Generalized Additive Models for Zero-Inflated Data with Partial Constraints

• Activity Number: 249
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Hai Liu*+ and Kung-Sik Chan
• Companies: Indiana University School of Medicine and The University of Iowa
• Keywords: Asymptotic normality ; Convergence rate ; EM algorithm ; Model selection ; Penalized quasi-likelihood

Abstract

Zero-inflated data abound in many scientific fields. Nonparametric regression with zero-inflated response may be studied via the zero-inflated generalized additive model (ZIGAM) with a mixture distribution of zero and a regular exponential family component. We propose the (partially) constrained ZIGAM, which assumes that some covariates affect the probability of non-zero-inflation and the regular exponential family distribution mean proportionally on the link scales. When the assumption obtains, the new approach provides a unified and efficient framework for modeling zero-inflated data. We develop an iterative estimation algorithm. Some asymptotic properties are derived. We also propose a Bayesian model selection criterion for choosing between the unconstrained and constrained ZIGAMs. The new methods are illustrated with both simulation and a real application of jellyfish abundance data.