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Re: st: constrained parameter in maximum likelihood estimation


From   eivind.bernhardsen@econ.uio.no
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: constrained parameter in maximum likelihood estimation
Date   Wed, 24 Sep 2003 19:40:16 +0200

Dear Jun Xu,

I do have an alternative suggestion:

If your reason for constraing the variable is to keep the likelihood function from settling in some local maximum outside the [0,1] range (that is you believe the global maximum can be found within this range), you can try to replace your parameter p with 1-(sqrt(1-(sqrt(p))^2))^2 at some place in your likelihood program. This fuction will return p in the [0,1] range and "." outside this range and thus keep the solver from iterating outside [0,1].

(Presumably you should use this one with care...)


Regards,
Eivind Bernhardsen


At 11:44 24.09.2003 -0500, you wrote:

Stata Listers:

I have a programming question using ml command: how to contrain some parameter to be estimated within certain range, for example, some probabilities [0,1]. One way that I can think of is to do some logit transformation like exp(p)/exp(1+exp(p)) and let ml freely estimates p. However, it is hard to get its standard error except using the delta method, which is not very accurate. Is there way in Stata, I can constrain the value of p, while at the same time direct get the asymptotic standard error without using any transformation or delta method? Thanks a lot.

Jun Xu
Doctoral Student
Department of Sociology
Indiana University at Bloomington

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