[R-meta] Problem with sigma-square in 3-level meta-analysis

Röhl, Sebastian @eb@@t|@n@roeh| @end|ng |rom un|-tueb|ngen@de
Fri Mar 10 08:40:00 CET 2023

Dear all,

We are conducting meta-analyses of correlational effects which are clustered in studies (or independent samples). Therefore we are using 3-level hierarchical random effects models (Sampling error within effect sizes within independent samples).
For one of our sub-analyses which 50 effects of 8 independent samples, the results of the rma.mv pointed to nearly no (5.710374e-12) variance component between the samples:

> overall_mod_cc <- rma.mv(zr, V=var, random = ~ 1| Sample_ID / nummer, data = data_cc, method = "REML")
> overall_mod_cc
Multivariate Meta-Analysis Model (k = 50; method: REML)
Variance Components:
            estim    sqrt  nlvls  fixed            factor 
sigma^2.1  0.0000  0.0000      8     no         Sample_ID 
sigma^2.2  0.0222  0.1489     50     no  Sample_ID/nummer

However, when I look directly at the manifest variances for the group means (0.225) and all effects (0.392), I conclude that there should actually be a much larger variance component between the independent samples.
(a) Am I making a thinking error here?
(b) Or could this be because the estimation of variance components using rma.mv() does not work reliably for the small number of studies (8)?
(c) And if (b) is correct - what model or function could I use instead for this partial analysis?

Thanks a lot for your help!


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