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

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