[R-meta] meta analysis of indirect effects metafor

Viechtbauer, Wolfgang (NP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Tue Sep 20 11:04:27 CEST 2022

Dear Anne,

Yes, that is correct.

And to answer your last question more broadly: As long as one has estimates (of whatever kind) that are 1) on the same scale (which either can be achieved by using a 'unitless' / standardized effect size measure, but would also apply if variables across studies are measured using the same measurement instrument / scale and one simply uses the 'raw estimates' directly), 2) are 'about the same thing/phenomenon' (or to use a slightly fancier term: 'commensurable'), and 3) one has (estimates of) the corresponding standard errors (or SE^2 = sampling variances), then one can combine them using standard meta-analytic methods.

To give a counterexample to 2): It would make little sense to combine a bunch of correlation coefficients between anxiety and depression and a bunch of correlation coefficients between height and weight in the same analysis. While they are measured on the same scale (criterion 1) and one can also compute the corresponding SEs (criterion 3), they are not reflections of the same underlying phenomenon and hence not commensurable. But it is actually in the eye of the beholder what is considered commensurable. In other words, while it is objectively nonsense to combine a correlation coefficient with a standardized mean difference or the mean height with a mean weight (they are not on the same scale; a suitable cartoon I like to use when discussing this point: https://condenaststore.com/featured/new-yorker-may-17th-1976-dana-fradon.html), there isn't an 'objective' way of defining what is commensurable. For example, Byrnes et al. (1999) did a meta-analysis on gender differences in risk taking. There are very diverse ways of assessing such gender differences, for example, through surveys asking about 'risky behaviors' (driving over the speed limit, smoking, etc.), through gambling tasks, choice dilemma tasks, etc. etc. One can compute standardized mean differences based on such diverse assessments of risk taking, but some might argue that combining them is comparing apples and oranges. A possible response to this is to empirically assess whether there are systematic differences between different types of assessments (via a moderator / meta-regression analysis) - which is also what Byrnes et al. (1999) did. In fact, one could in principle do the same with a bunch of correlation coefficients between anxiety and depression and a bunch of correlation coefficients between height and weight, although I don't know what such a comparison would really tell us (and even if the two groups of correlation coefficients happen to not differ, I still wouldn't be comfortable combining them into an overall aggregate).

So, instead of addressing your question directly - which I can't, since I do not know the specifics of what you mean by "moderation effects" - you should think about the above and come to your own decision whether combining these effects makes sense under these criteria.


>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Anne Olsen
>Sent: Tuesday, 20 September, 2022 10:11
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] meta analysis of indirect effects metafor
>We ran several studies where we had indirect effects, and we would like to
>report them in the form of meta-analyses. In one of the threads on stat
>exchange (here
>I found a comment suggesting that in the case all variables are the same
>and the model is the same across these studies, one could just calculate
>estimates and standard errors and put them into some package such as
>metafor. So this would be my case, but I am wondering what would be the
>exact code in metafor to calculate this?
>What I did was that I calculated variance ( vi=SE^2 ) and ran the following
> res <-rma.uni(yi=Mod_OSC,vi=vi,ni=N,slab=Studies, data=mydata)
> res
>Is this correct?
>Also, would the same procedure work for moderation effects?
>I  know this question is basic, but I have no previous experience with
>meta-analysis, and on the internet, I could not find some simple solution
>for which I am sure it is correct.
> Anne O.

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