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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/152773
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/152773


    Title: 比較與衡量線性迴歸模型中解釋變數的相對重要性指標
    Compare and evaluate the relative importance metrics for explanatory variables in the linear regression model
    Authors: 吳宏煇
    Wu, Hong-Huei
    Contributors: 鄭宗記
    Cheng, Tsung-Chi
    吳宏煇
    Wu, Hong-Huei
    Keywords: 多元線性迴歸
    相對重要性
    LMG 指標
    比例邊際變異分解指標
    Epsilon 指標
    優勢分析
    偏F 檢定
    熱圖
    拔靴法
    馬可夫鏈排序
    Date: 2024
    Issue Date: 2024-08-05 13:58:54 (UTC+8)
    Abstract: 多元線性迴歸模型中的解釋變數之相對重要性為許多研究領域關心的議題,找出重要變數有助於解釋模型以及模型之後續應用。本研究將回顧不同的衡量變數重要性的指標,包含簡單指標以及變異數分解指標兩大類。當中簡單指標受限於解釋變數間的相關性而容易有錯誤解讀,但仍可作為變數重要性排序的參考依據 (Nathans et al., 2012)。變異數分解的指標則能將全模型 (Full Model) 之 R2 分解成多個非負值,此量化了每個解釋變數對於全模型的貢獻,意義明確且容易比較,因此本研究著重於變異數分解指標並以簡單指標作為輔助。變異數分解的指標共有 4 種,分別為Lindeman,Merenda, & Gold (1980) 提出的 Lindeman, Merenda and Gold (LMG) 指標、Feldman (2005)提出的比例邊際變異分解 (Proportional Marginal Variance Decomposition, PMVD) 指標、Budescu (1993) 提出的優勢分析 (Dominance Analysis) 以及Johnson (2000) 提出的 Epsilon指標。以上四種指標使用不同觀點來衡量解釋變數對於全模型的貢獻,因此這些指標所衡量出的變數重要性排序往往並不完全相同,因為當解釋變數彼此相關時,變數對於模型的貢獻可分為獨特貢獻與因相關而引起的聯合貢獻,能夠影響變數貢獻的原因較複雜且廣泛。因此本研究旨在探討當變異數分解指標的重要性排序結果出現分歧時,是否可以利用簡單指標或多種統計方法和工具作為輔助,以辨別哪種指標的重要性排序結果較為合理,或者能夠綜合這些指標的結果,得出哪些變數實際上具有相同的重要性。
    Reference: Azen, R., & Budescu, D. V. (2003). The dominance analysis approach for comparing predictors in
    multiple regression. Psychological methods, 8(2), 129-148.
    Budescu, D. V. (1993). Dominance analysis: a new approach to the problem of relative importance
    of predictors in multiple regression. Psychological bulletin, 114(3), 542-551.
    Budescu, D. V., & Azen, R. (2004). Beyond global measures of relative importance: Some insights
    from dominance analysis. Organizational Research Methods, 7(3), 341–350.
    Deng, K., Han, S., Li, K. J., & Liu, J. S. (2014). Bayesian aggregation of order-based rank data.
    Journal of the American Statistical Association, 109(507), 1023–1039.
    Derryberry, D., Aho, K., Edwards, J., & Peterson, T. (2018). Model selection and regression tstatistics. The American Statistician, 72(4), 379–381.
    Feldman, B. E. (2005). Relative importance and value. Available at SSRN 2255827.
    Freedman, D. A. (1981). Bootstrapping regression models. The annals of statistics, 9(6), 1218–1228.
    Friedman, L., & Wall, M. (2005). Graphical views of suppression and multicollinearity in multiple
    linear regression. The American Statistician, 59(2), 127–136.
    Grömping, U. (2007a). Estimators of relative importance in linear regression based on variance
    decomposition. The American Statistician, 61(2), 139–147.
    Grömping, U. (2007b). Relative importance for linear regression in r: the package relaimpo. Journal
    of statistical software, 17, 1–27.
    Grömping, U. (2015). Variable importance in regression models. Wiley interdisciplinary reviews:
    Computational statistics, 7(2), 137–152.
    John, F. (2008). Bootstrapping regression models. Applied Regression Analysis and Generalized
    Linear Models, Thousand Oaks (CA), Sage, 587–606.
    Johnson, J. W. (2000). A heuristic method for estimating the relative weight of predictor variables in
    multiple regression. Multivariate behavioral research, 35(1), 1–19.
    Johnson, J. W., & LeBreton, J. M. (2004). History and use of relative importance indices in organizational research. Organizational research methods, 7(3), 238–257.
    Lebreton, J. M., Ployhart, R. E., & Ladd, R. T. (2004). A monte carlo comparison of relative importance methodologies. Organizational Research Methods, 7(3), 258–282.
    Lindeman, R. H., Merenda, P. F., & Gold, R. Z. (1980). Introduction to bivariate and multivariate
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    Nathans, L. L., Oswald, F. L., & Nimon, K. (2012). Interpreting multiple linear regression: a guidebook of variable importance. Practical assessment, research & evaluation, 17(9), n9.
    Pratt, J. W. (1987). Dividing the indivisible: Using simple symmetry to partition variance explained.
    In Proceedings of the second international tampere conference in statistics, 1987 (pp. 245–260).
    Tonidandel, S., & LeBreton, J. M. (2011). Relative importance analysis: A useful supplement to
    regression analysis. Journal of Business and Psychology, 26, 1–9.
    Wei, P., Lu, Z., & Song, J. (2015). Variable importance analysis: A comprehensive review. Reliability
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    Weisberg, S. (2005). Applied linear regression (Vol. 528). John Wiley & Sons.
    Description: 碩士
    國立政治大學
    統計學系
    111354001
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0111354001
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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