Goodness-of-Fit Statistics
The log-likelihood reported for the standard Poisson regression is –68.281. Compare this to the negative binomial model.
The log-likelihood reported for the negative binomial regression is –83.725. This is actually smaller than the log-likelihood for the Poisson regression, which indicates (without the need for a likelihood ratio test) that this negative binomial regression does not offer an improvement over the Poisson regression.
However, the chosen value of 1 for the ancillary parameter of the negative binomial distribution may not be optimal for this dataset. Another way you could test for overdispersion is to fit a negative binomial model with ancillary parameter equal to 0 and request the Lagrange multiplier test on the Statistics tab . If the test is not significant, overdispersion should not be a problem for this dataset.