Fisher得分法与EM算法在随机效应模型中的应用

随着随机模型的广泛应用,关于随机效应模型的参数估计一直是线性模型的最活跃的研究方向之一。我们经常估计这类模型的固定效应和方差成分。我们使用极大似然估计作为估计方差成分的一种技巧,为了考虑到估计固定效应时的自由度的损失,我们又会使用限制极大似然估计。计算方差成分的ML或者REML估计时,有很多迭代算法可以使用。我们关心的是Fisher得分法和EM算法应用到随机效应模型的方差成分上,通过使用这两种算法对随机效应模型的方差成分的极大似然估计和限制极大似然估计进行比较分析。本文给出EM算法用于求极大似然估计的具体公式补充证明,并对Fisher得分法在随机效应模型中的应用限制极大似然估计给予具体公式。

Application of EM algorithm and Fisher Score algorithm in Mixed Effects Model

With the wide application of mixed effects model,on the mixed effects model parameter estimation has been one of the most active research directions of the linear model.The mixed effects models are often used for estimating fixed effects and variance components family.We often use the MLE of variance components as a technique,in order to take into account the loss in degrees of freedom resulting from estimating fixed effects,we will use REMLE.There are many iterative algorithms that can be considered for computing the ML or REML estimates of variance components.Our concern is that the Fisher Score algorithm and EM algorithm is applied to the variance components of mixed effects model.By using the two algorithms on variance components of the mixed effects models,MLE and REMLE are compared and anlysised.In this paper,the EM algorithm is used to find MLE of the specific formula to supplement the proof,and give a specific formula that the Fisher Score algorithm is applied to the REMLE of variance components of mixed effects model.