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

[Simon Blomberg]

See this post:

http://finzi.psych.upenn.edu/R/Rhelp02a/archive/7144.html

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
Room 320 Goddard Building (8)
T: +61 7 3365 2506
http://www.uq.edu.au/~uqsblomb
email: S.Blomberg1_at_uq.edu.au

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an answer does not ensure that a reasonable answer can 
be extracted from a given body of data. - John Tukey.