Computational Methods for Mixed Effects Models

摘要本研究扩展了当前混合效应模型参数估计的计算方法和软件实现。特别强调的是模型的扩展，其中有几个层次的随机效应嵌套在一起。另一个重点是模型，其中主体内的反应非线性地依赖于感兴趣的参数。主要实现是在S计算机语言中，并补充了该语言中可用的当前图形和分析方法。当对几个“对象”或实验单元中的每一个进行多次测量时，所得到的数据称为重复测量数据。如果每个实验单元的数据是随时间收集的，它们也被称为纵向数据。这类数据的统计模型通常会同时包含固定效应和随机效应，固定效应是描述被选择的实验单位在群体中的典型行为的参数，随机效应是描述群体内变化的数量。同时具有固定效应和随机效应的模型称为混合效应模型。该研究为混合效应模型拟合观测数据提供了新的计算方法。新方法适用于并行计算机和其他高性能计算环境。这一点很重要，因为混合效应模型在制造业（集成电路设计的评估）和生物技术（动物育种中的遗传效应建模）中的一些应用涉及到将复杂模型拟合到数千甚至数百万个观察结果中；一项挑战当前计算机极限的任务。

Computational Methods for Mixed-Effects Models Douglas M. Bates, U. of Wisconsin - Madison Abstract This research extends current computational methods and software implementations for the estimation of parameters in mixed-effects models. There is a special emphasis on extensions to models where there are several levels of random effects nested within each other. Another emphasis is on models where the within-subject response depends nonlinearly on the parameters of interest. The primary implementation is in the S computer language and complements current graphical and analytical methods available in that language. When a response is measured on several occasions for each of several "subjects" or experimental units, the resulting data are called repeated-measures data. If the data on each experimental unit are collected over time, they are also known as longitudinal data. A statistical model for such data will usually incorporate both fixed effects, parameters that describe the typical behaviour in the population from which the experimental units are selected, and random effects, quantaties that describe the variation within the population. Models with both fixed effects and random effects are called mixed-effects models. This research provides new computational methods for fitting mixed-effects models to observed data. The new methods are suitable for use with parallel computers and with other high performance computing environments. This is important because some of the applications of mixed-effects models in manufacturing (evaluation of integrated circuit designs) and biotechnology (modelling of genetic effects in animal breeding) involve fitting complicated models to thousands and sometime millions of observations; a task that pushes the limits of current computers.