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generalized linear mixed models with a beta distribution

3 messages · Craig A Faulhaber, Brian Ripley

Craig A Faulhaber
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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 
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.

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
Brian Ripley
# 
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:

            

      
      
      
    

        
https://stat.ethz.ch/pipermail/r-help/2006-December/121567.html

            

      
      
      
    

        
But it did suggest modelling this in nlme via a variance specification, 
and that remains a good suggestion.

            

      
      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Craig A Faulhaber
    

    

      
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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: