English  |  正體中文  |  简体中文  |  Items with full text/Total items : 88295/117812 (75%)
Visitors : 23402066      Online Users : 149
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/124679
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/124679


    Title: 迴歸分析中共線性於Suppression與Collapsibility之效果探討
    Effects of Collinearity on Suppression and Collapsibility in Multiple Linear Regression
    Authors: 許斯淵
    Hsu, Szu-Yuan
    Contributors: 江振東
    許斯淵
    Hsu, Szu-Yuan
    Keywords: 共線性
    相關係數
    迴歸係數
    判定係數
    t 統計量
    Collinearity
    Correlation coefficient
    Regression coefficient
    R-square
    t-statistics
    Date: 2019
    Issue Date: 2019-08-07 16:00:35 (UTC+8)
    Abstract: 在探討一個連續型反應變數與一個以上的解釋變數之間的關係時,線性迴歸是一種經常被使用的統計方法。當額外的解釋變數加入模型時,研究者通常著重於迴歸係數估計值與其t統計量的行為表現以及判定係數(R-square)的增加程度等迴歸結果,然而這些結果與新加入的解釋變數及原先已存在於模型裡的解釋變數之間的共線性(collinearity)不無關係。本文主要在探討共線性的效果對於迴歸係數估計值與其t統計量以及判定係數的行為表現之影響。本文研究中發現,當額外的解釋變數加入模型時,新模型的迴歸分析結果可以完全透過三個相關係數以及原模型的判定係數來詮釋,因此可以進一步透過這些訊息來預期新的模型之下的迴歸結果。另一方面,藉由將額外加入的解釋變數視為研究所感興趣的解釋變數,而將原先存在於模型裡的解釋變數視為共變量(covariate),本文亦透過類似的方式來探討共線性的效果對於模型裡collapsibility之影響。所謂的collapsibility是指無論共變量是否存在於模型裡,皆不會影響到研究中所感興趣的解釋變數與反應變數之間的關係。整體而言,本文研究發現當共線性存在於線性迴歸模型中,並不一定會對於迴歸結果造成不好的影響。因此,當模型裡解釋變數間存在共線性時,變數是否從模型中移除必須謹慎思量。
    Linear regression is a statistical method that allows researchers to summarize and study the relationship between a response and one or more predictor variables. When adding a predictor into a model, we are most interested in knowing its estimated regression coefficient, the corresponding t-statistic, and the value of R-square that increases. One apparent issue that might impact the results is the collinearity between the added-predictor and those already in the model. In this study, we investigate behavior patterns of the estimated regression coefficient, the corresponding t-statistic and R-square as the collinearity varies. We argue that all the above mentioned statistics are functions of three correlation coefficients and an R-square, and provide summary tables that can be used to anticipate the behavior of the statistics. On the other hand, by treating the added-predictor as the predictor of interest, and those predictors already in the model as covariates, we are able the apply similar techniques to deal with the impact of collinearity on collapsibility, that is, whether the relationship between the response and the predictor of interest remains the same if the covariates are dropped from the model. Overall, we found that collinearity in a linear regression model may not necessarily yield ill effects as we normally think. We urge researchers to think twice before dropping a collinear predictor from further model consideration.
    Reference: Chiang, J. T. and Hsu, S. Y. (2018), “Revisiting the Effects of Collinearity in Multiple Linear Regression: High Collinearity May Not Cause the Serious Problems You Might Think,” (Unpublished manuscript).

    Clogg, C. C., Petkova, E, and Shihadeh, E. S. (1992), “Statistical Methods for Analyzing Collapsibility in Regression Models,” Journal of Educational Statistics, 17(1), 51-74.

    Clogg, C. C., Petkova, E, and Haritou, A. (1995), “Statistical Methods for Comparing Regression Coefficients between Models,” American Journal of Sociology, 100(5), 1261-1293.

    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.

    Currie, I. and Korabinski, A. (1984), “Some Comments on Bivariate Regression,” The Statistician, 33, 283-292.

    Darlington, R. B. (1968), “Multiple Regression in Psychological Research and Practice,” Psychological Bulletin, 69, 161-182.

    Dua, S., Bhuker, M., Sharma, P., Dhall, M., and Kapoor, S. (2014), “Body Mass Index Relates to Blood Pressure Among Adults,” North American Journal of Medical Sciences, 6(2), 89-95.

    Friedman, L., and Wall, M. (2005), “Graphical Views of Suppression and Multicollinearity in Multiple Linear Regression,” The American Statistician, 59, 127-137.

    Greenland, S., Robins, J. M., and Pearl, J. (1999), “Confounding and Collapsibility in Causal Inference,” Statistical Science, 14(1), 29-46.

    Hamilton, D. (1987), “Sometimes R^2>r_(yx_1)^2+r_(yx_2)^2: Correlated Variables Are Not Always Redundant,” The American Statistician, 41, 129-132.
    —— (1988), “Reply to [Comments by Freund and Mitra],” The American Statistician, 42, 90-91.

    Horst, P. (1941), “The Prediction of Personal Adjustment,” Social Science Research Council Bulletin, 48, 431-436.

    Kleinbaum, D. G., Kupper, L. L., Nizam, A., and Muller, K. E. (2008), Applied Regression Analysis and Other Multivariable Methods (4th ed.), Tomson-Brooks/Cole.

    Kutner, M., Nachtsheim, C., and Neter, J. (2004), Applied Linear Regression Models (4th ed.), McGraw-Hill/Irwin.

    Ludlow, L., and Klein, K. (2014), “Suppressor Variables: The Difference between ‘Is’ versus ‘Acting As’,” Journal of Statistics Education, 22(2), 1-28.

    O’Brien R. M. (2017), “Dropping Highly Collinear Variables from a Model: Why it Typically is Not a Good Idea,” Social Science Quarterly, 98(1), 360-375.

    Rencher, A. C. and Schaalje, G. B. (2008), Linear Models in Statistics (2nd ed.), John Wiley & Sons, Inc.

    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 Situations in Multiple Linear Regression,” Educational and Psychological Measurement, 66, 435-447.

    Velicer, W. (1978), “Suppressor Variables and The Semipartial Correlation Coefficient,” Educational and Psychological Measurement, 38, 953-958.

    Waller, N. G. (2011), “The Geometry of Enhancement in Multiple Regression,” Psychometrika, 76, 634-649.
    Description: 博士
    國立政治大學
    統計學系
    101354501
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0101354501
    Data Type: thesis
    DOI: 10.6814/NCCU201900647
    Appears in Collections:[統計學系] 學位論文

    Files in This Item:

    File SizeFormat
    450101.pdf1445KbAdobe PDF0View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    社群 sharing

    著作權政策宣告
    1.本網站之數位內容為國立政治大學所收錄之機構典藏,無償提供學術研究與公眾教育等公益性使用,惟仍請適度,合理使用本網站之內容,以尊重著作權人之權益。商業上之利用,則請先取得著作權人之授權。
    2.本網站之製作,已盡力防止侵害著作權人之權益,如仍發現本網站之數位內容有侵害著作權人權益情事者,請權利人通知本網站維護人員(nccur@nccu.edu.tw),維護人員將立即採取移除該數位著作等補救措施。
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback