Adding Level for non-repeated measurements

See below.

Best,
Wolfgang

-----Original Message-----
From: Tip But [mailto:fswfswt at 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 at 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 at 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 at 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.