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

[Viechtbauer, Wolfgang (SP)]

@James: Thanks - as always, your blog entries are a pleasure to read.

The model being used by Filippo (with 'mods = ~ 0 + outcome') suggests that this is a 'multivariate case' of the third type, although we don't know if there may be more than one estimate for a particular outcome type within some of the studies or not. Regardless, V should of course capture the dependencies in the estimates, whether they are covariances between two estimates for the same type of outcome or for two estimates corresponding two different outcome types.

In any case, I still don't understand what gls() has to do with anything here or how this relates to the original query or distinction between different uses of the term 'multivariate'.

Best,
Wolfgang

>-----Original Message-----
>From: Luke Martinez [mailto:martinezlukerm using gmail.com]
>Sent: Wednesday, 24 November, 2021 18:07
>To: James Pustejovsky
>Cc: Viechtbauer, Wolfgang (SP); R meta
>Subject: Re: [R-meta] multivariate fixed-effect meta-analysis
>
>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