# [R-meta] Assessing heterogeneity with random-effects models

Viechtbauer, Wolfgang (SP) wolfgang.viechtbauer at maastrichtuniversity.nl
Wed Apr 11 23:10:42 CEST 2018

```Dear Celia,

See my responses below.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-
>project.org] On Behalf Of Célia Sofia Moreira
>Sent: Wednesday, 04 April, 2018 18:08
>To: r-sig-meta-analysis at r-project.org
>Subject: [R-meta] Assessing heterogeneity with random-effects models
>
>Dear all,
>
>I'm performing a meta-analysis with metafor package and I have some basic
>questions regarding the assessment of residual heterogeneity.
>
>For random-effects univariate models (using rma function), residual
>heterogeneity can be assessed with
>- QE and QEp,
>- I2 (total heterogeneity / total variability),
>- H2 (total variability / sampling variability),
>- tau2 (estimated amount of total heterogeneity).
>
>For random-effects multilevel models (using rma.mv function),
>heterogeneity
>can be assessed with
>- QE and QEp,
>- tau2
>- sigma2.
>In this case:
>1) Is tau2 still being the estimated amount of total heterogeneity?

One cannot answer this in general, because rma.mv() fits all kinds of different models. You said 'random-effects multilevel model', so do you mean the model given here? http://www.metafor-project.org/doku.php/analyses:konstantopoulos2011 Then sigma^2.1 + sigma^2.2 is the total amount of heterogeneity. For the multivariate parameterization, this is equivalent to tau^2.

>2) May I define sigma2_1 as the variability/variance of the 3-level model
>at level 1?

In the example above, sigma^2.1 is the district and sigma^2.2 is the study within district variance. Not sure what you mean by 'level 1'.

>3) Why I2 and H2 is not defined?

See here: http://www.metafor-project.org/doku.php/tips:i2_multilevel_multivariate

>4) In all cases I performed, I got tau2=0. Is this a coincidence or does
>this fact always happen?

I don't know what model you are fitting, so I cannot answer this.

>5) Is there any other useful way  to assess heterogeneity in the
>multilevel case?

Not that I know of.

>Kind regards,
>celia

```

More information about the R-sig-meta-analysis mailing list