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Re: st: constrained linear least-squares problems without using ML


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: constrained linear least-squares problems without using ML
Date   Wed, 29 Jun 2011 10:27:33 +0200

On Wed, Jun 29, 2011 at 3:51 AM, ali hashemi wrote:
> I would like to estimate an OLS model (y=b1*x1+b2*x2) with proportionate
> coefficients which means considering the following constraints:
> b1>0
> b2>0
> b1+b2=1
>
> I tried to estimate this using ML (for more details: findit inequality
> constraints)
>
> It works for some cases. Unfortunately, for many other cases it keeps giving
> this message: "flat or discontinuous region encountered"
>
> I'm told that ML is not the best option to estimate constrained linear
> least-squares models. lsqlin in MATLAB and quadratic programming in R are
> solutions that I have found in other packages. However, I'm not aware of any
> alternative method in Stata? Does anyone have any idea how constrained
> linear least-squares models can be estimated without using ML?

If you go to <http://www.stata.com/support/faqs/stat/intconst.html>
you will see that the first thing it says is:

"Note:   The examples in this tutorial are for illustration purposes
only. If you need to fit a linear regression with interval
constraints, use the Stata command nl."

Now I expect you will still need to think very carefully about
starting values. If -ml- gets into trouble like that than I expect
that there is a good possibility that -nl- will also not converge
without good starting values. Even with good starting values you may
end up on a boundary solution, in which case it will not be easy to
get convergence whichever method you use.

Hope this helps,
Maarten

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


http://www.maartenbuis.nl
--------------------------
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