分层线性模型的最大后验估计

最大后验估计（MAPE）和最大似然估计（MLE）都是重要的参数点估计方法。在介绍一般分层线性模型（HLM）MAPE方法的基础上,给出这种方法的期望最大化算法（EM）的具体步骤,运用对数似然函数的二阶导数推导了MAPE估计的方差估计量。同时运用数据模拟比较了EM算法下的MAPE和MLE。对于固定效应的估计,两种方法得到的估计量是一致的。当组数较少时,EM计算的MAPE的方差协方差成分比MLE的更靠近真实值,而且MAPE的迭代次数明显小于MLE。

Maximum a Posteriori Estimate of Hierarchical Linear Model

Maximum a posteriori(MAP) estimation is an important method in statistical estimation.This research develops MAP estimation for Hierarchical Linear Model(HLM),and gives a detailed process of estimation and computational program.The expectation maximum(EM) algorithm was adapted to the concrete calculation,and the second derivatives of log likelihood function help us to obtain the estimators of variance and covariance components in this model according to asymptotic distribution theory of maximum likelihood e...