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
[R-meta] mathematical equation confidence and prediction intervals 3- and 4-level models
3 messages · Wolfgang Viechtbauer, Thölking, Theresa
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$sigma2)). I hope this is the level of detail you are looking for. Best, Wolfgang
-----Original Message----- From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Th?lking, Theresa Sent: Sunday, 18 September, 2022 17:02 To: r-sig-meta-analysis at r-project.org Subject: [R-meta] mathematical equation confidence and prediction intervals 3- and 4-level models Hello everybody, does anybody know the mathematical equation of how prediction and confidence intervals are calculated in 3-level and 4-level meta-analytic models in R? Thanks in advance. Best, Theresa
Dear Wolfgang, thanks for your explanation, that was very helpful. Best, Theresa
Von: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Gesendet: Sonntag, 18. September 2022 17:23:29 An: r-sig-meta-analysis at r-project.org Cc: Th?lking, Theresa Betreff: RE: mathematical equation confidence and prediction intervals 3- and 4-level models Dear Theresa, There isn't anything special about calculating the CI. It's just the pooled estimate +- the critical value (1.96 if test="z"; otherwise, the corresponding quantile from a t-distribution) times the standard error. For the PI, a sensible thing to do (assuming you are talking about a model where 'random' is something like '~ study/estimate' or '~ author/study/estimate' or something along those lines) is to compute it in the same way as for a 'standard' random-effects model as described here: https://www.metafor-project.org/doku.php/faq#for_random-effects_models_fitt but using the sum of all variance components as 'tau^2' (essentially: sum(res$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