การประมาณส่วนประกอบความแปรปรวนของตัวแบบสองปัจจัยข้ามกลุ่มด้วยวิธีการเฉลี่ยตัวแบบ / นรินทร์ทิพย์ เทียนสว่าง = An estimation of variance components for two crossed factors design by model averaging method / Narintip Teansawang
The objective of this study is to compare two methods of variance components estimation for two factorial crossed classification design; the model averaging method and the classical method. The classical method estimates all variance components directly by the full model while the model averaging method estimates those variance components using all possible reduced models and then averaging all of those estimates. The full model estimation for two factorial crosses classification design is as follows: Yijk = mu+alphai+beta j+(alpha beta)ij+epsilon ijk, i = 1, 2,...,a ; j = 1, 2,...,n Where Yijk is the kth observation for the ith level of factor A and the jth level of factor B, mu is grand mean, alpha i is the ith random effect of factor A, beta j is the jth random effect of factor B, (AlphaBeta)ij is the random effect for interaction effect for the ith level of factor A and the jth level of factor B, epsilon ijk is random error for the kth observation at the ith level of factor A and the jth level of factorB and alphai, betaj, (AlphaBeta)ij and epsilon ijk are independently and normally distributed with mean zero and variance sigma2alpha, sigma2beta, sigma2alpha beta and sigma2epsilon respectively, a is number of levels for factor A, b is number of levels for factor B, n is number of replication for each treatment combination. The parameters; sigma2alpha, sigma2beta, sigma2alpha beta and sigma2epsilon are variance components for the model. Monte Carlo Simulation is done through S-plus 2000 code. It is simulated under several siltuations due to the number of levels for factor A, the number of levels for factor B, the number of replication for each treatment combination and the coefficient of variation (C.V.) of the observed data. In this study, the simulation is specified at a=b=2, 3, 5 and 7 when n=3, 5 and 7 respectively. The coefficient of variation is specified at 5%, 15%, 25%, 35%, 45%, 55% and 65% respectively. The average of euclldean distance between the vector of variance component estimates and the vector of true values is a criteria for comparison between both methods. The result of the study shows the point estimates for each variance components using the model averaging method; for, the number of replication greater than the number of levels for both factors; provides shorter averaged distance than the one from the classical method. When the number of replication is less than or equal to the number of levels for both factors, the distance from the averaging method is more than the one from the classical method except the case that the number of replication and the number of levels for both factors are equal to 3. In summary, the point estimation of variance components for balanced design of two factorial crossed classification model using the model averaging method is better than the one from the classical method when the number of replication is greater than the number of levels for both factors.