# Re: [R] generalized linear mixed models with a beta distribution [Sec=Unclassified]

From: Simon Blomberg <s.blomberg1_at_uq.edu.au>
Date: Mon, 17 Mar 2008 16:38:06 +1000

See this post:

Cheers,

Simon.

On Mon, 2008-03-17 at 17:04 +1100, Steve Candy wrote:
>
> Craig A Faulhaber wrote:
>
>
>
> >I am interested in using a generalized linear mixed model with data
>
> > that best fits a beta distribution (i.e., the data is bounded between
>
> > 0 and 1 but is not binomial).
>
> ..
>
> >For clarification, here's what I'm trying to model:
>
> >I have a beta-distributed response variable (y). I have a fixed-effect
>
>
> >explanatory variable (treatment), and I'd like to include a random term
>
>
> >for individuals used in the experiment. The model in lmer would be: y
>
>
> >~ treatment + (1 | individual). As far as I can tell, the appropriate
>
>
> >link function for the model would be the logit.
>
>
>
> If you want to use a GLM you could use the binomial/logit
> quasi-likelihood approach for your ratio. Say the ratio is r=n/N then
> use binomial n with binomial total N (these do not have to be integers)
> but remember to use prior weights of 1/N and estimate the
> over-dispersion parameter. If you use the ratio, r, directly with a
> binomial total of 1 then the prior weights are simply 1 and can be
> ignored. This quasi-likelihood approach for a ratio was given by
> Wedderburn (1974) (see McCullagh and Nelder, 1989, Sec 9.2.4). BTW
> random effects with a beta distribution included in the linear predictor
> via a link function such as the logit can be fitted as a HGLM
> (Hierarchical Generalized Linear Model)(Lee and Nelder, 1996, 2001) for
> binomial data (i.e. considered binomial conditional on the random
> effects). Only the GenStat package is set up to fit HGLMs (as far as I
> know). (L & N, 1996, J.R.Statist.Soc B 58, 619-678; L & N 2001
> Biometrika 88, 987-1006).
>
>
>
> Hope this helps
>
> Steve Candy
>
>
>
>
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```--
Simon Blomberg, BSc (Hons), PhD, MAppStat.
Lecturer and Consultant Statistician
Faculty of Biological and Chemical Sciences
The University of Queensland
St. Lucia Queensland 4072
Australia
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