[R-meta] multivariate fixed-effect meta-analysis

[James Pustejovsky]

Actually, I think you could fit a model with gls that does include
correlated sampling errors:

gls(yi ~ 0 + outcome,
     weights = varFixed(~ vi),
     correlation = corCompSymm(rho, ~ 1 | studyID, fixed = TRUE),
     control = glsControl(sigma = 1),
     data = data)

I've always wondered about whether it would make sense to fit a model
like this but allowing the sampling correlation to be estimated rather
than fixed.

James

On Wed, Nov 24, 2021 at 11:07 AM Luke Martinez <martinezlukerm using gmail.com> wrote:
>
> Hi James,
>
> Yes exactly. However, obviously one can't replicate a meta-regression
> model like:
>
> rma.mv(yi ~ 0 + outcome, V = V_matrix, data = data)
>
> using nlme::gls() like:
>
> gls(yi~0 + outcome, weights = varFixed(~ vi), control=
> glsControl(sigma = 1), data = data)
>
> Because gls (and lme) doesn't allow a var-covariance matrix via their
> `correlation=` argument (?).
>
> That said, the following exactly match:
>
> rma.mv(yi ~ 0 + outcome, V = vi, data = data)
>
> gls(yi~0 + outcome, weights = varFixed(~ vi), control=
> glsControl(sigma = 1), data = data)
>
> Luke
>
>
> On Wed, Nov 24, 2021 at 10:47 AM James Pustejovsky <jepusto using gmail.com> wrote:
> >
> > The term "multivariate" is used in several different ways in the
> > meta-analysis (and mixed-effects models) literature. The metafor
> > documentation usually uses it in the broadest sense of a model with
> > more than one effect size estimate per independent sample. I think
> > Luke was referring to the stricter sense of a model for a set of
> > multi-variate effect size estimates (where each study contributes at
> > most one effect size estimate to each of several distinct categories).
> >
> > More on disambiguation here:
> > https://www.jepusto.com/what-does-multivariate-mean/
> >
> > On Wed, Nov 24, 2021 at 7:45 AM Viechtbauer, Wolfgang (SP)
> > <wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> > >
> > > >-----Original Message-----
> > > >From: Luke Martinez [mailto:martinezlukerm using gmail.com]
> > > >Sent: Tuesday, 23 November, 2021 20:38
> > > >To: Viechtbauer, Wolfgang (SP)
> > > >Cc: Filippo Gambarota; R meta
> > > >Subject: Re: [R-meta] multivariate fixed-effect meta-analysis
> > > >
> > > >Dear Wolfgang,
> > > >
> > > >Strictly, the model is fixed-effects multivariate (i.e., MANOVA type)
> > > >if Filippo has one effect size per outcome, right?
> > >
> > > I don't know what you mean by that. If you only specify V and no random effects, one could call it a multivariate fixed-effects model, just like used for example in this chapter:
> > >
> > > https://www.metafor-project.org/doku.php/analyses:gleser2009
> > >
> > > Whether one has one effect size per outcome or 20 is not relevant as long as V captures the covariance between the sampling errors of the estimates.
> > >
> > > >I mean to the extent that this is not the case, then will this model
> > > >diverge from a fixed-effect multivariate model and become more like
> > > >marginal models (i.e., nlme::gls() type)?
> > >
> > > Again, I can't follow your reasoning here.
> > >
> > > >Thanks,
> > > >Luke
> > > >
> > > >On Tue, Nov 23, 2021 at 1:22 PM Viechtbauer, Wolfgang (SP)
> > > ><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> > > >>
> > > >> With method="FE", 'random' is also ignored. You will see in the output that it
> > > >says "Variance Components: none".
> > > >>
> > > >> If 'cov_mat' captures the sampling error covariances, then this could be argued
> > > >to be a fixed-effects version of a multivariate model.
> > > >>
> > > >> Best,
> > > >> Wolfgang
> > > >>
> > > >> >-----Original Message-----
> > > >> >From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org]
> > > >On
> > > >> >Behalf Of Filippo Gambarota
> > > >> >Sent: Tuesday, 23 November, 2021 20:07
> > > >> >To: R meta
> > > >> >Subject: [R-meta] multivariate fixed-effect meta-analysis
> > > >> >
> > > >> >Hi!
> > > >> >I'm performing a multivariate meta-analysis with metafor, however I'm
> > > >> >not sure how to obtain the fixed-effect version. Given that I have not
> > > >> >enough data I'm not interested in estimating tau for each outcome and
> > > >> >the correlation among outcomes but only taking into account the
> > > >> >sampling error dependence. I'm using this function:
> > > >> >```
> > > >> >rma.mv(
> > > >> >    yi = eff_size,
> > > >> >    V = cov_mat,
> > > >> >    mods = ~ 0 + outcome,
> > > >> >    struct = "UN",
> > > >> >    random = ~ outcome|paper_id,
> > > >> >    method = "FE",
> > > >> >    data = data)
> > > >> >```
> > > >> >Of course, the struct argument is no more relevant (as the warning
> > > >> >message said) but I'm wondering if the result is what I'm looking for
> > > >> >because from the rma.mv documentation the method = "FE" is not
> > > >> >mentioned combined with a multivariate parametrization.
> > > >> >Thank you!
> > > >> >
> > > >> >--
> > > >> >Filippo Gambarota
> > > >> >PhD Student - University of Padova
> > > >> >Department of Developmental and Social Psychology
> > > >> >Website: filippogambarota.netlify.app
> > > >> >Research Group: Colab   Psicostat
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