[R-sig-ME] Non normal random effects

[Douglas Bates]

On Sat, Nov 27, 2010 at 6:43 AM, Eric Edeline <edeline at biologie.ens.fr> wrote:
> Dear John,
>
> thanks for your feed back and for the useful tutorial. Actually the random
> effect in question is normally distributed (I did not check before, sorry),
> so the problem comes from somewhere else. I am modeling fish body size from
> a large dataset as a function of many covariates, and adding a "species"
> effect (be it fixed or random) skews the residuals but drops the AIC:
>
> m1<-lmer(log(Length)
> ~log(Slope)+log(Width)+Temp*log(D)+Temp*log(Compint2)+Temp*log(Predln102)+Temp*Year
> +(1|Species/Station),
> data=Data, na.action=na.omit, REML=TRUE) #AIC 73427, skewed residuals

Just in terms of the model specification, do you really mean
(1|Species/Station)?  That expands to

 (1|Species) + (1|Species:Station)

and wouldn't reduce to (1|Station) in a model specification.  I think
you meant "species within station", which would be written as
(1|Station/Species) although I prefer the more explicit form
(1|Station) + (1|Station:Species)

> m2<-lmer(log(Length)
> ~log(Slope)+log(Width)+Temp*log(D)+Temp*log(Compint2)+Temp*log(Predln102)+Temp*Year
> +(1|Station),
> data=Data, na.action=na.omit, REML=TRUE) #AIC 147157, Gaussian residuals
>
> This looks puzzling to me. Would you have an idea for why introducing a
> normally distributed effect shews the residuals?
>
>
>
>
> On 11/26/2010 10:51 PM, John Maindonald wrote:
>>
>> Contrary to what is often claimed, it is not the normality of the
>> random effects themselves that matters, but the normality of
>> the sampling distribution of the relevant fixed effect.  In mixed
>> models, there is by comparison with iid models the additional
>> complication that normality can affect the trade-offs between
>> the different components in the fitted model.   Opportunities
>> for such trade-offs are large if there are several random effects
>> and there is imbalance or incompleteness (some combinations
>> of factor levels missing) in the fixed effects structure.  Non-normality
>> in the random effects can then be both hard to detect and have
>> implications for inference.
>>
>> There is an examination of a data set with a relatively complicated
>> random effects structure in the overheads at:
>> http://www.maths.anu.edu.au/%7Ejohnm/r-book/2edn/xtras/mlm-ohp.pdf
>>
>> John Maindonald             email: john.maindonald at anu.edu.au
>> phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
>> Centre for Mathematics&  Its Applications, Room 1194,
>> John Dedman Mathematical Sciences Building (Building 27)
>> Australian National University, Canberra ACT 0200.
>> http://www.maths.anu.edu.au/~johnm
>>
>> On 27/11/2010, at 7:04 AM, Eric Edeline wrote:
>>
>>
>>>
>>> Dear list,
>>>
>>> is non normality of random effects a serious issue for inference on the
>>> fixed effects? I am having a non normal random effect that tremendously
>>> improves model AIC.
>>>
>>> Thanks!
>>>
>>> --
>>> Eric Edeline
>>> Assistant Professor
>>> UPMC-Paris6
>>> UMR 7618 BIOEMCO
>>> Ecole Normale Supérieure
>>> 46 rue d'Ulm
>>> 75230 Paris cedex 05
>>> France
>>>
>>> Tel: +33 (0)1 44 32 38 84
>>> Fax: +33 (0)1 44 32 38 85
>>>
>>> http://www.biologie.ens.fr/bioemco/biodiversite/edeline.html
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>>
>>
>>
>
> --
> Eric Edeline
> Assistant Professor
> UPMC-Paris6
> UMR 7618 BIOEMCO
> Ecole Normale Supérieure
> 46 rue d'Ulm
> 75230 Paris cedex 05
> France
>
> Tel: +33 (0)1 44 32 38 84
> Fax: +33 (0)1 44 32 38 85
>
> http://www.biologie.ens.fr/bioemco/biodiversite/edeline.html
>
> _______________________________________________
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