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# Re: st: MLE Estimation of Poisson process

 From Sarit Weisburd To statalist@hsphsun2.harvard.edu Subject Re: st: MLE Estimation of Poisson process Date Thu, 10 Nov 2011 13:57:55 +0200

Dear statalist,

I think I have figured out how to run the MLE via MATA - but am
surprised the results are different from streg.
Does anyone know of a way to get a clear explanation of how streg
manages estimation with time varying covariates?
Or have any suggestions about what could be going on?

The MLE I estimate - which should match the streg estimation is:
Q(beta)=Integral ( xbeta* (dN(t)- exp(xbeta)) )
where dN(t) is a dummy variable equal to 0/1 (as in Cook & Lawless -
chapter 3.2).

The reason for the integral is that I am examining a duration with
time varying covariates.
In the data every row in my dataset is an interval over which all
covariates remain constant so their integral is simply computes as the
sum of length* xbeta* (dN(t)- exp(xbeta)) at each point.

This is the Mata code I use:

do {
i=0
hes=J(cols(X),cols(X),0)
do {
i=i+1
mu=exp(X[i,.]*b)
hes=hes+xlength[i,.]'X[i,.]*mu
} while (i<rows(X))
bold=b
cha=(bold-b)'(bold-b)/(bold'bold)
iter=iter+1
} while (cha>1e-16)

This is the streg command:
stset t1, failure(des) id(id) exit (time .)
streg police_exp precipitation night weekend, dist(exp) nohr

Any ideas???

Thanks,
Sarit

On Tue, Nov 8, 2011 at 9:21 PM, Sarit Weisburd
<sarit.weisburd@mail.huji.ac.il> wrote:
> 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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>

--
Sarit Weisburd

Doctoral Candidate
Department of Economics
Hebrew University
Mount Scopus Campus
Jerusalem 91905, Israel
sarit.weisburd@mail.huji.ac.il

*
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