[R-meta] rma.mv only for better SEs

[Simon Harmel]

Oh, all I knew was that ordinary multilevel estimates of fixed effect are
obtained via empirical Bayes (eb) and have the following algebraic relation
to their OLS counterparts.

Is there any reference that explains the nature of these weights and refers
to them as "weights"?


Beta_eb = Lambda * Beta_ols + (1 - lambda) * grand mean

where Lambda = Heterogeneity_betw. /  [Heterogeneity_betw. + (residual var.
/ n_clusters)]

On Mon, Jan 31, 2022 at 2:27 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> This is not correct. Also ordinary multilevel models have a weight matrix.
>
> >-----Original Message-----
> >From: Simon Harmel [mailto:sim.harmel using gmail.com]
> >Sent: Monday, 31 January, 2022 21:14
> >To: Viechtbauer, Wolfgang (SP)
> >Cc: R meta
> >Subject: Re: [R-meta] rma.mv only for better SEs
> >
> >This is very helpful, thank you so very much.
> >
> >Simon
> >ps. This may be loosely relevant but in ordinary multilevel models, we
> don't use
> >weights, but still random-effects' structures do have a bearing on the
> fixed
> >effect estimates. So, aside from weights, something else from
> random-effects must
> >have an impact on fixed-effect magnitude.
> >
> >On Mon, Jan 31, 2022 at 2:04 PM Viechtbauer, Wolfgang (SP)
> ><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> >Right, sorry, that was a typo.
> >
> >Best,
> >Wolfgang
> >
> >>-----Original Message-----
> >>From: Simon Harmel [mailto:sim.harmel using gmail.com]
> >>Sent: Monday, 31 January, 2022 19:29
> >>To: Viechtbauer, Wolfgang (SP)
> >>Cc: R meta
> >>Subject: Re: [R-meta] rma.mv only for better SEs
> >>
> >>Sure, but didn't you by any chance mean to say:
> >>"The random effects structure determines the weight matrix, which in turn
> >affects
> >>the estimates of the **fixed effects**".
> >>
> >>On Mon, Jan 31, 2022 at 12:23 PM Viechtbauer, Wolfgang (SP)
> >><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> >>The random effects structure determines the weight matrix, which in turn
> affects
> >>the estimates of the random effects.
> >>
> >>Best,
> >>Wolfgang
> >>
> >>>-----Original Message-----
> >>>From: Simon Harmel [mailto:sim.harmel using gmail.com]
> >>>Sent: Monday, 31 January, 2022 18:29
> >>>To: Viechtbauer, Wolfgang (SP)
> >>>Cc: R meta
> >>>Subject: Re: [R-meta] rma.mv only for better SEs
> >>>
> >>>I have done it, and in my case the results differ. But my point was, is
> my
> >>>explanation regarding why they differ accurate?
> >>>
> >>>On Mon, Jan 31, 2022 at 11:24 AM Viechtbauer, Wolfgang (SP)
> >>><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> >>>Just try it out and you will see what happens.
> >>>
> >>>Best,
> >>>Wolfgang
> >>>
> >>>>-----Original Message-----
> >>>>From: Simon Harmel [mailto:sim.harmel using gmail.com]
> >>>>Sent: Monday, 31 January, 2022 18:21
> >>>>To: Viechtbauer, Wolfgang (SP)
> >>>>Cc: R meta
> >>>>Subject: Re: [R-meta] rma.mv only for better SEs
> >>>>
> >>>>Thank you, Wolfgang. I asked this, because I noticed applying RVE to an
> >>rma.mv()
> >>>>model has no bearing on the estimates of fixed effects themselves, and
> just
> >>>>modifies their SEs.
> >>>>
> >>>>So, I wondered if the same rule, at least "in principle", should apply
> when we
> >>>go
> >>>>from rma() to rma.mv().
> >>>>
> >>>>But is there a principle regarding how random effects affect the fixed
> >effects?
> >>>>
> >>>>For instance, in:
> >>>>
> >>>>1- rma.mv(y ~ 1, random = ~ 1|study/obs), the overall average only
> represents
> >>>the
> >>>>average of study-level effects.
> >>>>
> >>>>But, in:
> >>>>
> >>>>2- rma.mv(y ~ 1, random = ~ 1|study/outcome/obs), the overall average
> >>represents
> >>>>the average of study-level effects additionally affected by the
> outcome-level
> >>>>effects within them.
> >>>>
> >>>>And thus, 1- and 2- may give different overall averages, right?
> >>>>
> >>>>Simon
> >>>>
> >>>>On Mon, Jan 31, 2022 at 11:00 AM Viechtbauer, Wolfgang (SP)
> >>>><wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> >>>>Generally, two models with different random effects structures will
> also give
> >>>you
> >>>>different estimates of the fixed effects (unless the estimates of the
> >>>>variance/covariance components happen to be such that the two models
> collapse
> >>>>down to the same structure).
> >>>>
> >>>>Best,
> >>>>Wolfgang
> >>>>
> >>>>>-----Original Message-----
> >>>>>From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org]
> >>On
> >>>>>Behalf Of Simon Harmel
> >>>>>Sent: Monday, 31 January, 2022 17:49
> >>>>>To: R meta
> >>>>>Subject: [R-meta] rma.mv only for better SEs
> >>>>>
> >>>>>Hello List Members,
> >>>>>
> >>>>>Reviewing the archived posts, my understanding is that my studies can
> >>>>>produce multiple effects, so I should use rma.mv() not rma().
> >>>>>
> >>>>>Also, I understand rma.mv() ensures that I get more accurate SEs for
> my
> >>>>>fixed effects relative to rma().
> >>>>>
> >>>>>BUT does that also mean that, by definition, rma.mv() should have no
> >>>>>bearing on the magnitude of the fixed effects themselves and only
> modifies
> >>>>>their SEs relative to rma()?
> >>>>>
> >>>>>Thank you,
> >>>>>Simon
>

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