Message-ID: <8f8bb4164e8e4a6a878753ae97a8a5d0@UM-MAIL3214.unimaas.nl>
Date: 2022-09-18T15:23:29Z
From: Wolfgang Viechtbauer
Subject: [R-meta] mathematical equation confidence and prediction intervals 3- and 4-level models
In-Reply-To: <44ad9c1fb47d4b399d56036ef80f7421@uni-trier.de>
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:
https://www.metafor-project.org/doku.php/faq#for_random-effects_models_fitt
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.
Best,
Wolfgang
>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On
>Behalf Of Th?lking, Theresa
>Sent: Sunday, 18 September, 2022 17:02
>To: r-sig-meta-analysis at 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.
>
>Best,
>Theresa