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st: Set constraint for a ml equation


From   "Yuyan Shi" <shiyuyan@gmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Set constraint for a ml equation
Date   Mon, 3 May 2010 18:53:44 -0400

Hi all,

I am estimating "mu", "sigma" and "delta" in a ml function like this:

Log likelihood = log(normalden(N/delta)),
Where N = pi-1+normal((ti-mu)/sigma). pi and ti are dependent variables.

The Stata program I wrote is:

******************************************************
program define myml
      args lnf lgmu lgsigma lgdelta
      tempvar P R N M S

      quietly gen double `P' = normal(($ML_y1-exp(`lgmu'))/exp(`lgsigma'))
      quietly gen double `R' = $ML_y2-1
      quietly gen double `N' = `P'+`R'
      quietly gen double `M' = exp(`lgdelta')
      quietly gen double `S' = log(normalden(`N'/`M'))
      quietly replace `lnf'=`S'
end
ml model lf myml (lgmu:Y1 Y2=$xvar) (lgsigma:Y1 Y2=$xvar) (lgdelta:Y1
Y2=$zvar)
ml max
**************************************************************

However, the convergence cannot be achieved. I know I should put some
constraints onto lgdelta for identification. I've tried several in equation
"lgdelta", such as noconstant, xvar=some arbitrary number, but still did not
work.

I have two separate question:
-	What kind of constraint should I put in equation "lgdelta"?
-	If I know delta is between 1 and 2, how should I write this extra
constraint? Is "invlogit" the appropriate function?

Thank you so much.

-  Yuyan




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