See for example the Gleser & Olkin chapter:
Gleser, L. J., & Olkin, I. (2009). Stochastically dependent effect sizes.
In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of
research synthesis and meta-analysis (2nd ed., pp. 357?376). New York:
Russell Sage Foundation.
https://www.metafor-project.org/doku.php/analyses:gleser2009
Best,
Wolfgang
-----Original Message-----
From: Filippo Gambarota [mailto:filippo.gambarota at gmail.com]
Sent: Monday, 03 January, 2022 18:02
To: Viechtbauer, Wolfgang (SP)
Cc: R meta
Subject: Re: [R-meta] fixed-effect multivariate model interpretation
Ah great! do you have any references for this? because I would like to
understand what is going on. Cochrane's Q-statistic is the deviation of
study from the estimated average effect weighted by the precision. In
the "average" effect is the average between outcomes? Or the formula is
different?
Thank you!
On Mon, 3 Jan 2022 at 17:12, Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
It's just the multivariate version of Cochrane's Q-test. It does not
random-effects model. It simply tests whether the observed amount of
is larger than expected based on the sampling variances (and their
when V includes those) and any moderators specified.
Best,
Wolfgang
-----Original Message-----
From: Filippo Gambarota [mailto:filippo.gambarota at gmail.com]
Sent: Monday, 03 January, 2022 17:11
To: Viechtbauer, Wolfgang (SP)
Cc: R meta
Subject: Re: [R-meta] fixed-effect multivariate model interpretation
Thank you Wolfgang!
So my related question is how this residual heterogeneity is estimated
to compute the Q statistic? Because if the model is still estimating and
the presence of heterogeneity, from a multivariate model I would have
one residual heterogeneity term for each outcome (the same as I have one
outcome if I fit the random-effect version).
On Mon, 3 Jan 2022 at 16:50, Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
Hi Filippo,
You can *assume* that there is no residual heterogeneity, but there may
is what the test of residual heterogeneity is testing here (whether your
assumption is correct or not).
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: Monday, 03 January, 2022 16:42
To: R meta
Subject: [R-meta] fixed-effect multivariate model interpretation
Hello!
I'm fitting for the first time a multivariate fixed-effect model using
metafor. The code is:
```
rma.mv(yi, V, mods = ~ 0 + outcome, data = data, test = "t")
```
Where V is the block variance-covariance matrix created with vcalc()
that represents the covariance between different outcome levels within
each study. The outcome is a factor that represents different effect
sizes measured on the same participants within a study.
The model as expected did not estimate tau for each outcome and test
all coefficients (each outcome mean with this parametrization) against
0 (both the omnibus test and each beta). My question is about the
*residual heterogeneity* parameter and the associated Q test. Under
this model, I should have assumed that there is no heterogeneity
within each outcome level so I'm not sure how to interpret the
residual heterogeneity in this case.
Thank you!
Filippo
--
Filippo Gambarota
PhD Student - University of Padova
Department of Developmental and Social Psychology
Website: filippogambarota.netlify.app
Research Group: Colab Psicostat