Re: st: boundary constraints within nl

["E. Paul Wileyto" <epw@mail.med.upenn.edu>]

I'm pasting in the same response I put in last time for the same sort of 
question.  The strategy is this...  assume that Stata will fit a 
parameter going from minus infinity to plus infinity.  You sustitute a 
form directly in place of that parameter that takes an unbounded input, 
and places bounds on it.

In your case it is simple... just exponentiate:

nl (y =  ({a}+{b}* x) * (1-x))

becomes

nl (y =  (exp({a})+exp({b})* x) * (1-x))

The estimates for a and b will actually be the logs of the parameters of 
interest.  After the estimate, use -nlcom- to retrieve your parameters 
and standard errors.

Paul


Here's the last email on the same subject...

> An easy way to impose b>0 is to substitute b=exp(c).  c is 
> unconstrained, and would have a range from minus to plus infinity, but 
> b would be greated than 0.
>
> Likewise, for k substitute k=((k2-k1)/(1+exp(m))+k1.  m is 
> unconstrained, but k would fall between k1 and k2.
> I use these tricks all the time and they work very well.  To get back 
> estimates and standard errors for b and k, use nlcom.
>
> P
>
> Olga Lyashevska wrote:
> Dear all,
>
> We have a negative exponential growth model.
> y=a exp(-kx)+b
> Is there is a way to impose constrains on model parameters such as b>0 
> and
> k1<k<k2?
>
>
> Thank you in advance,
> Olga
Marc Keuschnigg wrote:
> Hey,
>
> I am estimating non linear least squares models (nl) using equations 
> like: nl (y =  ({a}+{b}* x) * (1-x)).
> My question is, how do I impose parameter restrictions like a >=0 and 
> b >=0?
> I could log-transform the parameters, but I don't know how to do it 
> technically within the nl command.
>
> Thanks for helping,
> Marc
>
>
>
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--
E. Paul Wileyto, Ph.D.
Assistant Professor of Biostatistics
Tobacco Use Research Center
School of Medicine, U. of Pennsylvania
3535 Market Street, Suite 4100
Philadelphia, PA  19104-3309

215-746-7147
Fax: 215-746-7140
epw@mail.med.upenn.edu
http://mail.med.upenn.edu/~epw/ 
*
*   For searches and help try:
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*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/