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

[Viechtbauer, Wolfgang (SP)]

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