Steve Candy
2008-Mar-17 06:04 UTC
[R] generalized linear mixed models with a beta distribution [Sec=Unclassified]
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 ___________________________________________________________________________ Australian Antarctic Division - Commonwealth of Australia IMPORTANT: This transmission is intended for the addressee only. If you are not the intended recipient, you are notified that use or dissemination of this communication is strictly prohibited by Commonwealth law. If you have received this transmission in error, please notify the sender immediately by e-mail or by telephoning +61 3 6232 3209 and DELETE the message. Visit our web site at http://www.antarctica.gov.au/ ___________________________________________________________________________ [[alternative HTML version deleted]]
Simon Blomberg
2008-Mar-17 06:38 UTC
[R] generalized linear mixed models with a beta distribution [Sec=Unclassified]
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 > > > > > ___________________________________________________________________________ > > Australian Antarctic Division - Commonwealth of Australia > IMPORTANT: This transmission is intended for the addressee only. If you are not the > intended recipient, you are notified that use or dissemination of this communication is > strictly prohibited by Commonwealth law. If you have received this transmission in error, > please notify the sender immediately by e-mail or by telephoning +61 3 6232 3209 and > DELETE the message. > Visit our web site at http://www.antarctica.gov.au/ > ___________________________________________________________________________ > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.-- 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 Policies: 1. I will NOT analyse your data for you. 2. Your deadline is your problem. The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. - John Tukey.