Somewhere in Section 12.1.2, the section on the negative binomial model, enter this explicit explanation on the gamma portion of the gamma-poisson model:
I don’t believe McElreath plainly explained this in the text, but when we talk about the gamma-Poisson model as having two parameters, $\lambda$ and $\phi$, the $\lambda$ parameter is doing double duty. As with conventional Poisson models, $\lambda$ is the mean for the criterion. What might not be as clear is that $\lambda$ is also the mean of the gamma mixture distribution. So when you want to get a sense of the overall shape of the gamma-Poisson model-implied distribution of $\lambda$ parameters—one for each variable in the data set--, the distribution is gamma with a mean of $\lambda$ and shape of $\phi$. For a more detailed walk out of this, see Section 8.2 in Hilbe (2011).
It might be best to just add this as a footnote. Also, remember to add Hilbe (2011) to the reference list.
ASKurz
commented
2 years ago
Somewhere in Section 12.1.2, the section on the negative binomial model, enter this explicit explanation on the gamma portion of the gamma-poisson model:
It might be best to just add this as a footnote. Also, remember to add Hilbe (2011) to the reference list.