[R-sig-ME] Using r for multi-level meta-analysis

Mike Cheung mikewlcheung at gmail.com
Mon May 16 09:23:36 CEST 2016

Dear Isaac,

The mathematical models are identical in the metaSEM and metafor packages.
The main difference is the implementation--SEM vs. MLM. The meta3 and reml3
in the metaSEM package use ML and REML estimation methods, respectively.


On Mon, May 16, 2016 at 1:03 AM, איציק פרדקין <itzikf at outlook.com> wrote:

> 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, איציק פרדקין <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;
>>         [[alternative HTML version deleted]]
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> --
> ---------------------------------------------------------------------
>  Mike W.L. Cheung               Phone: (65) 6516-3702
>  Department of Psychology       Fax:   (65) 6773-1843
>  National University of Singapore
>  http://courses.nus.edu.sg/course/psycwlm/internet/
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