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

[Ben Bolker]

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.
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