[R-sig-ME] Beta-binomial distributions with lmer?

[ONKELINX, Thierry]

Dear Christine,

We had recently a vivid discussion on whether it is appropriate to model
percentages by a (quasi)binomial model. We were modelling the precentage
of leaves that is missing from trees. The mixed model with the binomial
family had random effects with extremly small variances. My colleague
argued that this percentage did not come from a bernouilli experiment.
And hence the binomial family was not appropriate. He suggested to put
the percentage on a 0 to 100 scale and apply a log(x+1) transformation.
This resulted in a linear mixed model with random effects that had
reasonable variances. This convinced me that the binomial family only
makes sense with binary data.

HTH,

Thierry


------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
methodology and quality assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium
tel. + 32 54/436 185
Thierry.Onkelinx at inbo.be
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

-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] Namens Ben Bolker
Verzonden: woensdag 10 juni 2009 15:59
Aan: Christine Griffiths
CC: r-sig-mixed-models at r-project.org
Onderwerp: Re: [R-sig-ME] Beta-binomial distributions with lmer?

  That's a good question, answers will differ.  Since "all models are
wrong" anyway, provided that a mean-variance relationship of V =
phi*N*p*(1-p) seems plausible, I would say you should go for it.  You're
near the cutting edge anyway ... (I don't have a copy, but you might see
whether Zuur et al's book has anything to say on the subject -- they're
very pragmatic ecologists, and I think they use GEE/quasi models quite a
lot ...)

  Ben Bolker


Christine Griffiths wrote:
> Thanks. I was hoping for a miracle that this had been developed within

> the last couple of months.
> 
> I am on the stats learning curve and am not quite sure how flexible to

> be with regards to distributions.  Is quasibinomial acceptable, 
> despite having data with a lot of 0s and a lot of 100s?
> 
> Many thanks in advance,
> Christine
> 
> --On 10 June 2009 09:18 -0400 Ben Bolker <bolker at ufl.edu> wrote:
> 
>>   No.  You can use a quasi-binomial model, although the support is a 
>> little bit spotty (and beware that
>> quasi- models may falsely report inflation of the random effects).
>>
>>   Ben Bolker
>>
>>
>> Christine Griffiths wrote:
>>> Hi R users,
>>>
>>> Just a query as to whether lme4 can handle beta-binomial 
>>> distributions as I  read that this was not available.
>>>
>>> If not, any suggestions on how to handle such a distribution to plot

>>> the following model:
>>> y<-cbind(Biotic,Abiotic)
>>> m1<-lmer(y~Treatment+Month.rain+(1|Month)+(1|Block/EnclosureID/Quadr
>>> at))
>>>
>>> y referring to percentage cover of biotic matter.
>>>
>>> Cheers,
>>> Christine
>>>
>>> _______________________________________________
>>> R-sig-mixed-models at r-project.org mailing list 
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>> --
>> Ben Bolker
>> Associate professor, Biology Dep't, Univ. of Florida bolker at ufl.edu /

>> www.zoology.ufl.edu/bolker GPG key: 
>> www.zoology.ufl.edu/bolker/benbolker-publickey.asc
> 
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list 
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models


--
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida bolker at ufl.edu /
www.zoology.ufl.edu/bolker GPG key:
www.zoology.ufl.edu/bolker/benbolker-publickey.asc

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