In Stata, xtnbreg
and xtpoisson
have the random effects estimator as the default option. You can always estimate the two parts separately by hand. See the count-data chapter of Cameron and Trivedi's Stata book for cross-sectional examples.
You also have the user-written hplogit
and hnlogit
for hurdle count models. These use a logit/probit for the first-stage and a zero-truncated poisson/negative binomial for the second stage. Also, a finite mixture model might be a nice approach (see user-written fmm
). There's also ztpnm.
All these are cross-sectional models.