Count responses : The basic Poisson regression is a GLM that can be estimated by glm() with family = poisson as explained above. Negative binomial GLMs are available via glm.nb() in package MASS. Another implementation of negative binomial models is provided by aod, which also contains other models for overdispersed data. Zero-inflated and hurdle count models are provided in package pscl. A reimplementation by the same authors is currently under development in countreg on R-Forge which also encompasses separate functions for zero-truncated regression, finite mixture models etc
https://cran.r-project.org/web/views/Econometrics.html

如果是频率学派的话，我当时用的是glmmTMB。贝叶斯的话用JAGS，Stan, INLA都是可以的，当然，贝叶斯的话模型要自己写。