bachlaw
commented
5 years ago Paul, I agree this would be a terrific add. With glmmTMB, the generalized poisson provides very good fits fairly quickly to overdispersed data, and as you point out can theoretically handle underdispersed data too, whereas the CMP takes forever, and while it can be more accurate it is tough to justify the cost. I recognize that glmmTMB uses optimization rather than sampling, but the generalized poisson seems to offer a flexible solution for both over and underdispersion. In terms of programming, I have had a hard time findiing helpful examples. INLA has an experimental version under the likelihood of gpoisson that includes a PDF vignette discussing the parameterization at some length. It doesn't seem to run reliably at the moment. There is also a paper discussing a zero-inflated implementation in BUGS, but with more math than code.
kdarras
rbcavanaugh
paul-buerkner
FErixon
The generalized poisson distribution has some potential when it comes to the estimation of underdispersed count data and is much more efficient to evaluate the the conway-maxwell poisson distribution. It may have trouble due to its complex support and it remains to be evaluated whether this distribution is robust enough to be implemented as a native family in brms. More information about the generalized poisson distribution may for instance be found at https://rdrr.io/cran/VGAM/man/genpoisson.html.