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st: Covariance Matrix transform in MLE estimation


From   Malcolm Wardlaw <malcolm@wardlaw.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Covariance Matrix transform in MLE estimation
Date   Wed, 29 Apr 2009 01:09:01 -0500

I have a quick question regarding recovering the Hessian variance- 
covariance matrix in MLE estimation.

I've got a mixed bernoulli type log-likelihood function that I'm using  
the inverselogit(-x-) trick in order to keep Stata from searching for  
lambda values less than 0 or greater than 1.  Essentially telling it  
to estimate x=logit(-lambda-) instead of -lambda- itself.

I know how to ask Stata for the transformed parameter and variance  
estimate (That is, transforming the logit(-lambda-) estimate into - 
lambda-. -->nlcom invlogit([logitkappa]_cons).  What I need are the  
covariance terms of the parameters.  Essentially the off diagonals of  
the Hessian matrix (as if I was estimating -lambda- itself along with  
the other parameters.  How do I recover that transformation?

Oh, and on a side note, does anyone know why you have to use tricks  
like that instead of just
telling Stata not to search for parameters there?

Malcolm




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