分层混合效应模型迭代广义最小二乘估计的大样本性质  

The Iterative Generalized Least Squares Estimation for Multilevel Mixed Effects Model

作　　者：王春雨[1] 田茂再[1,2,3] WANG Chunyu;TIAN Maozai(Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, 100872, P. R. China;School of Statistics, Lanzhou University of Finance and Economics, Lanzhou, Gansu, 730020, P. R. China;Xinjiang Social ＆ Economic Statistics Research Center, School of Statistics and Information, Xinjiang University of Finance and Economics, Urumqi, Xinjiang, 830012, P. R. China)

机构地区：[1]中国人民大学应用统计科学研究中心中国人民大学统计学院,北京100872 [2]兰州财经大学统计学院,兰州甘肃730020 [3]新疆社会经济统计研究中心新疆财经大学统计与信息学院,乌鲁木齐新疆830012

出　　处：《数学进展》2018年第4期613-623,共11页Advances in Mathematics（China）

基　　金：中国人民大学科学研究基金(中央高校基本科研业务费专项资金资助)项目成果(No.18XNL012)

摘　　要：在许多领域中,我们常常需要处理具有分层结构的数据.对于这类数据,分层混合效应模型通过对回归系数进一步建模来刻画出同一层内变量之间的相关性.模型中随机部分比较复杂,这使得协方差矩阵的估计方法成为大家关注的问题.Goldstein(1986)提出了迭代广义最小二乘估计,并将它应用于一类特殊的分层模型——方差成分模型中,本文对其进行推广,对更一般的分层混合效应模型给出迭代广义最小二乘的具体表达形式,并运用到经济实例的分析中.In many fields, we need to deal with hierarchically structured data. For this kind of data, multilevel mixed effects model can show the correlation of variables in the same level by making a model further for regression coefficients. Due to the complexity of the random part in this model, seeking an effective method to estimate the covariance matrix is an appealing issue. Iterative generalized least squares estimation method was proposed by Goldstein in 1986 and was applied for variance component models originally, a special case of multilevel model. In this paper, we extend the method to the general multilevel mixed effects model, derive its expressions in detail and apply it to economic data.

关 键 词：分层模型 迭代广义最小二乘估计 方差协方差成分 最大似然估计 

分 类 号：O212.1[理学—概率论与数理统计]