9: Poisson Regression

Overview Section

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.

Upon completion of this lesson, you should be able to:

  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

R Files

SAS Files