A score test of homogeneity in generalized additive models for zero-inflated count data

Abstract

Zero-Inflated Poisson (ZIP) models are often used to analyze the count data with excess zeros. In the ZIP model, the Poisson mean and the mixing weight are often assumed to depend on covariates through regression technique. In other words, the effect of covariates on Poisson mean or the mixing weight is specified using a proper link function coupled with a linear predictor which is simply a linear combination of unknown regression coefficients and covariates. However, in practice, this predictor may not be linear in regression parameters but curvilinear or nonlinear. Under such situation, a more general and flexible approach should be considered. One popular method in the literature is Zero-Inflated Generalized Additive Models (ZIGAM) which extends the zero-inflated models to incorporate the use of Generalized Additive Models (GAM). These models can accommodate the nonlinear predictor in the link function. For ZIGAM, it is also of interest to conduct inferences for the mixing weight, particularly evaluating whether the mixing weight equals to zero. Many methodologies have been proposed to examine this question, but all of them are developed under classical zero-inflated models rather than ZIGAM. In this report, we propose a generalized score test to evaluate whether the mixing weight is equal to zero under the framework of ZIGAM with Poisson model. Technically, the proposed score test is developed based on a novel transformation for the mixing weight coupled with proportional constraints on ZIGAM, where it assumes that the smooth components of covariates in both the Poisson mean and the mixing weight have proportional relationships. An intensive simulation study indicates that the proposed score test outperforms the other existing tests when the mixing weight and the Poisson mean truly involve a nonlinear predictor. 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.