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

The fixed effects are estimated using ML/REML estimation.

What you seem to be describing there are the EB estimates of the
cluster-specific intercepts (e.g., Snijders & Boskers, 1999, p. 58-59) for
a simple two-level 'empty' model with just a random intercept. With
additional fixed effects and/or random effects, things will get more
complex.

There are many books that go into this; for example Searle (1992), chapter
6 is very thorough.

I will bow out of further replies as typing is aggravating my arm.

Best,
Wolfgang

-----Original Message-----
From: Simon Harmel [mailto:sim.harmel at gmail.com]
Sent: Monday, 31 January, 2022 21:40
To: Viechtbauer, Wolfgang (SP)
Cc: R meta
Subject: Re: [R-meta] rma.mv only for better SEs

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 at maastrichtuniversity.nl> wrote:
This is not correct. Also ordinary multilevel models have a weight matrix.

-----Original Message-----
From: Simon Harmel [mailto:sim.harmel at 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 at maastrichtuniversity.nl> wrote:
Right, sorry, that was a typo.

Best,
Wolfgang

-----Original Message-----
From: Simon Harmel [mailto:sim.harmel at 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 at 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 at 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 at maastrichtuniversity.nl> wrote:
Just try it out and you will see what happens.

Best,
Wolfgang

-----Original Message-----
From: Simon Harmel [mailto:sim.harmel at 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 at 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 at 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