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

[Viechtbauer, Wolfgang (SP)]

>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.

But it doesn't. Neither

rma.mv(yi ~ 0 + outcome, V = vi, data = data)

nor

gls(yi~0 + outcome, weights = varFixed(~ vi), control=glsControl(sigma = 1), data = data)

are multivariate models in my book, as they do not account for any covariance between the estimates. In fact, these are just the same as

rma(yi, vi, mods = ~ 0 + outcome, data=dat)

and that's simply a wrong model when there are dependent estimates.

On the other hand, rma.mv(yi ~ 0 + outcome, V = V, data = data) with a proper V matrix is a multivariate (fixed-effects) model.

>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