# 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 13:23:47 -0500

I thought the logistic transformation was elegant. Penalty functions are brute force... And I cannot think of another approach that handles the restriction that well. The approach I indicated also points out that the number of parameters Rudolfo needs to estimate is one less than he thought because of the restriction. And after the model fit, it's very easy to use nlcom to get back estimates and standard errors for A,B, and C.

Paul

And once done, it

Nick Cox wrote:

Good point. I was thinking in simpler terms of e.g. a and (1 - a). I
know that does not guarantee that either parameter is between 0 and 1,
but there is perhaps a difference between gentle force and brute force
here. That is, if gentle force does not work and brute force is
essential you've learned something about the model fitting.
E. Paul Wileyto

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.

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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