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Re: st: Constrained ML estimation


From   "Stephen P. Jenkins" <stephenj@essex.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Constrained ML estimation
Date   Wed, 5 Nov 2003 10:21:46 +0000 (GMT Standard Time)

On Wed, 5 Nov 2003 11:11:24 +0100 Thomas Cornelissen <thoco@gmx.net> 
wrote:

> Dear all,
> I have a problem defining constraints on parameters for ML estimation. I
> manage to implement equality constraints, but no inequality constraints,
> such as sigma+AD4-0. The first line in the below example delivers the error
> message +ACI-Constraints invalid: not possible with test r(131)+ACI-
> 
> constraint define 1 +AFs-sigma+AF0AXw-cons+AD4APQ-0+ADs-
> ml model lf myll (b: lw +AD0- schooling experience experience2) (sigma:)+ADs-
> ml search+ADs-
> ml maximize+ADs-
> 
> Can anybody tell me, whether such restraints are possible?
> More generally, is it necessary to set a constraint to keep sigma positive,
> or will a well behaved ML function alway assure that the estimation result
> for sigma is positivie?

To take a concrete example, if one of your parameters is a variance, 
you may want to ensure that it is positive, or another is a correlation 
you may want to ensure it is bounded by -1 and 1.
The 'standard' way of doing this sort of thing using -ml- is to 
estimate the parameter in a transformed metric (which imposes the 
constraint), and then later to backtransform to get the parameter in 
the original metric (using the 'delta method' to get the s.e.): 
-_diparm- is your friend here.
To take the variance case again, you could estimate the log(variance), 
and so on.


Stephen
----------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Institute for Social and Economic Research (ISER)
University of Essex, Colchester, CO4 3SQ, UK
Tel: +44 (0)1206 873374. Fax: +44 (0)1206 873151.
http://www.iser.essex.ac.uk

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