# [R-meta] meta analysis of indirect effects metafor

Mike Cheung m|kew|cheung @end|ng |rom gm@||@com
Wed Sep 21 02:19:30 CEST 2022

```Dear Anne,

Apart from Wolfgang's excellent explanation of the general issues, there
are additional issues in analyzing indirect effects. Here are some of them.

1) Interpreting the indirect effect alone may be misleading if we ignore
the direct effect. It is preferable to include both of them in the
meta-analysis.

2) It is well-known that the sampling distribution of the indirect effect
is nonnormal. This is why researchers prefer using the bootstrap confidence
interval in testing indirect effect in primary studies. As the effect size
is nonnormally distributed, the accuracy of the meta-analysis is
questionable. We have yet to see some empirical support for it.

3) When we conduct a meta-regression on the indirect effect, there is more
than one way to interpret the intercept and slope. For example,

(a*b) = β₀ + β₁*x, where a*b is the indirect effect and x is a covariate.

β₁ is usually interpreted as the expected change in the indirect effect
(a*b) when x increases 1 unit. However, there are also two equivalent
interpretations:

(i) a = β₀/b + β₁*(x/b), β₁ is the expected change in a when x increases 1
unit "given b is 1."

(ii) b = β₀/a + β₁*(x/a), β₁ is the expected change in b when x increases 1
unit "given a is 1."

Meta-analytic structural equation model (MASEM) may avoid these issues by
synthesizing correlation matrices instead of indirect effect. The following
paper has a more detailed discussion of these issues.

Cheung, M. W.-L. (2022). Synthesizing indirect effects in mediation models
with meta-analytic methods. Alcohol and Alcoholism, 57(1), 5–15.
https://doi.org/10.1093/alcalc/agab044

Best,

Mike

On Tue, Sep 20, 2022 at 5:47 PM Anne Olsen <anne.olsen.1994 using gmail.com>
wrote:

> Dear Wolfgang,
> This is an amazing explanation! Thank you so so much!
> Best,
> 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:
> >
> ),
> > 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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>
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