Estimation in the Mixed Linear Models and QR Decomposition

Maximum likelihood estimation is one of the most important estimate methods in the mixed linear models, but to get the maximum likelihood estimates of variance components we must use iterative algorithms in the most cases. The QR decomposition transforms the design matrices into upper-triangle matrix, then we can decrease the orders of the matrices used in the iterative process, and reduce the amount of data in this process. By simulation, we show that QR decomposition can make EM algorithm run much more quickly and get almost the same results we get without QR decomposition. We also study the ANOVA estimation with QR decomposition.