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st: MLE Estimation of Poisson process


From   Sarit Weisburd <sarit.weisburd@mail.huji.ac.il>
To   statalist@hsphsun2.harvard.edu
Subject   st: MLE Estimation of Poisson process
Date   Tue, 8 Nov 2011 21:21:58 +0200

Dear statalist,

I have been estimating a poisson process with time-varying covariates using
the streg command but want to make sure streg is doing what I understand it
should be.
I therefore am trying to manually reach the same results via maximum
likelihood estimation but cannot figure out how to tell stata to calculate
the log likelihood function which includes an integral:

This is the log likelihood function, Q(beta)=I ( xbeta* (dN(t)
- exp(xbeta)) ) where dN(t) is a dummy variable equal to 0/1 (as in Cook &
Lawless - chapter 3.2).
I=integral

The reason for the integral is that I am examining a duration with time
varying covariates. For example - looking at the duration between car
accidents in a given location - and want to control for traffic flow that
changed multiple times in that duration.

What I would like stata to do is calculate the integral as a sum of
xbeta*(dN(t)-exp(xbeta))

over all splits in a given duration and then I could continue with MLE
estimation.

Does anyone have any suggestions about how this could be done?

Thanks,
Sarit
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