st: Re: Poisson model: how to impose restrictions on coefficients

 From "Patrick Fitzgerald" To Subject st: Re: Poisson model: how to impose restrictions on coefficients Date Thu, 13 Jun 2002 10:05:30 +1000

```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)

Notes

(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.

Best wishes,

Patrick F.

----- Original Message -----
From: <Sailangita@aol.com>
To: <statalist@hsphsun2.harvard.edu>
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
>
>
>
>
> Diafuka
> *
> *   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/
>

*
*   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/
```