[R-meta] multilevel meta-analysis using metafor

Wolfgang Viechtbauer wolfgang.viechtbauer at maastrichtuniversity.nl
Wed Aug 30 16:31:46 CEST 2017

Yes, this is indeed how you can approach this.

And yes, if the var-cov structured is misspecified (which it is in your 
case), then the fixed effects are still estimated unbiasedly (although 
not as efficiently). The problem is that the SEs of the fixed effects 
will not be correct. Using robust() allows you to get more appropriate 
estimates of the SEs (and hence more appropriate tests/CIs).


On 08/30/2017 03:10 PM, brauldeq wrote:

I understand that I could at first specify my model using model <-
rma.mv(yi, vi, random = ~ 1 | sample_nr/effect_nr, data = data). To
solve the problem concerning the covariances of the sampling errors I
would hereafter use robust.rma.mv(model, cluster=data$sample_nr, adjust
= T). Would this approach solve my problem?

Am I right to assume that the rma.mv(yi, vi, random = ~1 |
sample_nr/effect_nr) function would calculate proper estimate of effect
size but is problematic in terms of sampling errors?


Am 30.08.2017 14:05, schrieb Wolfgang Viechtbauer:
Please keep the mailing list in cc.

Yes, this means the subjects overlap, that is, the correlations are
computed based on the same sample. In that case, the correlations are
correlated. Equations for computing the covariances can be found in:

Steiger, J. H. (1980). Tests for comparing elements of a correlation
matrix. Psychological Bulletin, 87(2), 245-251.

There are various cases. Let's say there are four variables: x1, x2,
x4, and x4, all measured in the same sample. Then we have the case of
non-overlapping variables:

cov(cor(x1,x2), cor(x3,x4))

To compute that covariance, you will need the full 4x4 correlation

And there is the case of partially overlapping variables, for example:

cov(cor(x1,x2), cor(x1,x3))

To compute the covariance here, you will need cor(x2,x3) (obviously,
cor(x1,x2) and cor(x1,x3) you already have, otherwise you would not be
interested in their covariance).

Again, the necessary equations can be found in Steiger (1980).

If you do not have the information to compute the covariances, then we
are back to the situation where the covariances between the outcomes
cannot be computed. See previous posts on how to deal with that. For




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