[R-sig-ME] Is crossed random-effect the only choice?
Jack Solomon
kj@j@o|omon @end|ng |rom gm@||@com
Fri Jul 16 01:08:37 CEST 2021
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]]
> > >
> > > _______________________________________________
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> > >
> >
> > --
> > 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
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> >
>
> --
> 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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