การประมาณค่าองค์ประกอบความแปรปรวน ของแผนแบบการทดลองจตุรัสละตินด้วยวิธีการเฉลี่ยตัวแบบ / ศิริวลัย จันทบุตร = An estimation of variance components for latin square design by the model averaging method / Sirivalai Juntabut
The objective of this study is to compare two methods of variance component estimation for Latin Square 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 for the Latin Square design is as follows: Y[subscript ijk] = μ+τᵢ+α {u1D457}+ βk+{u1D700}[subscript ijk] ; i,j,k,=1,…,p Y[subscript ijk] Y[subscript ijk] is an observation data for the i th level of treatment factor, the j th level of row blocking factor, and the k th column blocking factor, µ is the grand mean; [subscript ti] is the i th random effect of treatment factor and [subscript ti] is independently and normally distributed with mean 0 and variance σ^2 [subscript τ] α j is the j th random effect of row blocking factor and α j is independently and normally distributed with mean 0 and variance σ^2 [subscript a] Bk is the k th random effect of column blocking effect and Bk is also independently and normally distributed with mean 0 and variance σ^2 [subscript β] σ^2 [subscript ε] is the random error for the observed data at the i th level of treatment factor, the j th level of row blocking factor, the k th level of column blocking factor, and {u1D700}[subscript ijk] is independently and normally distributed with mean 0 and variance [subscript ε] p is the number of levels for treatment factor, row blocking factor and column blocking factor, The parameters; σ^2 [subscript τ] σ^2 [subscript a] σ^2 [subscript β] and σ^2 [subscript ε] are variance components for the model. Monte Carlo simulation is done thorough S-plus 2000 code. It is simulated under several situations due to the number of levels for treatment factor, row blocking factor and column blocking factor. In this study, the simulation is specified at p = 3, p = 4 and p = 5. In addition, the coefficient of variation (CV) for the observed data is varied from 5%, 15%, 25%, 35%, 45% to 55%. The average of Euclidean distance between the vector of true values and the estimation vector of variance is a measure for comparison between both methods. The results for the study show that point estimates for variance components in the Latin Square design model using the model averaging method regardless the number of levels for treatment factor, the number of levels for row blocking factor and the number of levels for column blocking factor, and the coefficient of variation for the observed data, provide shorter averaged Euclidean distance than the ones from the classical method in all simulated situations.
