generalized linear mixed models with a beta distribution
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
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