From: Simon Blomberg <s.blomberg1_at_uq.edu.au>

Date: Mon, 17 Mar 2008 16:38:06 +1000

Date: Mon, 17 Mar 2008 16:38:06 +1000

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 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. ______________________________________________ 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.Received on Mon 17 Mar 2008 - 06:40:50 GMT

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