[R-meta] meta analysis of indirect effects metafor

Anne Olsen @nne@o|@en@1994 @end|ng |rom gm@||@com
Tue Sep 20 11:47:02 CEST 2022

Dear Wolfgang,
This is an amazing explanation! Thank you so so much!
Anne O.

On Tue, Sep 20, 2022 at 11:04 AM Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> 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.
> Best,
> Wolfgang
> >-----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
> >
> >Hello,
> >
> >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
> ><
> https://stats.stackexchange.com/questions/187463/how-does-one-run-a-meta-
> >analysis-on-indirect-mediated-effects>),
> >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
> >code
> >
> > 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.
> >
> >Thanks!
> > Anne O.

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