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From |
"E. Paul Wileyto" <epw@mail.med.upenn.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: boundary constraints within nl |

Date |
Fri, 06 Jun 2008 13:36:24 -0400 |

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:

* http://www.stata.com/support/faqs/res/findit.html

* http://www.stata.com/support/statalist/faq

* http://www.ats.ucla.edu/stat/stata/

**References**:**st: boundary constraints within nl***From:*Marc Keuschnigg <Marc.Keuschnigg@soziologie.uni-muenchen.de>

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