There are two critical assumptions that we have to test. First, that there is no problem with overdispersion (or underdispersion, for that matter), which means that the assumption of mean=variance is violated. Second, that there is no problem with zero inflation (i.e. excess zeros).

To test model fit we can use the estat gof command, which relies on postestimation.

More information help estat gof

Practical example

The first step is re-run the multiple Poisson regression model. The quietly option is included in the beginning of the command to suppress the output.

quietly poisson children siblings sex ib1.educ if pop_poisson==1, irr

Then we use the estat gof command, which produces quite some output:

estat gof

The fact that the p-values are below 0.05 means that the Poisson model does not fit our data, and we should explore other alternatives, such as negative binomial regression or zero-inflated Poisson regression. These will be presented in the following section.