# Negative Binomial Model Generating counts

I am working with crash data that measures injury severity using the values 1, 2, and 3, which correspond to Fatal, Seriously Injured, and Slight, respectively.

I am attempting to use a negative binomial model to analyze this data, but the negative binomial model is typically used for count data. How can I generate count data from these ordinal variables?

• You don’t want a negative binomial in this case. The negative binomial is supported on the integers and your data are not. Integers are just used to code the levels of the outcome. Instead, you might want to use an ordinal regression. Jul 2, 2023 at 1:40

$$\log(E(y)) = \mathbf{x}^T \beta$$
The expected value is thus supported on the positive reals and there may be a combination of covariates such that, when one extrapolates, $$E(y)$$ is outside the bounds of the data. How could the expected value be >3 when the data are at the very most 3?
Your data are ordinal so its probably better to model them as such. A technique like ordinal logistic regression is likely better because then you can estimate $$P(y \leq 1)$$ and $$P(y \leq 2)$$ (end through some algebra, $$P(y = 1)$$, $$P(y = 2)$$, and $$P(y = 3)$$.