A Score Test of Homogeneity for Generalized Additive Models for Zero-Inflated Count Data

• Activity Number: 692
• Type: Contributed
• Date/Time: Thursday, August 4, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Wei-Wen Hsu* and Gaowei Nian and David Todem and KyungMann Kim
• Companies: Kansas State University and IMS Health China Beijing Branch and Michigan State University and University of Wisconsin - Madison
• Keywords: Zero inflation ; Additive models ; goodness of fit ; score test ; fisheries data

Abstract

Zero-Inflated models are often assumed that the mean of baseline distribution and the mixture probability depend on covariates through regression technique. Typically, proper link functions, such as log and logit functions, coupled with a linear predictor were used to relate the covariates of interest. But, the predictor in the link function may not be necessary linear in parameters. For this, one popular model in the literature that can accommodate the nonlinear predictor is Zero-Inflated Generalized Additive Models (ZIGAM). However, for this class of models, it is nontrivial to conduct inferences on the mixture probability, particularly evaluating whether the mixture probability equals to zero. In this paper, we propose a generalized score test to evaluate the mixture probability under the framework of ZIGAM. Technically, the proposed score test is developed based on a novel transformation for the mixture probability coupled with proportional constraints on ZIGAM. The recreational fisheries data from the Marine Recreational Information Program (MRIP) survey conducted by National Oceanic and Atmospheric Administration (NOAA) are used to illustrate the proposed methodology.