You might get some ideas by looking at the examples on this UCLA web-page.
http://www.ats.ucla.edu/stat/spss/dae/poissonreg.htm
- When there seems to be an issue of dispersion, we should first check if our model is appropriately specified, such as omitted variables and functional forms. For example, if we omitted the predictor variable prog in the example above, our model would seem to have a problem with over-dispersion. In other words, a mis-specified model could present a symptom like an over-dispersion problem.
- Assuming that the model is correctly specified, you may want to check for overdispersion. There are several tests including the likelihood ratio test of over-dispersion parameter alpha by running the same regression model using negative binomial distribution (distribution = negbin).
- One common cause of over-dispersion is excess zeros, which in turn are generated by an additional data generating process. In this situation, zero-inflated model should be considered.
- If the data generating process does not allow for any 0s (such as the number of days spent in the hospital), then a zero-truncated model may be more appropriate.
- The outcome variable in a Poisson regression cannot have negative numbers.
- Poisson regression is estimated via maximum likelihood estimation. It usually requires a large sample size.
Bruce Weaver, Professor Lakehead University Canada
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