The Poisson Deviance for Regression

You’ve probably heard of the Poisson distribution, a probability distribution often used for modeling counts, that is, positive integer values. Imagine you’re modeling “events”, like the number of customers that walk into a store, or birds that land in a tree in a given hour. That’s what the Poisson is often used for. From the perspective of regression, we have this thing called Generalized Poisson Models (GPMs), where the response variable you are modeling is some kind of Poisson-ish type distribution. In a Poisson distribution, the mean is equal to the variance, but in real life, the…