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題名 複迴歸係數排列檢定方法探討
Methods for testing significance of partial regression coefficients in regression model作者 闕靖元
Chueh, Ching Yuan貢獻者 江振東
Chiang, Jeng Tung
闕靖元
Chueh, Ching Yuan關鍵詞 排列檢定
複迴歸模型
樞紐統計量
蒙地卡羅模擬
型一誤差
檢定力
Permutation test
Multiple regression model
Pivotal quantity
Monte Carlo simulation
Type I error
Power日期 2017 上傳時間 11-七月-2017 11:25:12 (UTC+8) 摘要 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.參考文獻 1.Anderson, M. J. (2001). Permutation tests for univariate or multivariate analysis of variance and regression. Canadian Journal of Fisheries and Aquatic Sciences, 58, 626-639.2.Anderson, M. J., and Legendre, P. (1999). An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model. Journal of Statistical Computation and Simulation, 62, 271-303.3.Anderson, M. J., and Robinson, J. (2001). Permutation tests for linear models. Australian and New Zealand Journal of Statistics, 43, 75-88.4.Freedman, D., and Lane, D. (1983). A nonstochastic interpretation of reported significance levels. Journal of Business and Economic Statistics, 1, 292-298.5.Kennedy, P. E. (1995). Randomization tests in econometrics. Journal of Business and Economic Statistics, 13, 85-94.6.Kennedy, P. E., and Cade, B. S. (1996). Randomization tests for multiple regression. Communications in Statistics – Simulation and Computation, 25, 923-936.7.Levin, B., and Robbins, H. (1983). Urn models for regression analysis, with applications to employment discrimination studies. Law and Contemporary Problems, 46, 247-267.8.Manly, B. F. J. (1991). Randomization, Bootstrap and Monte Carlo methods in biology (First Edition). London: Chapman and Hall.9.Manly, B. F. J. (1997). Randomization, Bootstrap and Monte Carlo methods in biology (Second Edition). London: Chapman and Hall.10.Manly, B. F. J. (2006). Randomization, Bootstrap and Monte Carlo methods in biology (Third Edition). London: Chapman and Hall.11.Oja, H. (1987). On permutation tests in multiple regression and analysis of covariance problems. Australian Journal of Statistics, 29, 91-100.12.O’Gorman, T. W. (2005). The performance of randomization tests that use permutations of independent variables. Communication in Statistics – Simulation and Computation, 34, 895-908.13.ter Braak, C. J. F. (1992). Permutation versus bootstrap significance tests in multiple regression and ANOVA. Bootstrapping and Related Techniques (K.-H. Jockel, G. Rothe and W. Sendler, Eds.), Berlin: Springer Verlag, 79-86. 14.Winkler, A. M., Ridgway, G. R., Webster, M. A., Smith, S. M., and Nichols, T. E. (2014). Permutation inference for the general linear model. NeuroImage, 92, 381-397. 描述 碩士
國立政治大學
統計學系
104354007資料來源 http://thesis.lib.nccu.edu.tw/record/#G0104354007 資料類型 thesis dc.contributor.advisor 江振東 zh_TW dc.contributor.advisor Chiang, Jeng Tung en_US dc.contributor.author (作者) 闕靖元 zh_TW dc.contributor.author (作者) Chueh, Ching Yuan en_US dc.creator (作者) 闕靖元 zh_TW dc.creator (作者) Chueh, Ching Yuan en_US dc.date (日期) 2017 en_US dc.date.accessioned 11-七月-2017 11:25:12 (UTC+8) - dc.date.available 11-七月-2017 11:25:12 (UTC+8) - dc.date.issued (上傳時間) 11-七月-2017 11:25:12 (UTC+8) - dc.identifier (其他 識別碼) G0104354007 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/110779 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 104354007 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents 第一章 緒論 1 第一節 研究背景與動機 1 第二節 研究目的 2 第三節 本文架構 2第二章 文獻探討 3 第一節 簡單線性迴歸模型下係數排列檢定方法 3 第二節 複迴歸模型下係數排列檢定方法 4第三章 文獻相關議題探討 11 第一節 迴歸係數估計值與t值之對等（equivalent）關係 11 第二節 Kennedy(1995) 方法下，t_2值自由度使用之探討 17 第三節 Oja (1987)方法下設計變數值之探討 21第四章 研究方法與設計 22 第一節 研究方法 22 第二節 研究設計 24第五章 研究結果 27 第一節 型一誤差機率 27 第二節 檢定力 33 第三節 小結 36第六章 結論與建議 38 第一節 結論 38 第二節 建議 39參考文獻 40附錄、 R程式碼 42 zh_TW dc.format.extent 1093299 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0104354007 en_US dc.subject (關鍵詞) 排列檢定 zh_TW dc.subject (關鍵詞) 複迴歸模型 zh_TW dc.subject (關鍵詞) 樞紐統計量 zh_TW dc.subject (關鍵詞) 蒙地卡羅模擬 zh_TW dc.subject (關鍵詞) 型一誤差 zh_TW dc.subject (關鍵詞) 檢定力 zh_TW dc.subject (關鍵詞) Permutation test en_US dc.subject (關鍵詞) Multiple regression model en_US dc.subject (關鍵詞) Pivotal quantity en_US dc.subject (關鍵詞) Monte Carlo simulation en_US dc.subject (關鍵詞) Type I error en_US dc.subject (關鍵詞) Power en_US dc.title (題名) 複迴歸係數排列檢定方法探討 zh_TW dc.title (題名) Methods for testing significance of partial regression coefficients in regression model en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 1.Anderson, M. J. (2001). Permutation tests for univariate or multivariate analysis of variance and regression. Canadian Journal of Fisheries and Aquatic Sciences, 58, 626-639.2.Anderson, M. J., and Legendre, P. (1999). An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model. Journal of Statistical Computation and Simulation, 62, 271-303.3.Anderson, M. J., and Robinson, J. (2001). Permutation tests for linear models. Australian and New Zealand Journal of Statistics, 43, 75-88.4.Freedman, D., and Lane, D. (1983). A nonstochastic interpretation of reported significance levels. Journal of Business and Economic Statistics, 1, 292-298.5.Kennedy, P. E. (1995). Randomization tests in econometrics. Journal of Business and Economic Statistics, 13, 85-94.6.Kennedy, P. E., and Cade, B. S. (1996). Randomization tests for multiple regression. Communications in Statistics – Simulation and Computation, 25, 923-936.7.Levin, B., and Robbins, H. (1983). Urn models for regression analysis, with applications to employment discrimination studies. Law and Contemporary Problems, 46, 247-267.8.Manly, B. F. J. (1991). Randomization, Bootstrap and Monte Carlo methods in biology (First Edition). London: Chapman and Hall.9.Manly, B. F. J. (1997). Randomization, Bootstrap and Monte Carlo methods in biology (Second Edition). London: Chapman and Hall.10.Manly, B. F. J. (2006). Randomization, Bootstrap and Monte Carlo methods in biology (Third Edition). London: Chapman and Hall.11.Oja, H. (1987). On permutation tests in multiple regression and analysis of covariance problems. Australian Journal of Statistics, 29, 91-100.12.O’Gorman, T. W. (2005). The performance of randomization tests that use permutations of independent variables. Communication in Statistics – Simulation and Computation, 34, 895-908.13.ter Braak, C. J. F. (1992). Permutation versus bootstrap significance tests in multiple regression and ANOVA. Bootstrapping and Related Techniques (K.-H. Jockel, G. Rothe and W. Sendler, Eds.), Berlin: Springer Verlag, 79-86. 14.Winkler, A. M., Ridgway, G. R., Webster, M. A., Smith, S. M., and Nichols, T. E. (2014). Permutation inference for the general linear model. NeuroImage, 92, 381-397. zh_TW
