Is crossed random-effect the only choice?
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 at 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 at gmail.com
<mailto:kj.jsolomon at 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 at gmail.com
<mailto:bbolker at 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
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