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

[Luke Martinez]

Sure, I meant more generally with a user-specified V_matrix in case it
is of some weird form (e.g., different for some studies).

Also, @Reza thank you (as always) for pointing out the equivalency of
gls to what metafor's fixed multivariate model does.

There is a tradition (called marginal modeling) where some do this
when errors are correlated but that the data are not multilevel in
structure (usually used in purely repeated measures data).

Given that the idea behind repeated measures modeling and multiple
outcomes modeling are kind of similar, then one can essentially use
gls() to replicate such models as demonstrated above.

Luke

On Wed, Nov 24, 2021 at 11:15 AM James Pustejovsky <jepusto using gmail.com> wrote:
>
> 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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