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

[Jack Solomon]

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> 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 mailing list
> > 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 mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

	[[alternative HTML version deleted]]