[R-sig-ME] Mixed model specification (control for location and repeated sampling of same location through time)

[Phillip Alday]

Dear Norman,

Random effects are fundamentally estimates of variance. Computing the 
variance from 3 items will lead to a very noisy estimate -- noisy to the 
point of "generally not useful".

Thierry has a nice write-up here:

https://www.muscardinus.be/2018/09/number-random-effect-levels/

This is also discussed on the GLMM FAQ:

https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html#should-i-treat-factor-xxx-as-fixed-or-random

On top of the variance bit, including Site as a fixed effect doesn't led 
to a horrible model in terms of number of parameters.

There is a common point of confusion that random effects are nuisance 
parameters and thus nuisance parameters, should as replicates, should be 
in the random effects. This isn't quite right.

Best,
Phillip

On 11/8/22 09:06, Norman DAURELLE via R-sig-mixed-models wrote:
> Dear list members, Brian, Thierry,
>
> I am not an expert, but I don't see why the number of sites would be a barrier to introducing it as a random effect.
>
> Would you care to explain the reasoning behind that statement ?
>
> To me, the Y ~ X1 + X2 + X3 + (1 | Site) part seems appropriate (I don't know about how to use the different dates, though).
>
> Sorry if this is not helpful, Brian.
>
> Cheers,
>
> Norman
>
>
>
>
> De: "Thierry Onkelinx via R-sig-mixed-models" <r-sig-mixed-models using r-project.org>
> �: "Brian Gill" <briangillphd using gmail.com>
> Cc: r-sig-mixed-models using r-project.org
> Envoy�: Jeudi 3 Novembre 2022 14:45:01
> Objet: Re: [R-sig-ME] Mixed model specification (control for location and repeated sampling of same location through time)
>
> Dear Brian,
>
> You have only 3 sites. That is too few to use as a random effect.
>
> Look into glmmTMB and INLA. They provide correlated random effects. Which
> is relevant for your Date variable.
>
> The glmmTMB formula might look like this: Y ~ Site + X1 + X2 + X3 +
> ar1(Date | Site)
> The INLA formula: Y ~ Site + X1 + X2 + X3 + f(Date, model = "rw1",
> replicate = as.integer(Site))
>
> Best regards,
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders
> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
> FOREST
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> thierry.onkelinx using inbo.be
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>
> Op ma 31 okt. 2022 om 18:55 schreef Brian Gill <briangillphd using gmail.com>:
>
>> I have three locations (Sites) where I repeatedly measured a number of
>> environmental variables (X1, X2, X3) and a response (Y; normally
>> distributed) over time. That is, I have data on each environmental variable
>> and the response at many time points for each of 3 sites. For each
>> timepoints all three sites were sampled.
>>
>> I want to model the response (Y) as a function of the environmental
>> variables (X1, X2, X3) while controlling for effects of Sites and Time. I
>> expect responses from the same site to be similar because they come from
>> the same location and responses measured at closer timepoints to be more
>> similar than those separated by more time.
>>
>> Can people please advise on an appropriate model specification.
>>
>> I've come up with the following so far:
>>
>> Y ~ Site + X1 + X2 + X3 + (1 | Date)
>>
>> Y ~ X1 + X2 + X3 + (1 | Site) + (1 | Date)
>>
>> My hangups are that I think these models treat Date categorically
>> (controlling for variation from a particular date, but not how close or far
>> dates are from each other). Also, a model allowing both random intercepts
>> and slopes might be better as responses could vary significantly in
>> magnitude and direction among sites.
>>
>> Any advice would be appreciated. Thanks!
>>
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>>
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