在傳統的迴歸模型架構下，統計推論的進行需要假設誤差項之間相互獨立，且來自於常態分配。當理論模型假設條件無法達成的時候，排列檢定（permutation tests）這種無母數的統計方法通常會是可行的替代方法。
在以往的文獻中，應用於複迴歸模型（multiple regression）之係數排列檢定方法主要以樞紐統計量（pivotal quantity）作為檢定統計量，進而探討不同排列檢定方式的差異。本文除了採用t統計量這一個樞紐統計量作為檢定統計量的排列檢定方式外，亦納入以非樞紐統計量的迴歸係數估計量b22所建構而成的排列檢定方式，藉由蒙地卡羅模擬方法，比較以此兩類檢定方式之型一誤差（type I error）機率以及檢定力（power），並觀察其可行性以及適用時機。模擬結果顯示，在解釋變數間不相關且誤差分配較不偏斜的情形下，Freedman and Lane (1983)、Levin and Robbins (1983)、Kennedy (1995)之排列方法在樣本數大時適用b2統計量，且其檢定力較使用t2統計量高，但差異程度不大；若解釋變數間呈現高度相關，則不論誤差的偏斜狀態，Freedman and Lane (1983)、Kennedy (1995) 之排列方法於樣本數大時適用b2統計量，其檢定力結果也較使用t2統計量高，而且兩者的差異程度比起解釋變數間不相關時更加明顯。整體而言，使用t2統計量適用的場合較廣；相反的，使用b2的模擬結果則常需視樣本數大小以及解釋變數間相關性而定。 / In traditional linear models, error term are usually assumed to be independently, identically, normally distributed with mean zero and a constant variance. When the assumptions cannot meet, permutation tests can be an alternative method.
Several permutation tests have been proposed to test the significance of a partial regression coefficient in a multiple regression model. t=b⁄(se(b)), an asymptotically pivotal quantity, is usually preferred and suggested as the test statistic. In this study, we take not only t statistics, but also the estimates of the partial regression coefficient as our test statistics. Their performance are compared in terms of the probability of committing a type I error and the power through the use of Monte Carlo simulation method. Situations where estimates of the partial regression coefficients may outperform t statistics are discussed.
| Identifer | oai:union.ndltd.org:CHENGCHI/G0104354007 |
| Creators | 闕靖元, Chueh, Ching Yuan |
| 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 |
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