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I am working in accident prediction modeling and I'm using SPSS Generalized Linear Model procedure with Negative Binomial distribution and Log Link Function.
Does anyone know the form in wich SPSS returns the dispersion parameter?
Is it the form Var(x)=mu+dispersion*mu^2?
All i know is that the dispersion parameter is equal to 0 for a Poisson distribution, where Var(x)=mu.
Many thanks in advance
Yes you have the form right, specifically the variance for the $j$th observation is:
$$\text{Var}(x_j) = \mu_j(1 + au_j)$$
Stata and SPSS have the same defaults, so I will refer to Stata's documentation (see page 5) for a nice walkthrough. This is the NB2 model from Cameron and Trivedi (which I have not read, but is cited as such in the Long and Freese Regression Models for Categorical Dependent Variables Using Stata).
It can be tricky when reading texts. Sometimes people refer to the dispersion as the entire thing in the parentheses (which changes per the mean estimate of the variable), but other times they only refer to $a$ (which is what the software reports). I've written a blog post translating between a few of the regularly used notations for negative binomial parameterizations.
You can estimate dispersion parameter by this address Analyze/Generalized linear Models/custom/select negative binomial distribution/link function =log/ then in estimation tab in scale parameter method select Fixed value if u run, you'll see overdispersion parameter in parameters estimation table.its value is next to the negative binomial
