Models for Count Data

The most common models for count data are the Poisson and the negative binomial model. The latter is used if there is overdispersion, i.e. if the variance is bigger than under the assumption of a Poisson model.

poisson broken_leg sex status

could be a simple example of a Poisson model in which the number of times an individual has experienced a broken leg (accidents are a typical case of a Poisson process) is related to variables sex and status.

For the negative binomial model, a number of different specifications is implemented in Stata.

nbreg broken_leg sex status

will estimate the same model as before, assuming a negative binomial model in which dispersion is related to the values of the covariates in the model. You may estimate a model in the dispersion is assumed to be constant with

nbreg broken_leg sex status, dispersion(const)

Finally, in a generalized negative binomial model, covariates may affect the dispersion. Thus,

gnbreg broken_leg sex status, lnalpha(status)

is considered as a possible influence not only on the dependent variable, but also on the dispersion parameter.