[R-sig-ME] Adding Level for non-repeated measurements
Tip But
|@w|@wt @end|ng |rom gm@||@com
Fri Mar 19 20:56:25 CET 2021
Thank you, Ben. The situation in your linked example is a bit different. In
your example, adding the random slope seems to be an overfit (as the
number of repeated measurements is limited) otherwise
theoretically possible.
But in my case, it seems adding a level is not theoretically possible. So,
there certainly is a gap in my knowledge resulting from a carryover from
mixed meta-regression models where we actually can have an
individual-specific random effects with the exact same data structure.
Thanks,
## data structure in mixed meta-regression:
studyID effectSizeID effectSize
1 1 .2
1 2 .1
2 3 .4
3 4 .3
3 5 .6
. . .
. . .
. . .
## data structure in ordinary mixed-models:
sch_id stud_id score
1 1 9
1 2 6
2 3 8
3 4 5
3 5 3
. . .
. . .
. . .
On Fri, Mar 19, 2021 at 2:32 PM Ben Bolker <bbolker using gmail.com> wrote:
>
>
> On 3/19/21 3:21 PM, Viechtbauer, Wolfgang (SP) 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.
>
> Not discussed in detail, but an example that mentions it in passing
> is here: https://ms.mcmaster.ca/~bolker/classes/uqam/mixedlab1.html (the
> "starlings" example)
>
> >
> >> 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.
> > _______________________________________________
> > R-sig-mixed-models using r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
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