Some Points of Discussion

1. • How do Poisson models differ from traditional linear regression models?

2. • What are the distributional assumptions of the Poisson regression model? For any count model?

3. • What is the dispersion statistic? How is it calculated?

4. • What is the relationship of Poisson standard errors to the dispersion tatistic?

5. • What is apparent overdisperson? How do we deal with it?

6. • How can a synthetic Monte Carlo Poisson model be developed?

7. • How are Poisson coefficients and rate-parameterized coefficients interpreted?

8. • What are marginal effects, partial effects, and discrete change with respect to count models?

Poisson regression is fundamental to the modeling of count data. It was the first model specifically used to model counts, and it still stands at the base of the many types of count models available to analysts. However, it was emphasized in the last chapter that because of the Poisson distributional assumption of equidispersion, using a Poisson model on real study data is usually unsatisfactory. It is sometimes possible to make adjustments to the Poisson model that remedy the problem of under- or over dispersion, but unfortunately often this is not possible. In this chapter, which is central to the book, we look at the nature of Poisson regression and provide guidelines on how to construct, interpret, and evaluate Poisson models as to their fit. The majority of fit tests we use for a Poisson model will be applicable to the more advanced count models discussed later.