Re: Using NonlinearFit/Regress?

• To: mathgroup at smc.vnet.net
• Subject: [mg33876] Re: [mg33856] Using NonlinearFit/Regress?
• From: "Johannes Ludsteck" <johannes.ludsteck at wiwi.uni-regensburg.de>
• Date: Sun, 21 Apr 2002 06:12:24 -0400 (EDT)
• Organization: Universitaet Regensburg
• Sender: owner-wri-mathgroup at wolfram.com

```Dear njg,
before trying anything else, you should check whether
the model fits your data. If parameters show the false sign,
this indicates that the model may not be identified or
simply false. So please consult a introductory statistics
or econometrics book before posting such questions.

However, if you anyway have to use the resrictions anyway,
you can do this, for example by applying a barrier constraint,
for example
NonlinearFit[x/(1+a (x-1) + a b x (x-1))
- If[a<=0||b<=0,Infinity,0.0],...]
However, this will complicate the minimization and you
have to provide two starting points for every parameter,
for example {a, {0.3,0.6}},{b,{0.3,0.6}}.

There are more sophistic methods to apply restrictions. You will
find them in intermediate or advanced statistics or econometrics
books.

Best regards,
Johannes

On 20 Apr 2002, at 2:49, redrooz at yahoo.com wrote:

> I am trying to estimate the parameters {a,b} in the
> function: x / (1 + a (x-1) + a b x (x-1)) using
> NonlinearFit[...].
>
> The model is known to be a CONCAVE function with
> 0 < a,b < 1 and b < a.  NonlinearFit/Regress
> always produces negative parameters (a discontinuous
> function); even if I try to condition them to be
> positive e.g., {a, 0, 1} and  {b, 0, 1}.
>
> Any suggestions about using NonlinearFit[...] with the
> above function?
>
> --njg
>

<><><><><><><><><><><><>
Johannes Ludsteck
Economics Department
University of Regensburg
Universitaetsstrasse 31
93053 Regensburg
Phone +49/0941/943-2741

```

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