  Regression for count data is widely performed by models such as Poisson,
negative binomial (NB) and zero-inflated regression. A challenge often faced by
practitioners is the selection of the right model to take into account
dispersion, which typically occurs in count datasets. It is highly desirable to
have a unified model that can automatically adapt to the underlying dispersion
and that can be easily implemented in practice. In this paper, a discrete
Weibull regression model is shown to be able to adapt in a simple way to
different types of dispersions relative to Poisson regression: overdispersion,
underdispersion and covariate-specific dispersion. Maximum likelihood can be
used for efficient parameter estimation. The description of the model,
parameter inference and model diagnostics is accompanied by simulated and real
data analyses.
