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

Anne Olsen @nne@o|@en@1994 @end|ng |rom gm@||@com
Wed Sep 21 09:28:10 CEST 2022

```Dear Mike,

Thank you very much for this nice explanation and for sharing the paper.

Currently, my knowledge of meta-analysis is completely basic. Thus, I
believe that I first must attend some good courses (which I am planning to
do) before 'experimenting' with different approaches. Yet, I am looking
meta-analysis.

Thank you!
Best,
Anne O.

On Wed, Sep 21, 2022 at 2:19 AM Mike Cheung <mikewlcheung using gmail.com> wrote:

> 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.
>> >
>> > 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
>> > (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).
>> >
>> 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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>
>
>

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