[gov2001-l] Beta Distribution Reparameterization

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