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# Subject: st: Imputing generalized Poisson-Model into Poisson.ado

 From Jhilbe@aol.com To statalist@hsphsun2.harvard.edu Subject Subject: st: Imputing generalized Poisson-Model into Poisson.ado Date Thu, 6 Mar 2008 10:09:46 EST

```About 2 weeks ago someone asked about under-dispersed  Poisson models. I
referred them to the generalized Poisson and 2-parameter  log-gamma models. Both
programs are in the data files that are posted with

Hilbe, Joseph (2007), Negative Binomial Regression, Cambridge Univ  Press
and
Hardin, James and Joseph Hilbe (2007), Generalized Linear Models  and
Extensions, second edition, Stata Press.

The log-gamma model is also posted to the SSC site, and can be downloaded
from there as well.

You do not have to buy the book(s) to download the  data sets. You can get
the generalized Poisson command program by going to  Stata's bookstore and
clicking on either book. If you go to Stata Press's web  site
(www.stata-press.com/) there is a clearly indicated place where one can go  to download the files
from any of the Stata Press books. If you have trouble  with the program, feel
free to directly contact me at hilbe@asu.edu. The  generalized Poisson is
called gpoisson.

I get StataList communcations  via the Digest, so only see them the day after
they are posted.

Joseph  Hilbe

========================================================
Date:  Wed, 05 Mar 2008 12:05:01 +0100
From: Markus_Koeller  <markus-koeller@web.de>
Subject: st: Imputing generalized Poisson-Model  into Poisson.ado

Hello everyone,

I want to use Stata to estimate  underdispersed Data with a Count Data Model.
I want to use a
generalized  Poisson Model to capture the underdispersed nature of data.

The  log-Likelihoodfunction of the generalized model is (i is index):

ln  L(a,b; yi)= sum from i=1 to n { yi log (ui/1+a*ui) + (yi-1) log (1+a*yi)
-  ui(1+a*yi)/(1+a*ui) - log(yi!)}

I think I have to manipulate the Poisson  function in the ado.-file.

My question: Does anyone know how to exchange  the Likelihoodfunction in the
ado.file or are
there certain things I have to  think about? How can I implement the
parametre a?

a is such that if  a<0 then 1+a*ui>0 and 1+a*yi>0, i.e.:
a>min(-1/max(ui),  -1/max(yi)).

Maybe one of you has implemented a count data model for  underdispersed data
already in the .ado
file and could sent it to  me?

I would be very grateful for any help.
Thanks a  lot,
Markus.

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