半参数广义线性混合效应模型的影响分析  

Influence Analysis of Generalized Partially Linear Mixed Models

作　　者：张浩[1] 朱仲义[2] 

机构地区：[1]华东师范大学统计系,上海200062 [2]复旦大学统计系,上海200433

出　　处：《应用数学学报》2007年第4期743-756,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10671038号)资助项目.

摘　　要：本文把随机效应当作是缺失数据并利用P-样条拟合非参数部分,从而得到了半参数广义线性混合效应模型(GPLMM)的MCNR估计算法;同时利用Q-函数,我们得到了模型的参数部分的广义Cook距离以及非参数部分的广义DFIT,此外,本文还研究了四种不同扰动情形的PLMM的局部影响分析,得到了相应的影响矩阵,最后,我们通过—个实际例子验证了所提出的诊断统计量的有效性。This paper proposes several case-deletion as well as local influence measures for assessing the influence of an observation for generalized partially linear mixed models（GPLMM）. The essential idea is to treat the latent random effects in the model as missing data and extend the MCNR algorithm by adding penalized spline to estimate the nonparamters. On the basis of the Q-function which is associated with the conditional expectation of the complete-data log-likelihood, we generate generalized Cook Distance and generalized DFIT for the parametric and nonparametric part respectively. Four different perturbation schemes are discussed. One real illustrative examples are presented to prove the methodology.

关 键 词：半参数回归 广义线性混合模型 局部影响 COOK距离 P-样条 

分 类 号：O212.2[理学—概率论与数理统计]