Estimation of a Missing Value in Randomized Complete Block Design When Treatment and Block are Random Effects

Abstract

This research aims to study and compare the 3 missing value estimation methods: Least Square (LS), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA), in randomized complete block design using both real and simulated data. We consider constraints of missing values (m), such as m = 1, 2 and assume coefficients of variation (C.V.) of 10%, 30%, and 50%. Additionally, we examine this experiment with three constants (h) 1, 2 and 3. The simulated data sizes are 9, 12, 15, 20, 21, 25, 28 and 35 with the number of treatments (t) equal to 3, 4, 5 and the number of blocks (b) equal to 3, 5, or 7. The number of iterations for each situation is 50000. The criteria for comparing the performance of missing value estimation methods for real and simulated data are the mean squared error (MSE) and the average MSE (AVG MSE) values, respectively. Both values from these estimation methods are insignificant. This means the methods are very high efficiency. The results are divided to 2 parts. For the real data set, if m = 1, the lowest MSE value is from the GA method. Nevertheless, the lowest MSE value is from the LS method when m = 2. For the simulated data, the LS method also has the smallest AVG MSE values for all situations. Lastly, the GA and LS methods get the smallest MSE values when h = 1.