Dear Gang, It seems that it is possible to use a univariate meta-analysis to handle your multivariate effect sizes. If you want to calculate a weighted average first, Hedges and Olkin (1985) has discussed this approach.
Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando, FL: Academic Press. Regards, Mike -- --------------------------------------------------------------------- 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/ --------------------------------------------------------------------- On Mon, Feb 8, 2010 at 6:48 AM, Gang Chen <gangch...@gmail.com> wrote: > Dear Mike, > > Thanks a lot for the kind help! > > Actually a few months ago I happened to read a couple of your posts on > the R-help archive when I was exploring the possibility of using lme() > in R for meta analysis. > > First of all, I didn't specify the meta analysis model for my cases > correctly in my previous message. Currently I'm only interested in > random- or mixed-effects meta analysis. So what you've suggested is > directly relevant to what I've been looking for, especially for case > (2). I'll try to gather those references you listed, and figure out > the details. > > Also I think I didn't state my case (1) clearly in my previous post. > In that case, all the effect sizes are the same and in the same > condition too (e.g., happy), but each source has multiple samples of > the measurement (and also measurement error, or standard error). Could > this still be handled as a multivariate meta analysis since the > samples for the the same source are correlated? Or somehow the > multiple measures from the same source can be somehow summarized > (weighted average?) before the meta analysis? > > Your suggestions are highly appreciated. > > Best wishes, > Gang > > > On Sun, Feb 7, 2010 at 10:39 AM, Mike Cheung <mikewlche...@gmail.com> wrote: >> Dear Gang, >> >> Here are just some general thoughts. Wolfgang Viechtbauer will be a >> better position to answer questions related to metafor. >> >> For multivariate effect sizes, we first have to estimate the >> asymptotic sampling covariance matrix among the effect sizes. Formulas >> for some common effect sizes are provided by Gleser and Olkin (2009). >> >> If a fixed-effects model is required, it is quite easy to write your >> own GLS function to conduct the multivariate meta-analysis (see e.g., >> Becker, 1992). If a random-effects model is required, it is more >> challenging in R. SAS Proc MIXED can do the work (e.g., van >> Houwelingen, Arends, & Stijnen, 2002). >> >> Sometimes, it is possible to transform the multivariate effect sizes >> into independent effect sizes (Kalaian & Raudenbush, 1996; Raudenbush, >> Becker, & Kalaian, 1988). Then univariate meta-analysis, e.g., >> metafor(), can be performed on the transformed effect sizes. This >> approach works if it makes sense to pool the multivariate effect sizes >> as in your case (2)- the effect sizes are the same but in different >> conditions (happy, sad, and neutral). However, this approach does not >> work if the multivariate effect sizes are measuring different >> concepts, e.g., verbal achievement and mathematical achievement. >> >> Hope this helps. >> >> Becker, B. J. (1992). Using results from replicated studies to >> estimate linear models. Journal of Educational Statistics, 17, >> 341-362. >> Gleser, L. J., & Olkin, I. (2009). Stochastically dependent effect >> sizes. In H. Cooper, L. V. Hedges, and J. C. Valentine (Eds.), The >> handbook of research synthesis and meta-analysis, 2nd edition (pp. >> 357-376). New York: Russell Sage Foundation. >> Kalaian, H. A., & Raudenbush, S. W. (1996). A multivariate mixed >> linear model for meta-analysis. Psychological Methods, 1, 227-235. >> Raudenbush, S. W., Becker, B. J., & Kalaian, H. (1988). Modeling >> multivariate effect sizes. Psychological Bulletin, 103, 111-120. >> van Houwelingen, H.C., Arends, L.R., & Stijnen, T. (2002). Advanced >> methods in meta-analysis: multivariate approach and meta-regression. >> Statistics in Medicine, 21, 589-624. >> >> Regards, >> Mike >> -- >> --------------------------------------------------------------------- >> 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/ >> --------------------------------------------------------------------- >> >> On Sat, Feb 6, 2010 at 6:07 AM, Gang Chen <gangch...@gmail.com> wrote: >>> In a classical meta analysis model y_i = X_i * beta_i + e_i, data >>> {y_i} are assumed to be independent effect sizes. However, I'm >>> encountering the following two scenarios: >>> >>> (1) Each source has multiple effect sizes, thus {y_i} are not fully >>> independent with each other. >>> (2) Each source has multiple effect sizes, and each of the effect size >>> from a source can be categorized as one of a factor levels (e.g., >>> happy, sad, and neutral). Maybe better denote the data as y_ij, effect >>> size at the j-th level from the i-th source. I can code the levels >>> with dummy variables into the X_i matrix, but apparently the data from >>> the same source are correlated with each other. In this case, I would >>> like to run a few tests one of which is, for example, whether there is >>> any difference across all the levels of the factor. >>> >>> Can metafor handle these two cases? >>> >>> Thanks, >>> Gang > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
