Adding Level for non-repeated measurements

-----Original Message-----
From: Tip But [mailto:fswfswt at gmail.com]
Sent: Friday, 19 March, 2021 19:01
To: Viechtbauer, Wolfgang (SP)
Cc: r-sig-mixed-models
Subject: Re: [R-sig-ME] Adding Level for non-repeated measurements

Oh! That clears up my confusion with?respect to 1 (Thank you so much)!? Do you
have a link that gets into the details of that?

With respect to 2, I hopefully will receive some insight as to how to handle the
fact that my students?in each school have been in frequent contact via some form
of treatment of residuals (my understanding is that allowing residuals to
correlate in a cross-sectional study is not an option)?

Once again, thank you for your clarification regarding my first question!
Joe

On Fri, Mar 19, 2021 at 12:46 PM Viechtbauer, Wolfgang (SP)
<wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:
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.