On 4/2/09 at about 16:32 you discussed using a beta distribution rather than the normal distribution for the regression of GMAT on GPA.  After class I went about trying to write this model using the mean and variance I found for the Beta distribution on wikipedia.  I came up with this:

Y=λ₀ + λ₁X + ε , where ε ~ Beta(α/(α+β), (α β) /[(α+β)²(α+β+1)]), Y= GPA, and X= GMAT.

My main concerns is regarding the mean as I do not think that I have that correct.  It seems that it would likely be zero here just like it is when errors are distributed normally.  So my question is whether or not I have written the model correctly? 

Anonymous:

On 4/2/09 at about 16:32 you discussed using a beta distribution rather than the normal distribution for the regression of GMAT on GPA.  After class I went about trying to write this model using the mean and variance I found for the Beta distribution on wikipedia.  I came up with this:

Y=λ₀ + λ₁X + ε , where ε ~ Beta(α/(α+β), (α β) /[(α+β)²(α+β+1)]), Y= GPA, and X= GMAT.

My main concerns is regarding the mean as I do not think that I have that correct.  It seems that it would likely be zero here just like it is when errors are distributed normally.  So my question is whether or not I have written the model correctly? 

The regression model is generally a model for the conditional distribution of Y given X=x.  You really don;t need an epsilon.  Just suppose that the distribution of Y given X=x is a beta distribution, with mean a function depending on the value of x. (It won;t be a linear function; the default is the same logistic function that is used in logistic regression analysis, which makes sense because the beta pdf is between 0 and 1.) 

More detail is given on the SAS documentation for PROC GLIMMIX which is the procedure that I used.  P 70 of http://support.sas.com/rnd/app/papers/glimmix.pdf

The DIST=BETA option implements the parameterization of the beta distribution in Ferrari and Cribari-Neto (2004). If Y has a beta ... 

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