count regression

Let’s say we’re interested in modeling the number of auto accidents that occur at various intersections within a city. Upon collecting data after a certain period of time, perhaps we notice two intersections have the same number of accidents, say 25. Is it correct to conclude these two intersections are similar in their propensity for auto accidents?

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.