Zero-inflated sum of Conway-Maxwell-Poissons (ZISCMP) regression

While excess zeros are often thought to cause data over-dispersion (i.e. when the variance exceeds the mean), this implication is not absolute. One should instead consider a flexible class of distributions that can address data dispersion along with excess zeros. This work develops a zero-inflated sum-of-Conway-Maxwell-Poissons (ZISCMP) regression as a flexible analysis tool to model count data that express significant data dispersion and contain excess zeros. This class of models contains several special case zero-inflated regressions, including zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), zero-inflated binomial (ZIB), and the zero-inflated Conway-Maxwell-Poisson (ZICMP). Through simulated and real data examples, we demonstrate class flexibility and usefulness. We further utilize it to analyze shark species data from Australia's Great Barrier Reef to assess the environmental impact of human action on the number of various species of sharks.