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RE: st: Nonlinear regression and constraints


From   "Daniel Schneider" <daniel.schneider@stanford.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Nonlinear regression and constraints
Date   Tue, 28 Jun 2005 22:43:06 -0700

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Richard Williams
> Sent: Tuesday, June 28, 2005 10:26 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Nonlinear regression and constraints
> 
> 
> At 09:04 PM 6/28/2005 -0700, Daniel Schneider wrote:
> >constraint define 1 X1MX1SQDIVX3 >= 0
> >constraint define 2 X2SQMX2DIVX3 >= 0
> >constraint define 3 X1MX1SQDIVX3 <= 1
> >constraint define 4 X2SQMX2DIVX3 <= 1
> >
> >Unfortunately, constraints() seems not to work with -nl-?
> >
> >Is there any other way to to do the constraints with -nl-?
> 
> Even if -nl- allowed the constraints option, I don't think 
> these would be 
> legal constraints; as far as I know, you can't use something 
> like >=, you 
> can only use =.

That might be possible. Let me clarify what I want to do: I want to find
the best (i.e. with the lowest SS) parameter values which are between 0
and 1 (including both), because by definition they can only be between
those two values.

> 
> Also, my impression is that -nl- doesn't need the constraints option 
> because constraints can be specified using the -nl- command itself.

Can you tell me how that can be done?

> 
> I'd be curious to know if there is some direct way to specify 
> a range of 
> values for the constraint, like you want; as far as I know, 
> there always 
> has to be some sort of equality statement.

Perhaps I am wrong thinking here about constraints. Perhaps "range of
values" would be a better term, as I explained above. My -nl- commands
gives me reasonable results in a statistical sense, but I know that by
definition my alpha and beta cannot be larger 1 or smaller than 0. 

> Is there some way to transform the equation, so that, say, 
> you wind up 
> taking the inverse logit of the parameters of the transformed 
> equation to 
> get back to the parameters of the original equation?  The 
> inverse logit of 
> any number will always range between 0 and 1.  You'll see programs do 
> little tricks like estimate the log of a parameter when the parameter 
> itself needs to be positive.
> 


That is of course and interesting idea. I'll have to check that and
reconsider the whole equation...

Daniel

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