5.9 Count regressions

The regression variants Poisson and Negative Binomial belong to the count regression family, and are used on data where the response variable counts the number of occurrences/events (positive integers).

Unlike ordinary linear regression (OLS), it is assumed that the response variable is not normally distributed, but left skewed and with a long right tail. This is a typical property of count data. More specifically, Poisson regressions assume that the response variable follows a Poisson distribution where the mean/expected value of the response variable is equal to the variance. Negative Binomial regression is a generalized variant of Poisson where the variance of the response variable is assumed to be higher than the mean value, i.e. that the spread is greater than for Poisson.

Poisson should therefore be chosen if the expected value for the dependent variable is equal to the variance. Otherwise (if the variance is greater) Negative Binomial regression should be used.