Using r for multi-level meta-analysis

Dear Mike

Thanks for your response.
I had the chance to read your paper on multilevel SEM implementation and
package you've written. I have some experience with MLM, but almost no
experience with the SEM framework. I was wondering then if you think the
results of both analyses (using MetaSEM vs. metafor) would be roughly
similar.  The basic idea is to conduct a meta analysis on
neuropsychological findings in anxiety patients, while controlling for the
fact that most studies have more than one measure and each measure more
than one subscale. Moderators at both study and outcome levels will be
probed.

Thanks a lot!
Isaac.

Sent from my iPhone

On 15 May 2016, at 15:52, Mike Cheung <mikewlcheung at gmail.com> wrote:

Hi,

The meta3 function in the metaSEM package has implemented the three-level
meta-analysis using the SEM approach. The metafor package has also
implemented it using the multilevel modelling approach.

Regards,
Mike

On Sunday, 15 May 2016, ????? ?????? <itzikf at outlook.com> wrote:

Dear R and MLM experts,I'm trying to figure out whether it's possible to
implement Van den Noortgate (2014) approach for three-level meta-analysis
in lme4 or nlme. In my data structure I have several outcomes per study,
and the three levels are: Level 1 - regressing observed effect size on its
estimated population effect size + residual errorLevel 2- regressing each
outcome and study estimated population effect size on the study overall
population effect size + errorLevel 3 - regressing each study overall
population effect size on the mean effect size of all studies + error
The special case of meta-analysis doesn't require the estimation of the
residual error at level 1, because it is estimated by the variance of the
effect size (e.g. variance of Hedges g), which is given for each outcome
and study. In a regular meta-analysis model, the inverse of this variance
is used to weight different studies when combining them to an overall mean
effect size.
Van den Noortgate provides a SAS script (using Proc mixed) for this
purpose. Specifically, he suggested that weighting effects sizes according
to their respective weight (1/variance of effect size) , and constraining
the residual error term to 1, which should constrain the residual error of
each outcome and study to the given variance of this effect size. I attach
below the SAS code he provided.

I was wondering whether it's possible to do the same by using R MLM
packages. specifically - I'm stuck with how to constrain the level 1 errors
to 1.
Thanks a lot!Isaac.


Proc mixed data=D method=reml;         class Study Outcome         model
ES= /solution ddfm=satterhwaite;         weight W;         random
intercept/sub=Study;         random intercept/sub=Outcome;         params 1
1 1/hold=3run;
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 Mike W.L. Cheung               Phone: (65) 6516-3702
 Department of Psychology       Fax:   (65) 6773-1843
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 http://courses.nus.edu.sg/course/psycwlm/internet/
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