A flexible regression model for zero- and k-inflated count data

摘要

Count data with inflated zeros commonly occur in numerous research studies. Accordingly, there is substantive literature regarding zero-inflated Poisson and analogous generalizable count regression models that account for data dispersion via excess zeros. Scenarios exist, however, where another count k0 tends to be inflated, thus there remains the need to develop a flexible regression model that can accommodate both inflated frequencies and any inherent data dispersion. This work achieves this goal by employing the Conway-Maxwell-Poisson (CMP) distribution. We develop a zero- and k-inflated Conway-Maxwell-Poisson (ZkICMP) distribution and corresponding regression that addresses over- and under-dispersed count data. We further discuss parameter estimation and other diagnostics by analytical and numerical methods, and illustrate superior performance of the ZkICMP regression via real data examples.