The Use Of the Bayesian Method and Restricted Maximum Likelihood in estimating of mixed Linear Components with random effects model with practical application.

Abstract

In this research we study a variance component model, Which is the one of the most important models widely used in the analysis of the data, this model is one type of a multilevel models, and it is considered as linear models , there are three types of linear variance component models ,Fixed effect of linear variance component model, Random effect of linear variance component model and Mixed effect of linear variance component model . In this paper we will examine the model of mixed effect of linear variance component model with one –way random effect ,and the mixed model is a mixture of fixed effect and random effect in the same model, where it contains the parameter (μ) and treatment effect (τ_i ) which  has a known probability distribution , The goal of this research The parameters of this mixed linear model will be estimated using the estimation methods, The method of the restricted maximum likelihood for one– way random model and bayesian method. When the bayes method includes a gibbs sampling, And the determine the best method in the application side by Coefficient of variation. The application side concluds the experience of the effect of varieties of oats plant (one –way) according to the randomized complete design with five replication and the experiment included six varieties of oats plant to represent a random sample drawn from a population at randomly, In order to study the effect of the six  varieties different of oats plant in some studied trait , Such as the quantity of grain yield measured (g /m²) . The results show that of practical application it was Concluded in through this reseearh The Pseudic method proved to be efficient of the significance of the differences between the treatments It also achieved the best in estimating the parameters of the model using the criterion of Coefficient of variation  where it was the lowest.