# [R-meta] tau^2 for multilevel models

Viechtbauer, Wolfgang (NP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Thu May 26 11:46:39 CEST 2022

```Dear Alexandra,

Yes, sum(example\$sigma2) can be considered the total amount of heterogeneity. It won't be exactly equal to example2\$tau2, but shouldn't be too dissimilar (0.323 vs. 0.313 in this example).

Sure, you could denote sum(example\$sigma2) as tau^2. In fact, you can fit model 'example' using this alternative parameterization (which is equivalent as long as rho is estimated to be > 0):

example3 <- rma.mv(yi, vi, random = ~ trial | alloc, data=dat)
example3

And here, example3\$tau2 is identical to sum(example\$sigma2).

https://www.metafor-project.org/doku.php/analyses:konstantopoulos2011

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Alexandra Voce
>Sent: Thursday, 26 May, 2022 11:30
>To: r-sig-meta-analysis using 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 using aic.gov.au<mailto:Alexandra.voce using aic.gov.au>
>W: www.aic.gov.au

```