the full
> variance-covariance matrix for the effects. So I would like to create
> a covariance matrix like in Berkley et al. (1988) example on metafor.
> I'm wondering if creating a matrix with all off-diagonal elements the
> covariance computed as: rho(assumed) * v1 * v2 is the same as fixing
> the rho value within the rma.mv function to my assumed correlation.
> Thank you!
>
> --
> Filippo Gambarota
>
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