[R] generalized linear mixed models with a beta distribution

[Craig A Faulhaber]

Thanks for the tips and clarifications.  I'm a newbie and don't always 
have the terminology down correctly.  My understanding is that one 
should be able to use generalized linear mixed models to model response 
variables that take any of the exponential family of distributions.  The 
beta distribution belongs to this family and can be modeled in PROC 
GLIMMIX in SAS.  I was hoping to find something similar in R.  Is 
modeling in nlme via a variance specification the best and/or only 
option available in R?

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.

Thanks again, Professor Ripley, for your comments and suggestions.

Craig

Prof Brian Ripley wrote:
> glmmPQL can fit the same GLM families as glm() can -- it does not list 
> _any_ .
>
> Howver, the beta distribution does not give a GLM family and hence 
> your subject line is strictly about a non-existent concept.  I'm 
> presuming that you want to model the logit of the mean of a beta by a 
> random effects model -- it is unclear what you want to do with the 
> other parameter.
>
> Note that the beta does fit into the framework of package gamlss, but 
> I am not aware of an option for random effects in that framework.
>
> On Wed, 12 Mar 2008, Craig A Faulhaber wrote:
>
>> Greetings,
>>
>> 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).  I noticed that the beta distribution is not
>> listed as an option in the "family objects" for glmmPQL or  lmer.  I
>> found a thread on this listserve from 2006 ("[R] lmer and a response
>> that is a proportion") that indicated that there was no package
>
> https://stat.ethz.ch/pipermail/r-help/2006-December/121567.html
>
>> available for mixed effects models with a beta distribution at that
>> time.  This thread also indicated that package betareg did not allow
>> inclusion of random effects.
>
> But it did suggest modelling this in nlme via a variance 
> specification, and that remains a good suggestion.
>
>> Does anyone know of a package or code for a generalized linear mixed
>> model that allows a beta distribution?  Transforming my data might allow
>> me to use another family, but I would rather not transform the data if
>> possible.  Thanks for your help!
>>
>> Sincerely,
>> Craig Faulhaber
>