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st: Cutoff estimation by MLE


From   Bradley Chen <ytchen@hsph.harvard.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Cutoff estimation by MLE
Date   Tue, 4 Dec 2007 09:22:52 -0500

Dear Statlisters,

I have a problem with estimating the ordered probit cutoff, and I realized that there is probably no precoded command in STATA doing what I want so I need to do the maximum likelihood estimation

This is what I want to estimate:
I have a dependent variable, which is a four category ordered response Yi={1,2,3,4}, whose value depends on a latent variable Y*=Xb+e
The observed Yi=j if C(j-1)<Y*<Cj with C0=minus infinity. And the most important part for me is that the cutoff level C is also a function of the observed characteristics: Cj=X*b'

So the the log likelihood equation I want to maximize is
L={Yi=1}*log(cnorm(-C1))+{Yi=2}*log(cnorm(C2-C1)-cnorm(-C1))++{Yi=3} *log(cnorm(C3-C1)-cnorm(-21))+{Yi=4}*log(cnorm(C1-C3)),
to attain the coefficients b' in the cutoff equation

Could someone kindly teach me how to write the STATA command?

Thanks a lot,
Bradley



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