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st: RE: RE: Exact Poisson Regression


From   "Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: Exact Poisson Regression
Date   Mon, 18 Feb 2008 10:12:18 -0800

I can heartily recommend this article - it's interesting and
informative.  What I'd like to see, also is something about the form of
the output.  I've found that the best program in the world (whatever
that may be!) isn't helpful if you have to search the output for what
you want and that process is susceptible to errors, especially for
beginners.

I'm thinking of issues related to hierarchical models and comparing
Stata results to Mplus results.  Stata is superior to Mplus on the
output score.

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
Jhilbe@aol.com
Sent: Saturday, February 16, 2008 7:14 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: Exact Poisson Regression

Gary Anderson asks about whether anyone has developed an exact negative

binomial 
command. No one has done that yet, but the folks at Cytel talked to me
about 
it back 
in November 2005 when I gave an ASA LearnStat course in the Boston
area. 
 
The parameterization of the exact negative binomial would take the
canonical 
form; ie 
it would not be the Poisson-gamma mixture model parameterization with
which  
most 
statisticians are familiar. Therefore, it would not have the same  
relationship to Poisson 
overdispersion as does the NB-2 type of negative binomial, which is  
estimated by using 
the default form of -nbreg-. The canonical negative binomial can be used
to  
model count 
data, and does a good job modeling data that is Poisson-overdispersed. I
say 
this because 
negative binomial models can be overdispersed as well. But, because it
does  
not have 
the log link as does Poisson (and NB-2), the canonical NB heterogeneity
or  
ancillary parameter 
it cannot be used for direct comparisons with Poisson overdispersion as
is  
NB-2. Again, an exact NB 
would be a canonical NB. 
 
I submitted a maximum likelihood canonical NB Stata program to SSC  last
year 
called -cnbreg-. 
It has all of the bells and whistles as the usual Stata maximum
likelihood  
commands.  I've been doing simulation studies on the NB-C model, as I
call  the 
canonical NB in "Negative Binomial Regression", comparing it with
Poisson, 
NB-2, and NB-1 models. I intend to publish the results when  completed.

NB-C is actually a nice model and can do a better job modeling some
types  of 
data than NB-2 or NB-1.
I think it is worth the effort to construct an exact NB command, but I
now  
doubt that Cytel will get to it. 
LogXact, Cytel's software application for modeling exact logistic and
exact  
Poisson models, is not alone any more in providing this capability to
its 
users.  SAS and SPSS can model exact logistic models, and Stata both
exact 
logistic and  exact Poisson. Because of the strong competition in this
regard, it is 
my  understanding that Cytel is emphasizing development of packages such
as 
East,  which is marketed to the clinical trials industry. I doubt that
it will 
develop  an exact NB now. And since there are no published algorithms
showing 
how to do  it, I very much doubt that SAS or SPSS will take it on. That
leaves 
Stata  Corp. An exact NB, although of canonical parameterization, still
would 
be  valuable for modeling counts with excessive correlation in the data.
There 
are  great reasons why I think it worth the effort.  
 
By the way, Bob Oster and I wrote an article for "The American
Statistician" 
(current issue) which compares the exact statistics capabilities  of 
StatXact/LogXact, SAS, SPSS, and Stata. Those of you who have an
interest in  exact 
statistics may find the review to be helpful. 
 
Joseph Hilbe
 
 
 



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