What about cases where a significant number of observations have a count of 0 (in the context of Poisson Regression)?

In many data generation processes for count data, it is possible that a lot of observations will have a count of zero. For example, if the outcome is something like the frequency of natural disasters, it is possible that in many time windows, no such events occur. When this is the case, it is common to use a Zero-Inflated Poisson model (ZIP).

The ZIP model extends the regular Poisson model by introducing a second component that is used to model the probability of a non-zero count occurring. If the count is non-zero, the regular Poisson distribution is used, and if the count is zero, zeroes are generated at a rate corresponding to the probability of observing a zero count in the data. The ZIP model is an example of a mixture model, where the data generation process is comprised of more than one distribution with a probability assigned to the likelihood that an observation comes from each component.