Re: st: nl command with restriction

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

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
Philadelphia, PA  19104-3309

215-746-7147
Fax: 215-746-7140
epw@mail.med.upenn.edu
http://mail.med.upenn.edu/~epw/ 
*
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