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

[Tip But]

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 using 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 using 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 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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