[R-sig-ME] Is crossed random-effect the only choice?
Thierry Onkelinx
th|erry@onke||nx @end|ng |rom |nbo@be
Mon Jul 19 19:19:18 CEST 2021
Dear Jack,
IMHO the discussion whether it is nested, partially nested, or crossed is
pointless. Use explicit nesting by creating random effects with unique
levels across the data. That is each level defines a unique state for that
variable, regardless any other variables. So if you consider the formula of
one study is the same as the formula of another study, then they get the
same level, otherwise they get a different level.
Best regards,
ir. Thierry Onkelinx
Statisticus / Statistician
Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx using inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be
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what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
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Op ma 19 jul. 2021 om 16:32 schreef Jack Solomon <kj.jsolomon using gmail.com>:
> Dear Thierry,
>
> Thank you for your interesting comment (H being nested in X). I read your
> informative webpage as well which was in large part in line with this
> comment: (https://stats.stackexchange.com/a/228814/140365).
>
> I think a little context can help. Think of H as a group of studies (each
> with one or more rows). And think of X as scientific formulas each of which
> a study has used (for all its rows) to measure the same construct.
>
> Given this context and the data below, do you think there is a "nesting"
> or a "crossing" (full or partial) relationship between studies (H) and the
> formulas (X) they used, why?
>
> Thanks, Jack
> H X
> 1 2
> 1 2
> 2 1
> 2 1
> 2 1
> 3 2
> 4 1
>
> On Mon, Jul 19, 2021 at 1:58 AM Thierry Onkelinx <thierry.onkelinx using inbo.be>
> wrote:
>
>> Dear Jack,
>>
>> In your example H is implicitly nested in X. See
>> https://www.muscardinus.be/2017/07/lme4-random-effects/ for
>> more information on nested vs crossed effects.
>>
>> Best regards,
>>
>> ir. Thierry Onkelinx
>> Statisticus / Statistician
>>
>> Vlaamse Overheid / Government of Flanders
>> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
>> AND FOREST
>> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
>> thierry.onkelinx using inbo.be
>> Havenlaan 88 bus 73, 1000 Brussel
>> www.inbo.be
>>
>>
>> ///////////////////////////////////////////////////////////////////////////////////////////
>> To call in the statistician after the experiment is done may be no more
>> than asking him to perform a post-mortem examination: he may be able to say
>> what the experiment died of. ~ Sir Ronald Aylmer Fisher
>> The plural of anecdote is not data. ~ Roger Brinner
>> The combination of some data and an aching desire for an answer does not
>> ensure that a reasonable answer can be extracted from a given body of data.
>> ~ John Tukey
>>
>> ///////////////////////////////////////////////////////////////////////////////////////////
>>
>> <https://www.inbo.be>
>>
>>
>> Op vr 16 jul. 2021 om 01:09 schreef Jack Solomon <kj.jsolomon using gmail.com>:
>>
>>> 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]]
>>> > > >
>>> > > > _______________________________________________
>>> > > > 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
>>> >
>>>
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>>>
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>>
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