There are quite a few types of outcome modeling count data hilbe pdf that will never meet ordinary linear model’s assumption of normally distributed residuals. A non-normal outcome variable can have normally distribued residuals, but it does need to be continuous, unbounded, and measured on an interval or ratio scale. Categorical outcome variables clearly don’t fit this requirement, so it’s easy to see that an ordinary linear model is not appropriate. It’s less obvious, because they are measured on a ratio scale, so it’s easier to think of them as continuous, or close to it.
But they’re neither continuous or unbounded, and this really affects assumptions. Continuous variables measure how much. Count variables measure how many.
0 is by far the most common value. And they’re discrete, not continuous. All those jokes about the average family having 1. 3 children have a ring of truth in this context.
Count variables often follow a Poisson or one of its related distributions. The Poisson distribution assumes that each count is the result of the same Poisson process—a random process that says each counted event is independent and equally likely. If this count variable is used as the outcome of a regression model, we can use Poisson regression to estimate how predictors affect the number of times the event occurred.