Parameter Estimation And Resolution Test Of One-way Classification Model

In statistics,linear mixed model is an important and special model.Compared with other models,linear mixed model has advantages in dealing with data with complex embedded structures(such as repeated data,interval data,etc.).In recent years,with the development of big data,data in the fields of medicine,biology,machine learning,and environmental science have become more and more complex.Therefore,linear mixed model has been widely used in various fields.Many scholars have made some valuable progress in the study of linear mixed models.Parameter estimation of fixed effects and variance components is a hot research problem in linear mixed models.This paper uses the least square estimation and two-step estimation to estimate the fixed effects of the one-way classification random-effects model.Maximum likelihood method and limited maximum likelihood method are used to estimate the different components.The likelihood equations of one-way classification model with unbalanced data have no explicit solution.In this paper,the EM algorithm is used for iterative solutions.R software is selected for numerical simulation to discuss the influence of the change of random effect dimension and variance component parameters on the estimated value,and the maximum likelihood estimation and restricted maximum likelihood estimation are compared and analyzed.The simulation results show that the EM algorithm has a good parameter estimation effect for the unbalanced one-way classification model,and the EM algorithm has the advantages of effectiveness and simplicity in parameter estimation.In terms of estimation accuracy,maximum likelihood estimation is superior to the restricted maximum likelihood estimate.In terms of computing speed,restricted maximum likelihood estimation is superior to maximum likelihood estimation.In addition,this paper also innovatively defines the parameter resolution of maximum likelihood estimation based on the EM algorithm under the one-way classification random effect model.Experiments show that the maximum likelihood estimation based on the EM algorithm can better distinguish the similar parameters under a certain threshold,and has good accuracy in parameter estimation,which can be verified with the experimental results of numerical simulation.In the case of big data,due to the complexity of the iterative calculation of likelihood estimation,this paper proposes a new estimation algorithm.It combines the least-squares estimation,two-step estimation,and the variance component estimation without iteration to obtain the fixed effect and the variance component estimation at the same time.Numerical simulation shows that the algorithm is feasible.Compared with the maximum likelihood and restricted maximum likelihood methods,it has better computational efficiency while maintaining estimation accuracy.