# Analysis of negative binomial distributions using glm.nb() in R

I have observations of four different groups of people. The dependent variable are count data (medical emergencies in the past 2 months). For each group, the dependent variable follows a negative binomial distribution with a maximum at 0. Now I would like to examine, if the factor "group" (meant to be categorical) is a significant factor for the number of reported medical emergencies. What I have done so far: I conducted a glm using glm.nb in R and examined the result of glm.nb using anova(). I would really appreciate, if someone could confirm for me, if this procedure is feasible for a negative binomial distributed response variable and a categorical factor.

My second question: anova() with the result of the glm.nb produces the warning: tests made without re-estimating 'theta'. As far as I understand, theta is a dispersion parameter for the negative binomial distribution. However, the distributions of observations in each of the four groups have very different dispersions. Does R calculate a "mean" theta for all four distributions?

## 1 Answer

This answer here may help- credit to G. Simpson

'the number quoted in parentheses is θ, the parameter of the Negative
Binomial distribution. This value is that estimated during fitting.
It is not ϕ, the  dispersion parameter,
and hence the two numbers should not necessarily be equal; they are just two
numbers.'