[R-meta] mathematical equation confidence and prediction intervals 3- and 4-level models

Viechtbauer, Wolfgang (NP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Sun Sep 18 17:23:29 CEST 2022

Dear Theresa,

There isn't anything special about calculating the CI. It's just the pooled estimate +- the critical value (1.96 if test="z"; otherwise, the corresponding quantile from a t-distribution) times the standard error.

For the PI, a sensible thing to do (assuming you are talking about a model where 'random' is something like '~ study/estimate' or '~ author/study/estimate' or something along those lines) is to compute it in the same way as for a 'standard' random-effects model as described here:


but using the sum of all variance components as 'tau^2' (essentially: sum(res$sigma2)).

I hope this is the level of detail you are looking for.


>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Thölking, Theresa
>Sent: Sunday, 18 September, 2022 17:02
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] mathematical equation confidence and prediction intervals 3-
>and 4-level models
>Hello everybody,
>does anybody know the mathematical equation of how prediction and confidence
>intervals are calculated in 3-level and 4-level meta-analytic models in R? Thanks
>in advance.

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