การเปรียบเทียบการทดสอบอัตราส่วนความควรจะเป็นแบบปกติ และการทดสอบอัตราส่วนความควรจะเป็นแบบมอนติคาร์โล สำหรับการวิเคราะห์ความถดถอยเชิงพหุ / วโรภาส ประดิษฐกำจรชัย = A comparison on regular likelihood ratio test and Monte Carlo likelihood ratio test for multiple regression analysis / Varopas Praditkamjornchai
The objective of this study is to compare the methods of hypothesis testing on the regression coefficient by 2 methods; Regular likelihood ratio test and Monte Carlo likelihood ratio test. The multiple regression analysis model is y = xβ+ε where y (nx1) is the vector of observation β [(p+1)x1] is the vector of regression coefficient X [nx(p+1)] is the matrix of independent variables that have multivariate standard normal distribution and correlation between independent variables are zero ε (nx1) is the vector of random error of the observation and ε is independently and normally distribution with mean equal to zero and variance equal to σ² l[subscript n]p is the number of independent variables, n is the sample sizes. To generate the data for this study, the Monte Carlo simulation technique is done using S-plus 2000 package. The number of independent variables is specified at 2,3,4 and 5 variables. The sample size is specified at 10,25,50 and 100. The standard deviation is specified at 1, 3, 5 and 7. The significance levels for this study are at 0.01 , 0.05 and 0.1 level. The probability of type I error and the power of the test are a measure for comparison for both methods. The results of this study can be summarized as follows: 1. Probability of type I error The two methods can control probability of type I error at all significance levels. 2. Power of the test Monte Carlo likelihood ratio test gives the higher power of the test than regular likelihood ratio test at all of the levels on difference of regression coefficients all of the number of independent variables all of the sample sizes all of the standard deviation and all of the significance levels. When the number of independent variables sample sizes and standard deviation are increase and the difference of regression coefficient is 90% of standard deviation regular likelihood ratio test gives approximately nearly the same power of the test level.