[R-sig-ME] Using r for multi-level meta-analysis
itzikf at outlook.com
Sun May 15 12:45:56 CEST 2016
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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