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

[Viechtbauer, Wolfgang (SP)]

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 using 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 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