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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 23:49:18 -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 11:23 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: RE: st: Nonlinear regression and constraints
> 
> 
> At 10:43 PM 6/28/2005 -0700, Daniel Schneider wrote:
> >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.
> 
> I wonder what happens to your theory/definitions if both 
> estimated values 
> are significantly greater than 1!  (Has a miracle occurred?) 
> But suppose 
> they are - can you then just impose the constraint that both 
> parameters 
> equal 1?  Maybe there is some cheating here, but if a 
> parameter is out of 
> range you could constrain it to be in range.


Without going to much into detail: my parameters are percentages. They
can only range from 0 to 1. There may be a better solution (i.e. a
solution that better fits the data) beyond 1, BUT, as I said, by
definition they cannot be above 1 (or below 0). So the best solution
that is possible has to be between 0 and 1.
My current model gives me values which are both below 0 (I changed the
equation a little bit, corrected a minor error, but that doesn't matter
for the problem).

The problem is that I cannot constrain the parameter at all in -nl- (or,
at least I don't know how). I tried  -cnsreg- as an alternative, but in
that case I need an additional constraint which turns my model into a
nonlinear model (because it really is nonlinear, and forcing it to be
not non-linear would probably just produce results that are even worse).

> > > 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?
> 
> The Stata 9 Reference Manual entry for -nl- has an example on pp. 
> 297-298.  Simplifying it a bit, the following will cause the 
> effects of the 
> 3 RHS vars to be equal:
> 
> . sysuse auto
> . nl (mpg = {b0} + {b1}*price + {b1}*weight + {b1}*displacement)
> 
> The reference manual basically says that this can save you 
> some typing over 
> doing the same thing in cnsreg. But, I also notice that -nl- 
> gives you an 
> R^2 stat, which was the request made in another thread today.

Yes it does (in my case this is a nice feature, because I can extend my
model and see if additional non-linearity can produce even better
results).

The approach you showed is basically something I already did in my
equation (this is slightly different than in my previous email, but the
concept remains the same):

nl (diff_diff = {alpha}*X1MX1SQDIVX3 - {beta}*X2MX2SQDIVX3 +
({alpha}+{beta})*X1X2DIVX3)

As you can see, I used alpha and beta twice. I could have used gamma
instead of alpha+beta and then tried to impose a restriction that it
should be equal to alpha+beta (that is what I am doing in -cnsreg-). 

I just got a new idea, I might try a two-step solution, I can
reformulate my equation and start estimating one parameter and then
using the result to estimate a second one... I'll give that a try.

Thanks!

Daniel Schneider


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