半参数广义线性随机效应模型的影响分析

Influence Analysis on Semiparametric Generalized Linear Mixed Model

该文系统研究了半参数广义线性随机效应模型的统计诊断与影响分析方法,证明了数据删除模型和均值漂移模型的等价性定理,给出了广义Cook距离等诊断统计量及异常点的Score检验统计量并研究了该模型的局部影响分析,分别对加权扰动模型,响应变量扰动模型得到了影响距阵的计算公式,最后通过一个实例验证了文中给出诊断方法的有效性.

In this paper, the authors present a unified diagnostic method for semiparametric generalized linear mixed model.The equivalency of case deletion model and mean shift outlier model is investigated and the diagnostic statistics such as cook distance, score test statistic for outlier tests are derived. Secondly, the local influence for the models is investigated and the counting formulas of influence matrices for case weights perturbation model and mean shift perturbation model are obtained. Finally, numerical example illustrates that the method is effective.