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

[Ben Bolker]

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
>         <mailto:R-sig-mixed-models using r-project.org> mailing list
>          > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>         <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
>         <mailto:R-sig-mixed-models using r-project.org> mailing list
>         https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>         <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