The Poisson distribution is the limiting distribution of the negative binomial as k->0; there is not an exact equivalence and it might be better to say "When the ancillary parameter is set to 0, the procedure proceeds as if you specified a Poisson distribution, thus the negative binomial link function is not available for k = 0."
Alex
________________________________
From: SPSSX(r) Discussion on behalf of David Hitchin
Sent: Thu 4/26/2007 4:41 AM
To:
[hidden email]
Subject: Negative binomial error?
In the generalised estimating equations routine of SPSS 15.0 the
Advanced Statistics Manual states:
"
Negative Binomial.
This distribution can be thought of as the number of trials required to
observe k successes and is appropriate for variables with non-negative
integer values. ... The fixed value of the negative binomial
distribution's ancillary parameter can be any number greater than or
equal to 0. When the ancillary parameter is set to 0, using this
distribution is equivalent to using the Poisson distribution.
Link Functions
The link function is a transformation of the dependent variable that
allows estimation of the model. The following functions are available:
À" Negative Binomial. f(x)=log(x / (x+(1/k)), where k is the ancillary
parameter of the negative binomial distribution. This is appropriate
only with the negative binomial distribution."
(Formula reformatted to avoid a superscript in this email)
This seems to contain a contradiction, and the program treats it as
such. If the ancillary parameter k is set to zero then 1/k is infinite.
David Hitchin
Locked
