非线性Poisson-Gamma回归模型中存在偏大离差时离差参数的齐性检验  

Testing for Homogeneity of Dispersion Parameters under Overdispersion in Nonlinear Poisson-Gamma Regression Models

作　　者：林金官[1] 韦博成[2] 

机构地区：[1]东南大学数学系,南京210096 [2]江苏教育学院数学系,南京210013

出　　处：《应用概率统计》2003年第3期277-285,共9页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(19631040);国家社会科学基金(02BTJ001)

摘　　要：Poisson回归模型广泛地应用于分析计数型数据,但该模型往往存在偏大离差(overdispersion)问题。刻画Poisson回归模型的偏大离差性的两种方法是拟似然方法和随机效应法(Lee ＆ Nelder,2000),已有许多作者利用随机效应法研究了Poisson模型的偏大离差的检验问题。但他们均假定随机效应是独立同分布的,本文对他们的假设进行检验。我们分别在组内效应一致和组内效应不一致的情形下,研究了存在偏大离差的Poisson-Gamma非线性随机效应模型中,随机效应方差(称为离差参数)的齐性检验问题,得到了离差参数齐性的score检验统计量。最后给出两个数值例子说明本文方法的应用。Poisson regression models are widely used in analyzing count data. However, overdispersion often exists in these models. Two ways of modelling overdispersion in Poisson regression models are quasi-likelihood approach and random-effect approach. Many authors have discussed the tests for detecting overdispersion in Poisson models using random-effect methods. But they all assumed that the random effects were mutually independent and identically ditributed. This paper presents the test for their assumptions. We develop two diagnostic tests for homogeneity of dispersion parameters in over-dispersion nonlinear random-effect Poisson-Gamma models conditionally on identical and diffrent within-subject effects respectively. The score test statistics are obtained and two numerical examples are given to illustrate our results.

关 键 词：离差参数 齐性 SCORE检验 非线性模型 偏大离差 Poisson-Gamma模型 随机效应 

分 类 号：O212.2[理学—概率论与数理统计]