[R-meta] weight in rmv metafor

[Viechtbauer, Wolfgang (SP)]

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 using wmich.edu]
>Sent: Sunday, 07 June, 2020 19:52
>To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis using 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 using 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 using r-
>project.org]
>>On Behalf Of Huang Wu
>>Sent: Sunday, 07 June, 2020 0:37
>>To: r-sig-meta-analysis using 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