การเปรียบเทียบเกณฑ์การคัดเลือกตัวแบบถดถอยแบบไม่ติดกลุ่ม / บุญจิรา มากอ้น = A comparison on the model selection criteria for nonnested regression models / Bunjira Makond
The objective of this study is to compare the accuracy of model selection criteria for non-nested linear regression model. The general linear regression model is shown as follow : Y = X{u1D6C3} + {u1D6C6} where Y is an (n x 1) vector of dependent variables, X is an (n x p) matrix of independent variables, {u1D6C3} is a (p x 1) vector of the regression coefficient, {u1D6C6} is an (n x 1) vector of errors, where {u1D6C6}~N(0, σ²I) ; σ²I is an (n x n) matrix of variance-covariance, n is a sample sizes and p is the number of unknown parametric regression coefficients. Model selection criteria for this research are Akaike's Information Criterion(AIC) which is defined by equation AIC = nlog(σ²) + 2p and Bayesian Information Criterion(BIC) which is defined by equation BIC = nlog(σ²) + log(n)p, where σ² = SSE/n, SSE is sum square error. The model which has minimum (AIC)BIC is the preferred model. For each selection, AIC(BIC) can select accurate model if the model has minimum MSE value. In this study, the datas are simulatd by S-PLUS 2000 package using Monte Carlo technique. The numbers of independent variables are 2, 3 and 4. The errors are normal distribution with mean 0 and standard deviations are 1, 5, 10 and 15. The sample sizes are 25, 50, 75 and 100. The levels of correlation among independent variables are 0, 0.5 and 0.99. Given proportion of miss selection values are 1%, 5% and 10%. Significance levels are 0.01 and 0.05. Proportion of miss selection values and result of testing hypothesis are used to compare the accuracy of two model selection criteria. The results of this study can be summarized as follow : 1. When the number of independent variables is 2, AIC and BIC give proportion of miss selection values are 0 for every levels of correlation among independent variables, sample size and standard deviations. 2. When the numbers of independent variables are 3 and 4, AIC give proportion of miss selection values less than BIC for all cases of this research. AIC and BIC give proportion of miss selection values increase when the number of independent variables increase and decrease when sample sizes increase.
