Evaluation of a New Variance Components Estimation MethodModied Hendersons Method 3 With the Application of Two Way Mixed Model

A two-way linear mixed model with three variance components as 1, 2 2 and 2 e is applied to evaluate the performance of modi…ed Henderson’s method 3 developed by Al-Sarraj and Rosen (2007). The focus of modi…ed procedure is on the estimation of 1 which variance components is mainly concerned. The modi…ed estimator is expected to perform better than unmodi…ed Henderson’s method 3 in terms of MSE. But it also follows the demerits of unmodi…ed one, i.e. lost uniqueness, negative estimates. The criteria used to show the performance of modi…ed estimator compared with unmodi…ed one, ML and REML are bias, MSE and the probability of getting negative estimate. Al-Sarraj and Rosen (2007) suggested us to divide the estimation of 1 of Henderson’s method 3 and its modi…ed into Partition I and Partition II. One way to solve the problem of lost unique estimators is to compare the MSE of Partition I and II, then select the one with smaller MSE. The performances of these estimators in terms of MSE are shown by the means of simulations. MSE e¤ects of imbalance and number of observations are given. Based on the MSE comparison of Partition I and II, there should exist a boundary value of 2 to favor Partition I, otherwise II. From the e¤ects of 2 and 2 1 to MSE, a ’small’values range of 2 2 < 0:1 is recommended to prefer to the Partition I of Henderson’s method 3 and its modi…ed compared with Partition II. Then, a ratio range of 2= 2 1 < 1:0 is obtained for wide application. Modi…ed Henderson’s method 3 has achieved substantially improvement over unmodi…ed one in terms of MSE, as well as the probability of getting negative estimate. It is also computationally faster than ML and REML and may for some cases performs better in terms of MSE. The split-plot design experiment application shows us that the modi…ed estimator can improve unmodi…ed one. Keywords: Variance components, Modi…ed Henderson’s method 3, MSE, Monte Carlo simulation.