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| Title: | 複迴歸係數排列檢定方法探討
Methods for testing significance of partial regression coefficients in regression model |
| Authors: | 闕靖元
Chueh, Ching Yuan |
| Contributors: | 江振東
Chiang, Jeng Tung
闕靖元
Chueh, Ching Yuan |
| Keywords: | 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 |
| Date: | 2017 |
| Issue Date: | 2017-07-11 11:25:12 (UTC+8) |
| Abstract: | 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. |
| Reference: | 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.
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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. |
| Description: | 碩士
國立政治大學
統計學系
104354007 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0104354007 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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