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Re: st: Imposing Parameter Restriction
Friday, August 6, 2004, 6:03:15 AM, Hyeok Jeong wrote:
> Dear Statalisters:
> I am trying to estimate a nonlinear model using "nl" and this is my first
> time of doing it. Let's say the model is written as "y= f(l;a,b)," where a
> and b are the parameters to be estimated. The model restricts the parameter
> space such that "0 < a < 1" and "b <1".
> Without imposing any restrictions, it turns out that estimates from "nl"
> method violate these restrictions.
If x has a theoretical bound between -1 and +1, then you may
parameterize x as
exp(y) - exp(-y)
x = ------------------------------ ,
exp(y) + exp(-y)
where y is a free, unrestricted parameter. You may also want to see
[R] Heckman for a different parameterization adopted by Stata.
For b<1, I guess you can do
b = -exp(y) + 1
where y is a free, unrestricted parameter.
Hope it helps.
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