Hi Clarence, I was just thinking about something like this for another project. I have been taking mu = a/(a+b) as the mean of the beta and s = (a+b) as the dispersion. Since mu needs to be between 0 and 1, I can reparameterize that with logit, and since s needs to be positive, I could reparameterize that with an log. BUT, my model has had some trouble fitting reasonable values for s with this parameterization, so I've also been reparameterizing s to ensure that it is bounded away from zero, for example s' is the unrestricted reparameterization and s = 1+exp(s'). This seems to help prevent the optimization from getting stuck at some undesirable local maximum. --Abie ________________________________________ From: gov2001-l-bounces at lists.fas.harvard.edu [gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Patrick Lam [plam at fas.harvard.edu] Sent: Wednesday, March 25, 2009 11:33 PM To: gov2001-l at lists.fas.harvard.edu Subject: Re: [gov2001-l] Beta Distribution Reparameterization i'm not sure how exactly you're running the routine, but from what i can see, s doesn't have to necessarily be negative from that equation if (mu*(1-mu))/var(y) > 1. since you can't define var(y) without either s or a, perhaps you're missing some constraint on s or a? remember that the logit, although it constrains 0 < mu < 1, doesn't constrain either a or b to be positive, which is what you need. 2009/3/26 Lee, Clarence <clee at hbs.edu<mailto:clee at hbs.edu>> Hi all, I?m struggling with this problem and I am wondering if any of you could help me out: So my response variable y is in the open interval (0,1), and I want to model a dataset using the Beta distribution. My question deals with how to reparameterize the shape parameters a and b and link it to my covariates (x?s) using a logit function. The best thing I?ve come up with so far is: 1) Define a new parameter mu, such that logit(mu) = X %*% coefficients 2) Define a new parameter s = a + b. We also know that var(y) = (mu*(1-mu))/(1+s). 3) Through this, I can solve for a and b, this is my reparamterization. The problem I keep running into is that, by solving for s from the equation var(y) = (mu*(1-mu))/(1+s), s turns out to be negative, since mu is always less than 1 and var(y) is also less than 1. Since the beta distribution is only defined for s>0, my optim routine just stops. Could someone who has experience with this tell me what piece of insight am I missing? There must be something I?m missing since my s values are all negative. Thanks a bunch! Clarence _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu<mailto:gov2001-l at lists.fas.harvard.edu> http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l -- Patrick Lam Department of Government and Institute for Quantitative Social Science, Harvard University http://www.people.fas.harvard.edu/~plam