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

[Tip But]

Dear Wolfgang,

Thanks, I meant a link that gets into the details of how taking the
sampling variances of effect sizes as known, allows to then add an
additional random-effect for the individual effect sizes themselves in
meta-regression? (which ordinary multilevel models can't do as I assume
scores can't come with their uncertainties).

On Fri, Mar 19, 2021 at 2:21 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> See below.
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: Tip But [mailto:fswfswt using 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?
>
> Sorry, no idea, but it's self-evident once you realize that such a random
> effect is identical to the error term.
>
> >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)?
>
> Adding a random effect at the school level in essence already fulfills
> this purpose. Such a model allows for the observations of pupils from the
> same school to be correlated (look into the intraclass correlation
> coefficient).
>
> >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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