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

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Graphical Abstract Summary: The levels of anaerobic butyric acid-producing sporeforming bacteria (BAB) in bulk tank raw milk from 7 similarly managed conventional dairy farms were studied. It is important to control and minimize BAB spores in raw milk to prevent late blowing defect in certain styles of cheese during aging. Different farm management practices such as bedding type used, cleaning agents, and udder clipping frequency may affect BAB spore concentrations in raw milk. We employed statistical models to test the relationship between farm-level factors and BAB spore concentrations. No significant association between management practices surveyed (i.e., bedding management, milking preparation procedures, teat and udder cleanliness scoring, holding area cleaning procedures, and udder clipping or flaming frequency) and BAB spore concentration was found, with one possible reason being the small sample size used. The minimum number of individual samples required was calculated using parameters from this study, demonstrating how this research can be used for future study design.

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