Adding Level for non-repeated measurements
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 at 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 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. 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 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:
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.
_______________________________________________ R-sig-mixed-models at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
_______________________________________________ R-sig-mixed-models at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models