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

[Filippo Gambarota]

Thank you Reza,
So If I get it correctly, for my situation need to create a
block-diagonal matrix with all off-diagonal elements equal to
variances * my assumed correlation and use the "UN" argument for the
matrix structure within rma.mv function. In other terms is like
assuming a compound symmetry structure but creating a custom V matrix


On Sat, 6 Nov 2021 at 22:25, Reza Norouzian <rnorouzian using gmail.com> wrote:
>
> 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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-- 
Filippo Gambarota
PhD Student - University of Padova
Department of Developmental and Social Psychology
Website: filippogambarota.netlify.app
Research Group: Colab   Psicostat