國立東華大學應用數學系

專    題    演    講

主講人：Prof. Wei-Wen Hsu

                 Department of Statistics, Kansas State University.

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

時  間：105 年 05月 27日 (星期五)  15:20-17:00

地  點：理工一館 A324會議室

摘 要

Zero-Inflated models are often assumed that the mean of baseline distribution and the mixture probability depend on covariates through regression technique. The most popular way is to adopt proper link functions, such as log and logit functions, coupled with a linear predictor to relate the covariates of interest. However, in practice, the predictor in the link function may not be necessary linear in parameters but curvilinear. For this, one popular model in the literature that can appropriately accommodate the nonlinear predictor is Zero-Inflated Generalized Additive Models (ZIGAM), which simply extends Zero-Inflated models to incorporate the use of Additive Models. But, for this class of models, it is nontrivial to conduct inferences for 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, where it assumes that the smooth components of covariates in the baseline mean and the mixture probability have proportional relationships. An intensive simulation study shows that the proposed score test outperforms the other existing tests when the mixture probability and the baseline 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.

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