In medical, environmental, and ecological studies, existence of excessive zeros in count data is common.
Among univariate Poisson models, for each of the response variables, the DIC value for the zero-inflated model was lower than that of the ordinary model, which is logical due to the existence of excessive zeros in both responses.
Excessive zeros when assessing these types of outcome measures are often due to the existence of a subpopulation of subjects who are not at risk for such a behavior during the study period.
In this example, the presence of excessive zeros reflects a proportion of subjects who were not at risk for the health condition or behavior of interest.
While the fact that the presence of excessive zeros itself is sufficient to justify the use of zero-inflated models, Vuong has developed a test to formally test whether a ZIP is superior to a Poisson regression.
It is clear that there are excessive zeros in the distribution.
As illustrated by the real data example presented, zero-inflated models have both conceptual and analytics advantages when there are excessive zeros. The zero-inflated models not only correct the overdispersion arising from the existence of structural zeros, but also allow for the distinction of different risk groups, providing better understanding of the data.