poisson regression

A count model is a linear model where the dependent variable is a count. For example, the number of times a car breaks down, the number of rats in a litter, the number of times a young student gets out of his seat, etc. Counts are either 0 or a positive whole number, which means we need to use special distributions to generate the data.

Hurdle Models are a class of models for count data that help handle excess zeros and overdispersion. To motivate their use, let's look at some data in R. The following data come with the AER package. It is a sample of 4,406 individuals, aged 66 and over, who were covered by Medicare in 1988. One of the variables the data provide is number of physician office visits.

When it comes to modeling counts (i.e., whole numbers greater than or equal to 0), we often start with Poisson regression. This is a generalized linear model where a response is assumed to have a Poisson distribution conditional on a weighted sum of predictors. For example, we might model the number of documented concussions to NFL quarterbacks as a function of snaps played and the total years experience of his offensive line. However, one potential drawback of Poisson regression is that it may not accurately describe the variability of the counts.