# Re: st: nl command with restriction

 From "E. Paul Wileyto" To statalist@hsphsun2.harvard.edu Subject Re: st: nl command with restriction Date Mon, 11 Feb 2008 12:16:59 -0500

Rudolfo stated that the parameters are all positive and sum to 1, so the values are going to act like proportions, even if you don't think of them that way. We use this approach all the time to put bounds on estimates.

Paul

Nick Cox wrote:

Rodolfo's parameters add to 1. His problem differs from that of various
responses that are all proportions and thus add to 1.
Nick
n.j.cox@durham.ac.uk
E. Paul Wileyto

It might be easiest to incorporate a transform into the equation you are

estimating. -nl- will expect coefficients that range from minus to plus

infinity. You could get everything you want by transforming as a multinomial logistic probability.

suppose you want to estimate A, B, and C which add to 1. -nl- variable b0.. ranges - to + inf.
replace the parameters in your equation with :

A=exp(b0)/(1+exp(b0)+exp(b1))
B=exp(b1)/(1+exp(b0)+exp(b1)
C=1/(1+exp(b0)+exp(b1))

Rodolfo Coelho Prates wrote:

I estimated a Cobb-Douglas function with additive error (nl command),
the

coeficients are negative and the sum are larger than one, in some
cases.
I need that the coeficients are larger than zero and the sum of the
coeficients are equal to one. How can I estimate the function with
restriction in Stata?
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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

215-746-7147
Fax: 215-746-7140
epw@mail.med.upenn.edu
http://mail.med.upenn.edu/~epw/
*
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* http://www.ats.ucla.edu/stat/stata/