[R-meta] formula of variance of mean effect from a RE model with 1/vi with weights

[Yefeng Yang]

Dear Wolfgang,
Brilliant! The general form looks quite complex: Var[b] = (X'WX)^-1 X'W Var[y] WX (X'WX)^-1.

If we do not consider predictor analysis (i.e., intercept-only MA model), can I bother you to reformulate it using non-matrix notation?  I appreciate it!

Best,
Yefeng
________________________________
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> on behalf of Yefeng Yang via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org>
Sent: Monday, 24 April 2023 18:38
To: r-sig-meta-analysis using r-project.org <r-sig-meta-analysis using r-project.org>
Cc: Yefeng Yang <yefeng.yang1 using unsw.edu.au>
Subject: [R-meta] formula of variance of mean effect from a RE model with 1/vi with weights

Dear experts,
I see the rma() in metafor package can run a random-effects meta-analysis with inverse sampling variance (say vi) as weights (setting weights = 1/vi). I wonder about the formula used to calculate the variance (or standard error) of the overall mean in this model. I would be grateful if someone can provide the corresponding estimator.


Best
Yefeng Yang PhD
UNSW, Sydney


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