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

[Viechtbauer, Wolfgang (NP)]

See slide 7 in this presentation:

https://www.wvbauer.com/lib/exe/fetch.php/talks:2016_viechtbauer_srsm_weights.pdf

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Yefeng Yang via R-sig-meta-analysis
>Sent: Monday, 24 April, 2023 11:01
>To: r-sig-meta-analysis using r-project.org
>Cc: Yefeng Yang
>Subject: Re: [R-meta] formula of variance of mean effect from a RE model with
>1/vi with weights
>
>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