[R-sig-ME] Is crossed random-effect the only choice?
Thierry Onkelinx
th|erry@onke||nx @end|ng |rom |nbo@be
Mon Jul 19 08:58:24 CEST 2021
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
> > >
> > > _______________________________________________
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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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