[R-sig-ME] Is crossed random-effect the only choice?

[Jack Solomon]

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
> >         <mailto:R-sig-mixed-models using r-project.org> mailing list
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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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