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

[Ben Bolker]

Christine Griffiths wrote:
> 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

   If you transformed the data in some significant way, then the
residual variances aren't necessarily going to be comparable, so
I'm not sure I would take that as confirmation.

I think Thierry meant to suggest a LMM (i.e., assume normal
distributions, no transformation after the initial one) rather
than a GLMM (link function/exponential-family distribution or
quasi-distribution).

You may find more on "stabilizing variance" rather
than "stable variance" -- what I meant was that the variability in the
Pearson residuals (residuals scaled by the expected standard deviation,
which is what lmer gives you) should be independent of the fitted value
-- so try plot(sqrt(residuals(model)) ~ fitted(model)) and see if the
"amplitude" appears reasonably constant (this is approximately the same
as the "scale-location" plot that plot.lm gives you for a linear model).


> 
> --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
> 
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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