Yeap B Y, Davidian M
Department of Medicine, Harvard Medical School and Massachusetts General Hospital, Boston 02114-2696, USA.
Biometrics. 2001 Mar;57(1):266-72. doi: 10.1111/j.0006-341x.2001.00266.x.
Hierarchical models encompass two sources of variation, namely within and among individuals in the population; thus, it is important to identify outliers that may arise at each sampling level. A two-stage approach to analyzing nonlinear repeated measurements naturally allows parametric modeling of the respective variance structure for the intraindividual random errors and interindividual random effects. We propose a robust two-stage procedure based on Huber's (1981, Robust Statistics) theory of M-estimation to accommodate separately aberrant responses within an experimental unit and subjects deviating from the study population when the usual assumptions of normality are violated. A toxicology study of chronic ozone exposure in rats illustrates the impact of outliers on the population inference and hence the advantage of adopting the robust methodology. The robust weights generated by the two-stage M-estimation process also serve as diagnostics for gauging the relative influence of outliers at each level of the hierarchical model. A practical appeal of our proposal is the computational simplicity since the estimation algorithm may be implemented using standard statistical software with a nonlinear least squares routine and iterative capability.
分层模型包含两种变异来源，即在总体中的个体内部和个体之间；因此，识别可能在每个抽样水平出现的异常值很重要。分析非线性重复测量的两阶段方法自然允许对个体内随机误差和个体间随机效应的各自方差结构进行参数建模。当违反通常的正态性假设时，我们基于休伯（1981年，《稳健统计学》）的M估计理论提出一种稳健的两阶段程序，以分别处理实验单元内的异常反应以及偏离研究总体的个体。一项关于大鼠慢性臭氧暴露的毒理学研究说明了异常值对总体推断的影响，从而体现了采用稳健方法的优势。两阶段M估计过程生成的稳健权重也可作为诊断工具，用于衡量分层模型各水平上异常值的相对影响。我们提议的一个实际优点是计算简单，因为估计算法可以使用具有非线性最小二乘例程和迭代能力的标准统计软件来实现。
