Statistical Models for Count Data with Excess Zeros: A Review

KyungMann Kim
University of Wisconsin-Madison, USA

Count data are routinely analyzed using Poisson (P) distributions.  Due to population heterogeneity, however, they often exhibit over-dispersion known as the extra-Poisson variation.  This extra-Poisson variation can be handled in one of two ways, maximum quasi-likelihood method or a latent variable model leading to negative binomial (NB) distribution with a gamma mixing distribution for the Poisson mean.  Still there are situations where these models perform poorly because of excess zeros in the count.  There are two similar, but conceptually different approaches to handling excess zeros.   In what is commonly known as zero-inflated (ZI) models, we may view the data as being generated from a mixture model with a point mass at zero representing “excess” zeros and a standard non-degenerate distribution including “true” zeros.  This mixture model allows for mixture of two different populations, one non-susceptible for events (resulting in excess zeros) and the other susceptible (including true zeros).  In contrast, the so-called hurdle (H) models may be conceptualized as having zeros only from a non-susceptible population and can be modeled using two processes, one generating zeros (“choice”) and the other generating only the positive counts (“intensity”) from a truncated count distribution.  In this presentation, I will show examples of count data with excess zeros from the literature in various disciplines and applications and review recently developed marginal mean models for count data with excess zeros for illustration.