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

Abstract

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 k>0 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.