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The k‐ZIG: Flexible Modeling for Zero‐Inflated Counts
Author(s) -
Ghosh Souparno,
Gelfand Alan E.,
Zhu Kai,
Clark James S.
Publication year - 2012
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2011.01729.x
Subject(s) - negative binomial distribution , count data , zero inflated model , poisson distribution , overdispersion , zero (linguistics) , covariate , bayesian probability , statistics , mathematics , quasi likelihood , econometrics , computer science , poisson regression , population , linguistics , philosophy , demography , sociology
Summary Many applications involve count data from a process that yields an excess number of zeros. Zero‐inflated count models, in particular, zero‐inflated Poisson (ZIP) and zero‐inflated negative binomial (ZINB) models, along with Poisson hurdle models, are commonly used to address this problem. However, these models struggle to explain extreme incidence of zeros (say more than 80%), especially to find important covariates. In fact, the ZIP may struggle even when the proportion is not extreme. To redress this problem we propose the class of k‐ZIG models. These models allow more flexible modeling of both the zero‐inflation and the nonzero counts, allowing interplay between these two components. We develop the properties of this new class of models, including reparameterization to a natural link function. The models are straightforwardly fitted within a Bayesian framework. The methodology is illustrated with simulated data examples as well as a forest seedling dataset obtained from the USDA Forest Service’s Forest Inventory and Analysis program.