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

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
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 
( 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 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  <>
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,

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