The k-ZIG: Flexible Modeling for Zero-Inflated Counts
Article first published online: 20 FEB 2012
© 2012, The International Biometric Society
Volume 68, Issue 3, pages 878–885, September 2012
How to Cite
Ghosh, S., Gelfand, A. E., Zhu, K. and Clark, J. S. (2012), The k-ZIG: Flexible Modeling for Zero-Inflated Counts. Biometrics, 68: 878–885. doi: 10.1111/j.1541-0420.2011.01729.x
- Issue published online: 26 SEP 2012
- Article first published online: 20 FEB 2012
- Received March 2011. Revised November 2011. Accepted November 2011.
- Bayesian modeling;
- Link function;
- Log score loss;
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.