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st: Re: Poisson model: how to impose restrictions on coefficients
Since a2 + a3 = 1, a3 = 1 - a2, and you can re-write your model as:
Y = a1 X1 + a2 X2 + (1 - a2) X3 + a4 X4 + error term,
which can be rearranged to
Y = a1 X1 + a2 (X2 - X3) + X3 + a4 X4 + error term,
so that you can fit the model you want using the STATA "poisson" command by
(1) creating a new variable, Z = X2 - X3 and fitting the model
Y = a1 X1 + a2 Z + a4 X4
(2) setting the option offset(X3).
The Poisson regression command for this would then be:
poisson outcome x1 z x4, offset(x3)
(a) I assume you wish to fit Y = log(mean of outcome).
(b) You don't estimate 4 coeffficients, but 3, as a3 is now completely
specified in terms of a2.
(c) Only FYI. If (a) holds, then the error term is added to the outcome
itself, not Y.
----- Original Message -----
Sent: Saturday, June 08, 2002 11:15 PM
Subject: st: Poisson model: how to impose restrictions on coefficients
> Dear All:
> I need help on how to impose restrictions on coefficients.
> I am running a poisson model like this:
> Y = a1 X1 + a2 X2 + a3 X3 + a4 X4 + error term
> I want to impose a2 + a3 = 1
> Thanks in advance.
> * For searches and help try:
> * http://www.stata.com/support/faqs/res/findit.html
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
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