[R-sig-ME] Adding Level for non-repeated measurements
Viechtbauer, Wolfgang (SP)
wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Fri Mar 19 18:46:29 CET 2021
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.
>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
>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:
>what you refer to as "individual-specific" random-effects are used in, for
>example, multi-level meta-regression models with a normally distributed response
>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?
>On Fri, Mar 19, 2021 at 2:57 AM David Duffy <David.Duffy using qimrberghofer.edu.au>
>> 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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