การประมาณค่าพารามิเตอร์ในสมการถดถอยเชิงเส้นอย่างง่ายของข้อมูลระยะยาว - พัชรีภรณ์ พรหมหมัด (จุฬาลงกรณ์มหาวิทยาลัย, 2004)
The objective of this study is to compare the value of the parameter in simple linear regression of longitudinal data when errors follow a first-order autoregressive process, with the Two-Stage Estimation (TS) and Maximum Likelihood Estimation (MLE). The study is compared under the terms of the value of autoregressive of 0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8 and 0.9 with the sample sizes of 20,30,40,50 and 60. The periods of data collection for replicate are 3, 6 and 12. The data are simulated by Monte Carlo technique with S-Plus 2000 program and repeated 500 times for each situation to calculate for Root Mean Square Error (RMSE). The conclusions of this study are as follows: In the case of low autoregressive level (0.1 to 0.3) the Maximum Likelihood estimator, set RMSE to the minimum in all sample size and all periods of data collection for replicate. In the case of medium autoregressive level (0.4 to 0.6) majority the Maximum Likelihood estimator, set RMSE to the minimum in all sample size and all periods of data collection for replicate except at autoregressive are 0.6, periods of data collection for replicate are 12 and sample size are 40 and 50 the Two - Stage estimator set RMSE to the minimum. In the case of high autoregressive level (0.7 to 0.9) majority the Maximum Likelihood estimator, set RMSE to the minimum at periods of data collection for replicate are 3 and 6 in all sample size except at autoregressive are 0.9, the periods of data collection for replicate are 6 and sample size 30, 40, 50 and 60 and the periods of data collection for replicate are 12 in all high autoregressive level and all sample size the Two - Stage estimator set RMSE to the minimum. When considering factor effecting, it is found that the RMSE directly the autoregressive but inversely effects by sample size and periods of data collection for replicate. This means that the errors form estimation are higher when the autoregressive increasing or sample size and periods of data collection for replicate decreasing. Maximum Likelihood estimator and Two Stage estimator are not different in RMSE. Therefore, we can use Two Stage estimation instead of Maximum Likelihood estimation. As the latter approach requires probability density function but the first approach does not. In practical, it is convenient to use Two Stage estimation rather than Maximum Likelihood estimation.