[R-sig-ME] Question regarding GLMMs and proportional data

[ONKELINX, Thierry]

Dear Rachel,

IMHO you should choose the most appropriate distribution depending on the nature of the response. If it comes for  a number of Bernoulli trails, then the binomial family makes more sense than the gamma. I presume that the denominator is integer? If the denominator is real, then the data generating process is not a set of Bernoulli trials.

I'm not sure if you can compare AIC among models with a different family.

Best regards,

Thierry

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx op inbo.be
www.inbo.be

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~ Sir Ronald Aylmer Fisher

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-----Oorspronkelijk bericht-----
Van: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces op r-project.org] Namens Rachael Eaton
Verzonden: woensdag 21 januari 2015 20:59
Aan: r-sig-mixed-models op r-project.org
Onderwerp: [R-sig-ME] Question regarding GLMMs and proportional data

Hello,

I am having some trouble identifying the best model structure for my data.
I am trying to construct models to look at a response variable of proportions. These data are highly skewed toward zero, with a max value of 0.2. I also have one random variable and a few fixed effects. Therefore, I decided to use GLMM. I applied a log-transformation of (1 + the response variable). I then modeled these using glmer with a gamma family with an inverse link.

Following concerns from a colleague, I also tried modeling the untransformed data with a binomial family, since I know the denominators for my proportion data. However, the model fit for this approach was not as strong as for the gamma approach. AIC strongly favored the model using the gamma distribution over the model using the binomial distribution.

If you have any recommendations or suggestions on how best to model these data I've described, I would greatly appreciate it.

--
*Rachael Eaton*
PhD Candidate
Department of Zoology
Graduate Program in Ecology, Evol Biology & Behavior Michigan State University rachaeleaton.weebly.com <http://www.rachaeleaton.weebly.com>

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