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

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Sun Nov 7 11:56:14 CET 2021

```The recently added vcalc() function in metafor allows you to do exactly that:

https://wviechtb.github.io/metafor/reference/vcalc.html

In fact, under the examples, you will find an illustration of this using the Berkley et al. (1988) data as an example.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Filippo Gambarota
>Sent: Sunday, 07 November, 2021 8:43
>To: Reza Norouzian
>Cc: R meta
>Subject: Re: [R-meta] multivariate meta-analysis assuming the correlation
>
>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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