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RE: st: nl command with restriction


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: nl command with restriction
Date   Mon, 11 Feb 2008 17:55:18 -0000

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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