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Re: st: Covariance Matrix transform in MLE estimation


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Covariance Matrix transform in MLE estimation
Date   Wed, 29 Apr 2009 12:50:35 +0000 (GMT)

--- On Wed, 29/4/09, Malcolm Wardlaw wrote:
> 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?

use -nlcom-:
nlcom (kappa: invlogit([logitkappa]_cons)) ///
      (x1: x1) (x2:x2), post

This will leave the variance covariance matrix between
kappa x1 and x2 behind in e(V).
 
> 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?

I am speculating, but it might because this way you can
avoid estimates at the boundery of the parameter space. 

-- Maarten

-----------------------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://home.fsw.vu.nl/m.buis/
-----------------------------------------


      

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