September 2012
Intermediate to advanced
286 pages
8h 7m
English
Appendix L
Negative Binomial Regression
(Source: Cameron and Trivedi [1])
In the Poisson regression model 
has mean 
and variance 
. We now relax the variance assumption, because data almost always reject the restriction that the variance equals the mean, and we maintain the assumption that the mean is 
.
We use the general notation
(L.1) 
to denote the conditional variance of 
. It is natural to continue to model the variance as a function of the mean, with
(L.2) 
for some specified function 
and where 
is a scalar parameter. Most models specialize this to the general variance function
(L.3)
where ...
