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

[Viechtbauer, Wolfgang (SP)]

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.