[R-meta] Multilevel meta-analysis with a categorical moderator | subgroup analysis using meta-regression

[Reza Norouzian]

Hi Katharina,

The model that I linked to in my previous response is simply equivalent to
(and a shortcut for) running your "full.model" three times, each time
setting the "subset=" argument in your rma.mv() call to one of the
"pertype" categories (as Wolfgang correctly noted, make sure you profile
your variance estimates).

This shortcut is also nice as it allows you to test hypotheses that involve
one or more of the "pertype" categories from a single model.

Please feel free to clarify what you want to achieve and we may be able to
further assist you.

Reza

ps. It may also be useful to think about: why, in the first place, you want
to conduct a subgroup analysis? I usually conduct subgroup analysis of the
sort you inquired about when, among other things, (a) the categories of the
moderator of interest are theoretically quite distinct, (b) I'm not willing
to allow any "push-and-pull" between the categories of that moderator when
some of the studies contain more than one category of the moderator in
them, (c) there is a strong tradition that requires conducting this type of
subgroup analysis in the relevant field of research, and (d) the subgroup
shortcut model is indeed empirically (e.g., via AICc) superior to its
"push-and-pull" alternative (the "mod.pertype" model in your example).

On Tue, Apr 16, 2024 at 11:12 AM Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> There should be three tau^2 values and three gamma^2 values. The former
> are the between-sample variances and the later are the within-sample
> variances.
>
> I would strongly suggest to run profile() on this model to check that all
> variance components are identifiable.
>
> https://wviechtb.github.io/metafor/reference/profile.rma.html
>
> Best,
> Wolfgang
>
> > -----Original Message-----
> > From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org>
> On Behalf
> > Of Katharina Agethen via R-sig-meta-analysis
> > Sent: Tuesday, April 16, 2024 17:04
> > To: Reza Norouzian <rnorouzian using gmail.com>; R Special Interest Group for
> Meta-
> > Analysis <r-sig-meta-analysis using r-project.org>
> > Cc: Katharina Agethen <katharina.agethen using th-owl.de>
> > Subject: Re: [R-meta] Multilevel meta-analysis with a categorical
> moderator |
> > subgroup analysis using meta-regression
> >
> > Hi Reza,
> >
> > Thank you so much for your prompt reply. That is really helpful to me.
> >
> > After adjusting my code, I now obtain three tau^2 values based on my
> three
> > subgroups. Does it still make sense to compute the variance components
> for the
> > different levels (between/within sample) so that I may report the
> variance
> > components of the "overall" predictor "pertype"? If needed, how would I
> compute
> > tau^2(3) (between samples) and tau^2(2) (within samples) for the
> moderation
> > analysis?
> >
> > Best,
> > Katharina
> >
> > Von: Reza Norouzian <rnorouzian using gmail.com>
> > Gesendet: Tuesday, April 16, 2024 12:04 PM
> > An: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-
> > project.org>
> > Cc: Katharina Agethen <katharina.agethen using th-owl.de>
> > Betreff: Re: [R-meta] Multilevel meta-analysis with a categorical
> moderator |
> > subgroup analysis using meta-regression
> >
> > Hi Katharina,
> >
> > Yes, for the type of model you're using, it's possible to use a single
> model to
> > conduct a subgroup analysis.
> >
> > See for example:
> https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2022-
> > June/004074.html
> >
> > Reza
> >
> > On Tue, Apr 16, 2024, 3:25 AM Katharina Agethen via R-sig-meta-analysis
> > <mailto:r-sig-meta-analysis using r-project.org> wrote:
> > Dear all,
> >
> > I'm currently working on a meta-analysis on collective orientation and
> job
> > performance. I'm conducting a multilevel meta-analysis to account for
> dependency
> > in the data because multiple predictors (i.e., several measures of
> collective
> > orientation) and multiple outcomes (i.e., several measures of job
> performance
> > (e.g., task performance, contextual performance)) were often assessed in
> the
> > same sample. Correlation values were converted to Fisher's z scale.
> >
> > The code for the main effect is as follows:
> >
> > full.model <- http://rma.mv(yi = z,
> >                      V = vz,
> >                      slab = samid,
> >                      data = df,
> >                      random = ~ 1 | samid/esid,
> >                      test = "t",
> >                      method = "REML",
> >                      dfs="contain")
> >
> > summary(full.model)
> >
> > full.model.robust <- robust(full.model, cluster=df$samid, clubSandwich =
> TRUE)
> > summary(full.model.robust)
> >
> > In addition, I want to test the type of performance (pertype) as a
> categorical
> > moderator (i.e., general, in-role, extra-role). I fitted a
> meta-regression model
> > with pertype as the categorical moderator based on all studies:
> >
> > mod.pertype <- http://rma.mv(yi = z,
> >                     V = vz,
> >                     slab = samid,
> >                     data = df,
> >                     random = ~ 1 | samid/esid,
> >                     test = "t",
> >                     method = "REML",
> >                     dfs="contain",
> >                     mods = ~ pertype)
> >
> > summary(mod.pertype)
> >
> > mod.pertype.robust <- robust(mod.pertype, cluster=df$samid, clubSandwich
> = TRUE)
> > summary(mod.pertype.robust)
> >
> > Am I right that, in this case, the amount of residual heterogeneity will
> be the
> > same in each subgroup?
> > Is it possible to fit a multilevel model with the subgroups using meta-
> > regression while allowing the amount of residual heterogeneity to vary
> across
> > subgroups?
> >
> > I understand that I could fit three separate multilevel models for each
> subgroup
> > and then compare the estimates using a Wald-type test. But I'm wondering
> whether
> > I can fit a single model with varying heterogeneity across subgroups?
> > I read Wolfgang's examples of how to compare estimates from independent
> meta-
> > analyses and subgroups (http://www.metafor-
> > project.org/doku.php/tips:comp_two_independent_estimates). But I'm not
> sure how
> > to apply these examples to a multilevel meta-analysis with categorical
> > moderators.
> >
> > Thanks a lot for your help.
> >
> > Best,
> > Katharina
> >
> > --
> > Katharina Agethen
> > Research Assistant
> > Human Resource Management
> >
> > OWL University of Applied Sciences and Arts
> > Department of Business Administration and Economics
> > Campusallee 12
> > 32657 Lemgo, Germany
>

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