[R-meta] multilevel meta-analysis using metafor

[brauldeq]

Following 
https://stackoverflow.com/questions/44811867/multilevel-meta-analysis-using-metafor 
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?

Thanks,
Denise




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 
> matrix.
> 
> 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
> example:
> 
> https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2017-August/000097.html
> https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2017-August/000094.html
> 
> Best,
> Wolfgang
> 
> --
> Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry 
> and
> Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 
> MD
> Maastricht, The Netherlands | +31 (43) 388-4170 | 
> http://www.wvbauer.com
> 
> On 08/30/2017 01:19 PM, brauldeq wrote:
> Dear Wolfgang,
> 
> thanks for your fast reply. I do not quite understand what you mean by
> "overlap in the subjects used to compute the various correlation
> coefficients within the same study". Each of the multiple (dependent)
> effect sizes within one particular study is based on the same
> participants. For example, one study would report multiple correlations
> for the relationship between scholastic achievement (i.e. GPA) and
> various self-efficacy measures (i.e. subject-specific self-efficacy,
> general self-efficacy, self-efficacy for self-regulated learning, etc.)
> that were all based on the same set of participants.
> Would that mean an overlap in subjects? Or would I be able to use
> rma.mv(yi, vi, random = ~ 1 | sample_nr/effect_nr, data = se_ach)?
> 
> Thanks for your advice.
> 
> Best regards,
> Denise
> 
> Am 30.08.2017 13:07, schrieb Wolfgang Viechtbauer:
> Yes, that would be appropriate/sufficient, assuming there is no
> overlap in the subjects used to compute the various correlation
> coefficients within the same study. But I suspect that may not be the
> case. If so, the covariances of the correlations are not 0 (as is
> assumed by the model below).
> 
> Best,
> Wolfgang
> 
> On 08/30/2017 11:54 AM, brauldeq wrote:
> Dear fellow researchers,
> 
> I am currently conducting a meta-analysis for my master's thesis in
> psychology. For that matter, I stumbled upon your metafor package which
> has been very helpful for me!
> 
> However, I have some trouble implementing the right R code for my
> analysis. I am running a meta-analysis on the relationship between
> self-efficacy and scholastic achievement (using correlation
> coefficients). It will be analyzed using multilevel analysis using a
> random-effects model because I have several articles with multiple
> effect sizes which I want to include individually controlling for their
> dependency. Therefore, I have (dependant) effect sizes that are nested
> within (independent) samples.
> Each independent sample is coding with an unique number in the variable
> "sample_nr" and each dependant effect size for a certain sample is 
> coded
> with an unique number in "effect_nr". So, a sample with multiple effect
> sizes would be coded with an identical "sample_nr" and different
> "effect_nr" for each effect size. My R code is as follows:
> 
> rma.mv(yi, vi, random = ~ 1 | sample_nr/effect_nr, data = se_ach)
> 
> Is this the right code for my purpose?
> 
> Thank you for your advice.
> 
> Best regards,
> Denise Braul