Adding Level for non-repeated measurements

Fri, Mar 19, 2021 10:46 AM

Dear Joe,

Meta-analysis is different. In a meta-analysis, the sampling variances (one per estimate) are pre-specified and this allows us to add a random effect corresponding to each estimate to the model. In a multilevel model with a normally distributed response variable, you cannot do this. Well, you can do this, but this random effect is the same as the error term and hence completely confounded.

Best,
Wolfgang

-----Original Message-----
From: Tip But [mailto:fswfswt at gmail.com]
Sent: Friday, 19 March, 2021 18:06
To: David Duffy
Cc: r-sig-mixed-models; Viechtbauer, Wolfgang (SP)
Subject: Re: [R-sig-ME] Adding Level for non-repeated measurements

Dear?David,

Thank you for your response. As my toy example?showed, we do have a normally
distributed response variable.

As to 1), I have seen (e.g., see variable `id` in:
https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-July/000896.html) that
what you refer to as "individual-specific" random-effects are used in, for
example, multi-level meta-regression models with a normally distributed response
variable.

In the context of multi-level meta-regression models with a normally distributed
response variable, the addition of "effectSize-specific" (="individual-specific")
random-effects often account for the variation at the level of individual
estimates of effect size. That is: "effectSize ~ 1 + (1 | studyID / effectSizeID)"
where the data looks like:

studyID? ? ? effectSizeID? ? ?? effectSize
1? ? ? ? ? ? ? ? ? ?1? ? ? ? ? ? ? ? ? ? ? ? .2
1? ? ? ? ? ? ? ? ? ?2? ? ? ? ? ? ? ? ? ? ? ? .1
2? ? ? ? ? ? ? ? ? ?3? ? ? ? ? ? ? ? ? ? ? ? .4
3? ? ? ? ? ? ? ? ? ?4? ? ? ? ? ? ? ? ? ? ? ? .3
3? ? ? ? ? ? ? ? ? ?5? ? ? ? ? ? ? ? ? ? ? ? .6
.? ? ? ? ? ? ? ? ? ? .? ? ? ? ? ? ? ? ? ? ? ? ? .
.? ? ? ? ? ? ? ? ? ? .? ? ? ? ? ? ? ? ? ? ? ? ? .
.? ? ? ? ? ? ? ? ? ? .? ? ? ? ? ? ? ? ? ? ? ? ? .

So, I reasoned if? "(1 | studyID / effectSizeID)" is possible in the context of
multi-level meta-regression models with a normally distributed response variable,
then,? "(1 | sch_id / stud_id)" is possible in the context of multi-level models
with a normally distributed response variable where the data looks like:

sch_id ? ? ? stud_id? ? ? ? ? ? ?score
1? ? ? ? ? ? ? ? ? ?1? ? ? ? ? ? ? ? ? ? ? ? 9
1? ? ? ? ? ? ? ? ? ?2? ? ? ? ? ? ? ? ? ? ? ? 6
2? ? ? ? ? ? ? ? ? ?3? ? ? ? ? ? ? ? ? ? ? ? 8
3? ? ? ? ? ? ? ? ? ?4? ? ? ? ? ? ? ? ? ? ? ? 5
3? ? ? ? ? ? ? ? ? ?5? ? ? ? ? ? ? ? ? ? ? ? 3
.? ? ? ? ? ? ? ? ? ? .? ? ? ? ? ? ? ? ? ? ? ? ? .
.? ? ? ? ? ? ? ? ? ? .? ? ? ? ? ? ? ? ? ? ? ? ? .
.? ? ? ? ? ? ? ? ? ? .? ? ? ? ? ? ? ? ? ? ? ? ? .
### Is my reasoning?flawed here?

As to 2), I can certainly allow the variances in each "sch_id" to be different.
But does this address the correlations among students in each school, correct?

Many thanks,
Joe

On Fri, Mar 19, 2021 at 2:57 AM David Duffy <David.Duffy at qimrberghofer.edu.au>
wrote:
Joe wrote:

I have a cross-sectional (i.e., non-repeated measurements) dataset from
students ("stud_id") nested within many schools ("sch_id").
1- Given above, should we possibly add an additional random-effect for
"stud_id"? If yes, why?
2- Given above, should we also allow residuals in each school (e_ij) to
correlate? If yes, why? (I have a bit of a conceptual problem understanding
this part given the cross-sectional nature of our study.)

I think this is more a slightly-harder-than-elementary stats question rather than
a "technical" query. If this was some types of
GLMM, then the answer to 1 would be yes eg poisson GLMM then an individual-
specific random effect adds in one type of
extra-poisson variation. This is not the case for the gaussian (hopefully you see
why). As to 2, consider how the *variance* of your
measurement could be different within each school.

Adding Level for non-repeated measurements

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