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研究生:劉家齊
論文名稱:迴歸分析中Suppression與Enhancement現象之探討
論文名稱(外文):research suppression and enhancement phenomenon in regression
指導教授:江振東江振東引用關係
學位類別:碩士
校院名稱:國立政治大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
畢業學年度:103
語文別:中文
論文頁數:49
中文關鍵詞:迴歸分析抑制變數
外文關鍵詞:SuppressionEnhancement
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自Horst (1941)提出suppressor變數一詞起,由於後續許多研究採用不盡相同思維之著眼點,也就衍生出許多不同定義的suppressor變數。Horst (1941)著重在判定係數的變化,Darlington (1968)、Conger (1974) 及 Cohen and Cohen (1975)則著重在迴歸係數的變化, Velicer (1978)則改用semipartial correlation coefficient來定義suppressor變數,再度將焦點轉回Horst (1941)的思維。Currie and Korabinski (1984)引進enhancement一詞,以便與suppression有所區分。
為了釐清這些紛擾的名詞定義,第二章、三章中,我們分別回顧enhancement與suppression兩現象。第四章中,我們針對enhancement、suppression兩種現象的關聯性,依據四種不同的面向進行比較。第五章,我們針對suppressor變數存在的情況下,藉由模擬實驗的方式,探討stepwise regression、forward selection、backward elimination三種變數選取方式的可能缺憾。第六章為總結。

Since Horst (1941) introduced the term of suppressor variable, many different definitions of suppressor variables have appeared in literature. Originally, Horst (1941) based the definition on the coefficient of determination. Darlington (1968), Conger (1974) and Cohen and Cohen (1975) paid more attention on the regression coefficients instead. On the other hand, Velicer (1978) used semipartial correlation coefficient to define a suppressor variable, and directed the focus back to that of Horst (1941). In order to differentiate the two similarly related ideas, Currie and Korabinski (1984) proposed the term of enhancement to describe exclusively the situations reflected by the definition of Horst (1941) or Velicer (1978).
In order to clarify the ambiguities resulting from various definitions of suppressor variable in literature, we first reviewed enhancement and suppression respectively in Chapters 2 and 3. In Chapter 4, we investigated their relationships from four different perspectives. In Chapter 5, we studied the possible drawbacks on using stepwise regression, forward selection, and backward elimination these three variable selection procedures on the presence of a suppressor variable. Conclusions are provided in Chapter 6.


第一章. 引言 6
第一節. Suppression與 Enhancement 6
第二節. 實例說明 9
第三節. 符號定義與公式 10
第二章. Enhancement現象探討 12
第一節. Classical Suppressor 12
第二節. Reciprocal Suppressor 或V-suppressor 13
第三節. 判定係數 與相關係數 的函數關係 14
第四節. Enhancement的出現機率與相關議題 16
第三章. Suppression現象探討 20
第一節. Negative Suppressor 20
第二節. C-suppressor 20
第三節. V-suppressor與其迴歸係數的關係 21
第四章. Enhancement 與 Suppression 之關聯性 23
第一節. 依 來做區分 23
第二節. 依 及 來做區分 25
第三節. 依定義來做區分 27
第四節. 藉由向量幾何圖形來做區分 29
第五章. Suppressor變數在模型變數選取時的可能影響 34
第一節. 模擬實驗中的變數生成 34
第二節. 三種選取變數的方式 36
第三節. Suppressor 變數被選入模型的機率 36
第六章. 總結 40
參考文獻 41
附錄 43


Bertrand, P.V., and Holder, R.L. (1988). “A quirk in multiple regression: The whole regression can be greater than the sum of its parts.” The Statistician, 37, 371-374.
Currie, I., and Korabinski, A. (1984). “Some comments on bivariate regression.” The Statistician, 33, 283–292.
Cohen, J., and Cohen, P. (1975). Applied multiple regression/correlation analysis for the behavioral sciences, New Jersey: Lawrence Erlbaum Associates.
Conger, A.J. (1974). “A revised definition for suppressor variables: a guide to their identification and interpretation.” Educational and Psychological Measurement, 34, 35-46
Darlington, R.B. (1968). “Multiple regression in psychological research and practice.” Psychological Bulletin, 69,161-182
Dayton, M. (1972). “A method for constructing data which illustrate a suppressor variable.” The American Statistician, 26, 36.
Feldman, B. (2005), “Relative Importance and Value.” Unpublished manuscript(Version 1.1, March 19 2005).
Friedman, L., and Wall, M. (2005). “Graphical views of suppression and multicollinearity in multiple linear regression.” The Educational and Psycgological Measurment, 2005, 59, 127-137.
Hamilton, D. (1987). “Sometimes : Correlated variables are not always redundant.” The American Statistician, 41, 129-132.
Holling, H. (1983). “Suppressor structures in the general linear model.” Educational and Psychological Measurement, 43, 1-9.
Horst, P. (1941). “The role of prediction variables which are independent of the criterion.” In Horst, P.(Ed.): The prediction of personal adjustment . Social Science Research Bulletin, 48, 431-436.
Lindeman, R. H., Merenda, P. F., and Gold, R. Z. (1980). Introduction to Bivariate and Multivariate Analysis. Glenview, IL: Scott, Foresman.
Lynn, H.S. (2003). “Suppression and confounding in action.” The American Statistician, 57, 58-61.
Lutz, G. (1983). “A method for construction data which illustrate there types of suppressor variable.” Educational and Psychological Measurement, 43, 373-377.
Newton, R. G. and Spurrel, D. J. (1967). “Examples of the use of elements for clarifying regression analysis.” Applied Statistics, 16, 165-172.
Pratt, J. W. (1987). “Dividing the indivisible: Using simple symmetry to partitionvariance explained”, in T. Pukkila and S. Puntanen (eds.), Proceedings of the Second International Conference in Statistics (University of Tampere, Tampere,Finland) pp. 245–260.
Schey, H.M. (1993). “The relationship between the magnitudes of SSR(x2) and SSR(x2|x1): A geometric description.” The American Statistician, 47, 26-30.
Shieh, G. (2001). “The inequality between the coefficient of determination and the sum of squared simple correlation coefficients.” The American Statistician, 55, 121–124.
Shieh, G. (2006). “Suppression situation in multiple linear regression.” The Educational and Psychological Measurement, 66,435-447.
Smith, R.L., Ager, J.W., and Williams, D. L. (1992). “Suppressor variables in multiple regression/correlation.” Educational and Psychological Measurement, 52, 17-29.
Velicer, W. (1978). “Suppressor variables and the semipartial correlation coefficient.” Educational and Psychological Measurement, 38, 953-958.

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