[R-meta] How does the rma.mv function handle multiple inferences within a study-level

[Divya Ravichandar]

Thank you for your explanation of how the weight matrix is computed.

A followup question, on the 'sigma^2' only terms in the variance matrix
[terms in matrix positions (3,4) & (4.3)].

I assume (based on running the example above) the sigma^2 here is different
from the sigma^2 used along the diagonal. Is this correct? If yes, is a
sigma^2 estimated based on just the values corresponding to study c in the
example?

Thank you

On Wed, Apr 1, 2020 at 1:21 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Dear Divya,
>
> The model you are using implies the following structure for the marginal
> var-cov matrix of the estimates:
>
> [SE_1^2 + sigma^2                                                   ]
> [                 SE_2^2 + sigma^2                                  ]
> [                                  SE_3^2 + sigma^2 sigma^2         ]
> [                                  sigma^2          SE_4^2 + sigma^2]
>
> The weight matrix is the inverse thereof. See:
>
> library(metafor)
>
> case <- data.frame(Study=c("a","b","c","c"), ES=c(-1.5,-3,1.5,3),
> SE=c(.2,.4,.2,.4))
> res <- rma.mv(ES, SE^2, random = ~ 1 | Study, data=case)
> res
>
> vcov(res, type="obs")
> weights(res, type="matrix")
>
> The model estimate is then given by b = (X'WX)^(-1) X'Wy, where X is just
> a column vector of 1s, W is the weight matrix above, and y is a column
> vector with the 4 effect sizes.
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Divya Ravichandar
> Sent: Wednesday, 01 April, 2020 21:59
> To: r-sig-meta-analysis using r-project.org
> Subject: [R-meta] How does the rma.mv function handle multiple inferences
> within a study-level
>
> My use case is presented in the dataframe below. Studies a,b and c are to
> be integrated in a meta-analysis using: rma.mv(ES, SE^2, random = ~ 1 |
> Study, data=case)
>
> In this case, studies a & b have one inference each but because of my study
> design two inferences exist for study c.  I am curious as to how the 2
> inferences under study c are weighted in the meta-analysis calculation as
> compared to the inference for studies a &b.
>
> case <- data.frame(Study=
>
> c("a","b","c","c"),Effect_size=c(-1.5,-3,1.5,3),Standard_error=c(.2,.4,.2,.4))
>
> Thanks
> --
> *Divya Ravichandar*
> Scientist
> Second Genome
>


-- 
*Divya Ravichandar*
Scientist
Second Genome

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