Likelihood Estimation And EM Algorithm For Variance Components In Linear Mixed Effect Models

Linear mixed effects model is a special kind of linear model,which is an important branch of modern statistics.It can handle complex data with the embedded structure,and has wide application value in every field of social life.This paper deduced the variance components form of one-way classification random effect model and the general linear mixed effects model,and given the general expression of variance components used the maximum likelihood estimate and the restricted maximum likelihood estimate.Due to the likelihood equations with no explicit solution,this paper derived the EM algorithm of the maximum likelihood estimate and the restricted maximum likelihood estimate.Based on likelihood estimation method and the EM iterative algorithm,through R software for numerical simulation,estimated the variance components,explained the estimated results,and applied to the practical problems of the design of experiment.From simulation results,using the EM iterative algorithm to estimate variance component of one-way classification random effects model,calculated the absolute error is in the range of 0.1,mean square error(MSE)within the scope of 0.02,the error is small,and the iterative is convergent.