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

[Jack Solomon]

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


On Sat, Jul 10, 2021, 10:36 PM Jack Solomon <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> 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]]