分析具有巢狀誤差結構的迴歸模式時,惹忽略隨機誤差項之間的相關性,而採用最小平方(OLS)估計量所導出的標準 F 統計量(以 F<sup>S</sup>表之)進行檢定,會導致過大的型 I 錯誤機率;若將隨機誤差項之間的相關性納入考量,而採用廣義最小平方(GLS)估計量所導出的 F 統計量 (以 F<sup>GLS</sup>表之),則計算上會較為繁雜。因此我們藉由轉換方式,將模式轉換成隨機誤差項之間彼此獨立的新模式後,再以 F<sup>S</sup> 進行檢定,其結果與直接以 F<sup>GLS</sup> 檢定相同,且可使計算較為方便。由於模式轉換所需的轉換矩陣為母體變異數的函數,因此當母體變異數未知時,我們以 Henderson 的常數配適 (fitting-of-constants)方法來估計之。藉由模擬結果得知,若各段的觀察個數相等,則不論巢狀誤差結構為二段式(two-stage)或三段式(three-stage),廣義最小平方估計量(GLS)均較最小平方估計量(OLS)表現穩定,且 F<sup>GLS</sup> 在檢定力及實際顯著水準方面的表現也都比 F<sup>S</sup> 好。 / When analyzing the regression model with nested-error structure, if the correlations between errors are ignored, and conduting the model adequacy test by the standard F statistic (F<sup>S</sup>) led from the ordinary leastsquares estimator (OLSE) , then the type I error rate will be inflated. However, if the corrlated structure is considered and the model is tested by F<sup>GLS</sup> led from the general least-squares estimator (GLSE) , the calculation will be more complicate. The model can be transformed to a new model with independent random errors and then, tested by F<sup>S</sup> . The result is the same as the one by F<sup>GLS</sup> , also it is more convenient for calculation. Since the transformation matrix is a function of variance components, we estimate variance components by Henderson's fitting-of-constants when they are unknown. Through simulation, it is concluded that if the observations in each stage of nested-error structure are the same, the GLSE is more stable than the OLSE in both two-stage and tree-stage structures. Also, the power and the sizes of F<sup>GLS</sup> will perform better than those of F<sup>S</sup> .
Identifer | oai:union.ndltd.org:CHENGCHI/B2002002104 |
Creators | 賴昭如 |
Publisher | 國立政治大學 |
Source Sets | National Chengchi University Libraries |
Language | 中文 |
Detected Language | English |
Type | text |
Rights | Copyright © nccu library on behalf of the copyright holders |
Page generated in 0.0018 seconds