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

[Christine Griffiths]

Dear Ben and Thierry,

Thank you for the advice. I tried to do both suggested methods, however got 
stumped on Ben's suggestion of logit. Thierry's suggestion did improve the 
variances (e.g. 7.7e-04 to 1.94 for the residual variance) when I used 
quasipoisson family errors. Given that the values aren't discrete I am not 
sure this is correct. Ben you only suggest this method if it leads to 
"stable variance". I have tried searching what is meant by this term, but 
have not found any information. If you could clarify or point me in the 
right direction I would gratefully appreciate the assistance.

Cheers
Christine

--On 10 June 2009 10:25 -0400 Ben Bolker <bolker at ufl.edu> wrote:

>   Yes, but ...
>   If the data get "scrunched" near 100% (as well as near zero), then
> I'm not sure that this procedure would lead to stable variances?
> (If it does, that's great.) Why not logit((proportion+m)/(1+2*m)) [where
> m is a small value which can be interpreted as coming from a Bayesian
> prior, if you like] instead? Once we've done all that, we're getting
> pretty close to a quasi-binomial model anyway ...  (It sounds like all
> the N values are the same in this example anyway, so there's no scaling
> of variance with N to worry about.)
>
> ONKELINX, Thierry wrote:
>> 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
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
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>
>
> --
> 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



----------------------
Christine Griffiths
School of Biological Sciences
University of Bristol
Woodland Road
Bristol BS8 1UG
Tel: 0117 9287593
Fax 0117 3317985
Christine.Griffiths at bristol.ac.uk
http://www.bio.bris.ac.uk/research/mammal/tortoises.html