[R-meta] tau^2 for multilevel models

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On
Behalf Of Alexandra Voce
Sent: Thursday, 26 May, 2022 11:30
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] tau^2 for multilevel models

Dear mailing list,

If I have a multilevel model, say:

dat <- get(data(dat.bcg))
dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg, data=dat.bcg)

example <- rma.mv(yi, vi, random = ~ 1 | alloc/trial, data=dat)

Is the sum of the sigma^2 values in this model equivalent to tau^2 that would be
calculated in a more general random effects model, e.g..

example2 <- rma(yi, vi, data=dat)

By equivalent, I mean is it correct to state that the sum of sigma^2 values in a
multilevel model reflects the estimated amount of total heterogeneity? Is there
any reason it could be considered incorrect to detail this value (sigma^2_between
+ sigma^2_within) as tau2?

Thank you,
Alexandra

Dr Alexandra Voce
Research Analyst
Australian Institute of Criminology
E: Alexandra.voce at aic.gov.au<mailto:Alexandra.voce at aic.gov.au>
W: www.aic.gov.au