Beta-binomial distributions with lmer?
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
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---------------------- 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