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

[Viechtbauer, Wolfgang (NP)]

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