[R-sig-ME] Adding Level for non-repeated measurements

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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 using 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.
>

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