Poisson regression is also a special case of the generalized linear model, where the random component is specified by the Poisson distribution. This usually works well when the response variable is a count of some occurrence, such as the number of calls to a customer service number in an hour or the number of cars that pass through an intersection in a day. Unlike the binomial distribution, which counts the number of successes in a given number of trials, a Poisson count is not bounded above.
When all explanatory variables are discrete, the Poisson regression model is equivalent to the log-linear model, which we will see in the next lesson. For the present discussion, however, we'll focus on model-building and interpretation. We'll see that many of these techniques are very similar to those in the logistic regression model.
- Objective 9.1
Explain the assumptions of the Poisson regression model and use software to fit it to sample data.
- Objective 9.2
Distinguish between a Poisson count and a rate.
- Objective 9.3
Interpret an offset and how it differs from a predictor in the Poisson rate regression model.
- Objective 9.4
Recognize overdispersion when modeling count data and determine appropriate measures to account for it.
Lesson 9 Code Files
Data Files: crab.txt, cancer.txt
Useful Links Section
- Poisson function in SAS : http://support.sas.com/documentation/cdl/en/lrdict/64316/HTML/default/viewer.htm#a000245925.htm
- Poisson regression via GENMOD: https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_genmod_sect006.htm
- Fitting GLMs in R : http://www.statmethods.net/advstats/glm.html