[R-sig-ME] Is crossed random-effect the only choice?
Jack Solomon
kj@j@o|omon @end|ng |rom gm@||@com
Mon Jul 19 16:31:59 CEST 2021
Dear Thierry,
Thank you for your interesting comment (H being nested in X). I read your
informative webpage as well which was in large part in line with this
comment: (https://stats.stackexchange.com/a/228814/140365).
I think a little context can help. Think of H as a group of studies (each
with one or more rows). And think of X as scientific formulas each of which
a study has used (for all its rows) to measure the same construct.
Given this context and the data below, do you think there is a "nesting" or
a "crossing" (full or partial) relationship between studies (H) and the
formulas (X) they used, why?
Thanks, Jack
H X
1 2
1 2
2 1
2 1
2 1
3 2
4 1
On Mon, Jul 19, 2021 at 1:58 AM Thierry Onkelinx <thierry.onkelinx using inbo.be>
wrote:
> Dear Jack,
>
> In your example H is implicitly nested in X. See
> https://www.muscardinus.be/2017/07/lme4-random-effects/ for
> more information on nested vs crossed effects.
>
> Best regards,
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders
> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
> FOREST
> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
> thierry.onkelinx using inbo.be
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> www.inbo.be
>
>
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> Op vr 16 jul. 2021 om 01:09 schreef Jack Solomon <kj.jsolomon using gmail.com>:
>
>> Dear Ben,
>>
>> Just to make sure, the structure of my data is below. With this data
>> structure, I wonder why ~ (1|H) + (1|X) would indicate that H and X are
>> crossed random-effects?
>>
>> Because theoretically every value of X is capable of meeting every value
>> of
>> H (Or because each value of X means the same thing across any given value
>> of H)?
>>
>> Does this also mean each unique cluster (separately for H & X) is
>> considered correlated with another cluster?
>>
>> Thank you, Jack
>>
>> H X
>> 1 2
>> 1 2
>> 2 1
>> 2 1
>> 2 1
>> 3 2
>> 4 1
>>
>> On Thu, Jul 15, 2021 at 8:46 AM Ben Bolker <bbolker using gmail.com> wrote:
>>
>> >
>> >
>> > On 7/15/21 9:44 AM, Jack Solomon wrote:
>> > > Dear Ben,
>> > >
>> > > In the case of #3 in your response, if the researcher intends to
>> > > generalize beyond the 3 levels of the categorical factor/ predictor X,
>> > > then can s/he use: ~ (1|H) + (1|X)?
>> > >
>> > > If yes, then H and X will be crossed?
>> > >
>> > > Thanks,
>> > > Jack
>> >
>> > Yes, and yes.
>> > >
>> > >
>> > > On Sat, Jul 10, 2021, 10:36 PM Jack Solomon <kj.jsolomon using gmail.com
>> > > <mailto:kj.jsolomon using gmail.com>> wrote:
>> > >
>> > > Dear Ben,
>> > >
>> > > Thank you for your informative response. I think # 4 is what
>> matches
>> > > my situation.
>> > >
>> > > Thanks again, Jack
>> > >
>> > > On Sat, Jul 10, 2021 at 8:30 PM Ben Bolker <bbolker using gmail.com
>> > > <mailto:bbolker using gmail.com>> wrote:
>> > >
>> > > The "crossed vs random" terminology is only relevant in
>> > > models with
>> > > more than one grouping variable. I would call (1|X) " a
>> random
>> > > effect
>> > > of X" or more precisely "a random-intercept model with
>> grouping
>> > > variable X"
>> > >
>> > > However, your question is a little unclear to me. Is X a
>> > > grouping
>> > > variable or a predictor variable (numeric or categorical) that
>> > > varies
>> > > across groups?
>> > >
>> > > I can think of four possibilities.
>> > >
>> > > 1. X is the grouping variable (e.g. "hospital"). Then ~
>> (1|X)
>> > > is a
>> > > model that describes variation in the model intercept /
>> baseline
>> > > value,
>> > > across hospitals.
>> > >
>> > > 2. X is a continuous covariate (e.g. annual hospital
>> > > budget). Then if
>> > > H is the factor designating hospitals, we want ~ X + (1|H)
>> > > (plus any
>> > > other fixed effects of interest. (It doesn't make sense /
>> isn't
>> > > identifiable to fit a random-slopes model ~ (H | X) because
>> > budgets
>> > > don't vary within hospitals.
>> > >
>> > > 3. X is a categorical / factor predictor (e.g. hospital size
>> > class
>> > > {small, medium, large} with multiple hospitals measured in
>> each
>> > > size
>> > > class: ~ X + (1|H) (the same as #2).
>> > >
>> > > 4. X is a categorical predictor with unique values for each
>> > > hospital
>> > > (e.g. postal code). Then X is redundant with H, you shouldn't
>> > > try to
>> > > include them both in the same model.
>> > >
>> > > On 7/10/21 4:55 PM, Jack Solomon wrote:
>> > > > Hello Allo,
>> > > >
>> > > > In my two-level data structure, I have a cluster-level
>> > > variable (called
>> > > > "X"; one that doesn't vary in any cluster). If I intend to
>> > > generalize
>> > > > beyond X's current possible levels, then, I should take X
>> as
>> > > a random
>> > > > effect.
>> > > >
>> > > > However, because "X" doesn't vary in any cluster,
>> therefore,
>> > > such a random
>> > > > effect necessarily must be a crossed random effect (e.g.,
>> "~
>> > > 1 | X"),
>> > > > correct?
>> > > >
>> > > > If yes, then what is "X" crossed with?
>> > > >
>> > > > Thank you,
>> > > > Jack
>> > > >
>> > > > [[alternative HTML version deleted]]
>> > > >
>> > > > _______________________________________________
>> > > > R-sig-mixed-models using r-project.org
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>> > > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
>> > > >
>> > >
>> > > --
>> > > Dr. Benjamin Bolker
>> > > Professor, Mathematics & Statistics and Biology, McMaster
>> > University
>> > > Director, School of Computational Science and Engineering
>> > > Graduate chair, Mathematics & Statistics
>> > >
>> > > _______________________________________________
>> > > R-sig-mixed-models using r-project.org
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>> > > <https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models>
>> > >
>> >
>> > --
>> > Dr. Benjamin Bolker
>> > Professor, Mathematics & Statistics and Biology, McMaster University
>> > Director, School of Computational Science and Engineering
>> > Graduate chair, Mathematics & Statistics
>> >
>>
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