[R-meta] fixed-effect multivariate model interpretation

[Viechtbauer, Wolfgang (SP)]

It's just the multivariate version of Cochrane's Q-test. It does not estimate a random-effects model. It simply tests whether the observed amount of variability is larger than expected based on the sampling variances (and their covariances when V includes those) and any moderators specified.

Best,
Wolfgang

>-----Original Message-----
>From: Filippo Gambarota [mailto:filippo.gambarota using 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 in order
>to compute the Q statistic? Because if the model is still estimating and testing
>the presence of heterogeneity, from a multivariate model I would have expected
>one residual heterogeneity term for each outcome (the same as I have one tau per
>outcome if I fit the random-effect version).
>
>On Mon, 3 Jan 2022 at 16:50, Viechtbauer, Wolfgang (SP)
><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>Hi Filippo,
>
>You can *assume* that there is no residual heterogeneity, but there may be. That
>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 using 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