[R-meta] Guidance regarding balance in fixed- and random-effects

[Luke Martinez]

Thank you Wolfgang.

My concern was that wouldn't the subsequent models like (2) shown
below where moderators return ZERO variance for some of the initially
non-ZERO levels in (1) be overparameterized?

That is, IF:

(1) rma.mv(yi, vi, random = ~ 1 | lab / study / outcome / time /
rowID) ==> All levels give non-ZERO variance

(2) rma.mv(yi ~ mod1*mod2, vi, random = ~ 1 | lab / study / outcome /
time / rowID) ==> Now, "lab" & "outcome" give ZERO variance

THEN: is (2) overparameterized?

IF yes, THEN reparameterize (1) to make its random part match (2):

(11) rma.mv(yi, vi, random = ~ 1 | study / time / rowID) ==> All
levels give non-ZERO variance

(22) rma.mv(yi ~ mod1*mod2, vi, random = ~ 1 | study / time / rowID)
==> All levels give non-ZERO variance

On Thu, Oct 14, 2021 at 7:21 AM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>
> If the estimate of sigma^2 for lab is zero, then
>
> rma.mv(yi, vi, random = ~ 1 | lab / study / outcome / time / rowID)
>
> and
>
> rma.mv(yi ~ mod1*mod2, vi, random = ~ 1 | study / time / rowID)
>
> are identical. So I would not bother to manually drop the lab random effect, since in essence this happens automatically.
>
> In general, I would use (1) for all analyses since this is the a priori chosen model that is meant to reflect the dependencies and sources of heterogeneity you think may be relevant. If some components end up being 0 in some models, then so be it, but I would stick to one model for all analyses.
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
> >Behalf Of Luke Martinez
> >Sent: Wednesday, 13 October, 2021 23:26
> >To: R meta
> >Subject: [R-meta] Guidance regarding balance in fixed- and random-effects
> >
> >Dear Experts,
> >
> >Forgive my modeling question. But in answering RQs like: what is the
> >overall effect of X, I often fit an intercept-only model with several
> >nested levels, like:
> >
> >(1) rma.mv(yi, vi, random = ~ 1 | lab / study / outcome / time / rowID)
> >
> >In the above model, all levels reveal heterogeneity in them.
> >
> >But then in answering other RQs, when I add a couple of moderators,
> >some of the levels (e.g., "outcome" AND "lab") return ZERO
> >heterogeneity making me fit a simpler model, like:
> >
> >(2) rma.mv(yi ~ mod1*mod2, vi, random = ~ 1 | study / time / rowID)
> >
> >Question: When this happens, does this mean that I should go back and
> >refit model (1) without "outcome" AND "lab" to uniform the random
> >specification of model (1) and model (2)?
> >
> >OR, model (1) is appropriate for RQ1 and model (2) is appropriate for RQ2s?
> >
> >Thank you for your perspectives,
> >Luke