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

[Ben Bolker]

  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
>> _______________________________________________
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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
> 
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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