Zero‐inflatedmodeling partII:Zero‐inflatedmodels for complex data structures

Abstract

The prequel to this review provided an extensive treatment of classic zero‐inflated count regression models where a univariate discrete distribution is used for the count regression component of the model. The treatment of zero inflation beyond the classic univariate count regression setting has seen a substantial increase in recent years. This second review paper surveys some of this recent literature and focuses on important developments in handling zero inflation for correlated count settings, discrete time series models, spatial models, and multivariate models. We discuss some of the available computational tools for performing estimation in these settings, while again highlighting the diverse data problems that have been addressed using these methods. This article is categorized under: Statistical Models > Multivariate Models Statistical Models > Generalized Linear Models Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

A Class of Copula-Based Bivariate Poisson Time Series Models with Applications

“…Note that the pmf (1) is a mixture of the degenerate distribution with a point mass at zero and a Poisson distribution. There is a large literature associated with the ZIP, starting from [15] to [16].…”

Zero-state Coupled Markov Switching Count Models for Spatio-temporal Infectious Disease Spread

“…That is, there are often many more zeros in the counts than can be predicted by the usual Poisson and negative binomial count models. Lambert (1992) proposed the zero inflated Poisson (ZIP) model to deal with excess zeros in count data, and this approach, with various extensions (see Young et al (2020)), has been applied in many fields including epidemiology. In a disease mapping application of the ZIP model, the presence/absence of the disease is generated through a Bernoulli process and then, when the disease is present, the number of reported cases is generated through a Poisson process (Fernandes et al, 2009).…”