Poisson model
In the previous section, we discussed models where the response variable was categorical. In this section, we will look at a model for count data. Count data is like categorical data (the categories are integers), but there are an infinite number of levels (0, 1, 2, 3, and so on). We model count data with the Poisson distribution. In this section, we will start by examining the Poisson distribution and its properties. Then, we will model a count variable with explanatory variables using the Poisson model.
The Poisson distribution
The Poisson distribution is given by the following formula:
P(k) = λ k e −λ _ k !
Here, λ is the average number of events and k is the number of events for which we would like the probability. P(k) is the probability that the k events occur. This distribution is used to calculate the probability of k events occurring in a fixed time interval or a defined space.
The shape...
