[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 at 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 at maastrichtuniversity.nl> wrote:

-----Original Message-----
From: Luke Martinez [mailto:martinezlukerm at 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 at 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 at 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