非线性异方差分层模型及其参数估计

Nonlinear Modeling of Heteroscedastic Hierarchical Data via ECM Algorithm

提出了一类非线性异方差分层模型,研究了其固定效应和方差分量的极大似然估计问题.主要采用了期望条件最大化算法(Expectation Conditional Maximization Algorithm)和蒙特卡罗积分法(Monte-Carlo integration method).对于随机效应和模型误差的方差-协方差矩阵,本文既考虑了一般的非结构化形式,也考虑了诸如自回归(AR(1))和复合对称等的结构化形式.仿真模拟的结果显示本文提出的模型及参数估计方法表现良好.此外,本文还将该类模型和估计方法应用到中国官方经济数据上,得到了一些有意义的结论.

We propose a class of nonlinear hierarchical models for the analysis of hierarchical data with heteroscedastieity and investigate the maximum likelihood es- timation of the fixed effects and variance components. The expectation conditional maximization algorithm （ECM） and Monte-Carlo integration methods are employed. Various forms of the variance-covariance matrices are considered for the random ef- fects and model errors, including the unstructured variance-covariance matrices and the structured ones, such as AR（1） and compound symmetry. Some simulations are implemented and perform well. We also apply our methods to an official Chinese data set and illustrate the utility of our proposed model and estimation method.