[R-meta] Weight argument in rma.uni models

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Wed Oct 2 14:49:55 CEST 2019

Dear Tina,

I assume you mean the rma.mv() function, not rma.uni().

If you don't specify W, then weights are applied automatically. See:


and search for "Together with the variance-covariance matrix of the sampling errors". However, for the model you show, the model implied marginal variance-covariance matrix of the observed outcomes (M) is not diagonal, but also has off-diagonal elements. So, there is actually an entire weight matrix.

Also, in 'res5', M (and hence the weight matrix W = M^(-1)) will incorporate the estimates of the two variance components (for EffectSize_ID_NEW and Study), while 'res6' only uses 1/Variance_New as the weights and doesn't consider the two variance components.


-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Tina Dudenhöffer
Sent: Wednesday, 02 October, 2019 13:48
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Weight argument in rma.uni models

Dear all,

I am working with the rma.uni function to fit a multivariate random effects model.

I see that the W argument is an optional argument to specify a user-defined weight matrix. I was curious if any weight is applied if I don’t specify this argument. 
Specifically, I am wondering if the inverse variance weight is applied “automatically”, considering I am specifying the V argument in the model itself.

In terms of my model, I am wondering about the difference between these:

res5 <- rma.mv(EffectSize_NEW, Variance_New, method="REML",random = list(~ 1 | EffectSize_ID_NEW, ~ 1 | Study), data=Data)

res6 <- rma.mv(EffectSize_NEW, Variance_New, W=weight, method="REML",random = list(~ 1 | EffectSize_ID_NEW, ~ 1 | Study), data=Data)

Note: the argument weight in my dataset is simply: 1/Variance_New

Hope this is all clear.

Many thanks and kind regards,

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