Logistic Regression Using SAS®: Theory and Application

9.2. The Poisson Regression Model

The Poisson regression model gets its name from the assumption that the dependent variable has a Poisson distribution, defined as follows. Let y be a variable that can have only non-negative integer values. We assume that the probability that y is equal to some number r is given by

Equation 9.1

where λ is the expected value (mean) of y and r!=r(r–1)(r–2)...(1). Although y can only take on integer values, λ can be any positive number. For λ=1.5, the probabilities for the Poisson distribution are graphed in Figure 9.1.

Figure 9.1. Poisson Distribution for λ =1.5

As λ gets larger, the mode moves away from ...