[R-meta] weight in rmv metafor

Of course the weights "impact the estimated fixed effects". But whether
studies with multiple effect sizes tend to receive more weight depends on
various factors, including the variances of the random effects and the
sampling error (co)variances.

A more detailed discussion around the way weighting works in rma.mv
models can be found here:

http://www.metafor-project.org/doku.php/tips:weights_in_rma.mv_models

Note that weights(res, type="rowsum") currently only works in the 'devel'
version of metafor, so follow
https://wviechtb.github.io/metafor/#installation if you want to reproduce
this part as well.

I hope this clarifies things.

Best,
Wolfgang

-----Original Message-----
From: Huang Wu [mailto:huang.wu at wmich.edu]
Sent: Sunday, 07 June, 2020 19:52
To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis at r-project.org
Subject: RE: [R-meta] weight in rmv metafor

Dear Dr. Viechtbauer,

Thank you very much for your helpful reply.

To be clear, I wonder if the multivariate approach will downweight

estimates

from a study that contains multiple effect sizes?
I saw in a previous posts (https://stat.ethz.ch/pipermail/r-help/2017-
February/444703.html), your said, "if you fit an appropriate model to the
data at hand, the 'default weights' used by rma.mv() will be just fine."
Does that mean that weights in rma.mv model would not impact the

estimated

fixed effects?
I found that in the forest plot I generate through forest(), studies with
multiple effect sizes tend to have bigger weights. I also used weights()

to

check the weights given to each effect sizes and found the same thing (see
below for my code). I wonder if the weights for each effect sizes

presented

in forest plot is correct?

Thank you very much again for your help.

Best wishes
Huang

Vt <- impute_covariance_matrix(vi = try$v,  #known correlation vector
                                  cluster = try$ID, #study ID
                                 r = 0.80) #assumed correlation

Mt <- rma.mv(yi=d, #effect size
                  V = Vt, #variance (tHIS IS WHAt CHANGES FROM HEmodel)
                  random = ~1 | ID/IID, #nesting structure
                  test= "t", #use t-tests
                  data=try,
                  method="REML")
weights(Mt)

From: Viechtbauer, Wolfgang (SP)
Sent: Sunday, June 7, 2020 6:56 AM
To: Huang Wu; r-sig-meta-analysis at r-project.org
Subject: RE: [R-meta] weight in rmv metafor

Dear Huang,

The weighting in rma.mv() models is more complex than in 'simple' models
fitted with rma() (same as rma.uni()). Depending on the particular model

you

are fitting with rma.mv(), the model-implied marginal var-cov matrix of

the

estimates (which you can see with vcov(<model>, type="obs")) is not just a
diagonal matrix (as is the case for rma() models), but also involves
covariances. The inverse of this matrix is the weight matrix, which is

then

also not just a diagonal matrix.

For example, when some studies contribute multiple estimates, we might
consider fitting a multilevel/multivariate model with random effects for
studies and random effects for estimates within studies. When the

estimated

between-study variance component is greater than zero, then this implies a
certain amount of covariance for effects from the same study. This leads

to

negative off-diagonal elements in the weight matrix for estimates from the
same study. As a result, if the ith study contributes k_i estimates, it is
not treated as if there were k_i independent studies.

This has been discussed in the past on this mailing list, so you might

want

to search the archives for some relevant posts. Googling for:

site:https://stat.ethz.ch/pipermail/r-sig-meta-analysis/ rma.mv weights

brings up some relevant posts.

Roughly speaking, the robust variance estimation method works as follows.

We

start with a 'working model' that is hopefully some decent approximation

to

the true model and that also captures the dependencies in the estimates.
This model provides us with the estimates of the fixed effects. However,
because we might not be able to capture all dependencies correctly with

this

working model, the var-cov matrix of the estimated fixed effects might not
be correct. Hence, based on the working model, we can use the robust
variance estimation method to obtain a var-cov matrix that is
(asymptotically) correct and use this for testing the fixed effects.

Therefore, the robust variance estimation method does not actually lead to
changes in the estimated fixed effects. Those are determined based on the
working model. That is why coef_test() will give you the exact same
estimates of the fixed effects as those from the working model you use as
input to this function.

That is why it is important to use a working model that is at least some
decent approximation. While the fixed effects estimates might even be
unbiased when using a really poor working model, the estimates will not be
very efficient.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-

project.org]

On Behalf Of Huang Wu
Sent: Sunday, 07 June, 2020 0:37
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] weight in rmv metafor

Hi, all,

I am conducting a multivariate meta-analysis using rmv in metaphor

package.

I wonder how rmv calculate weights for each effect sizes? I wonder if
studies with more effect sizes get more total weights?

I read an article saying "The robust variance estimation methods upweight
effect sizes that are estimated with greater precision (due to

differences

in sample sizes, level of randomization, predictive power of covariates,
etc.) and downweight estimates from studies that contribute multiple

effect

size estimates". (Kraft,Blazar, Hogan, 2018). Is that right?

I am using rmv in metafor package to estimate the model and use coef_test

in

sandwich package to do significance test. Both give the same pooled

effect

sizes though. I understand that weights also impact pooled effect size
estimate. In this case, how will robust variance estimation impact my

weight

mean effect size? Thanks

Best wishes
Huang