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題名 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作者 吳宏煇
Wu, Hong-Huei貢獻者 鄭宗記
Cheng, Tsung-Chi
吳宏煇
Wu, Hong-Huei關鍵詞 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
馬可夫鏈排序日期 2024 上傳時間 5-八月-2024 13:58:54 (UTC+8) 摘要 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。 參考文獻 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 analysis (Vol. 4). Scott, Foresman Glenview, IL. 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 Engineering & System Safety, 142, 399–432. Weisberg, S. (2005). Applied linear regression (Vol. 528). John Wiley & Sons. 描述 碩士
國立政治大學
統計學系
111354001資料來源 http://thesis.lib.nccu.edu.tw/record/#G0111354001 資料類型 thesis dc.contributor.advisor 鄭宗記 zh_TW dc.contributor.advisor Cheng, Tsung-Chi en_US dc.contributor.author (作者) 吳宏煇 zh_TW dc.contributor.author (作者) Wu, Hong-Huei en_US dc.creator (作者) 吳宏煇 zh_TW dc.creator (作者) Wu, Hong-Huei en_US dc.date (日期) 2024 en_US dc.date.accessioned 5-八月-2024 13:58:54 (UTC+8) - dc.date.available 5-八月-2024 13:58:54 (UTC+8) - dc.date.issued (上傳時間) 5-八月-2024 13:58:54 (UTC+8) - dc.identifier (其他 識別碼) G0111354001 en_US dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/152773 - 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) 111354001 zh_TW dc.description.abstract (摘要) 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。 zh_TW dc.description.tableofcontents 第一章 緒論 1 第二章 文獻回顧 3 第三章 研究方法 26 第四章 模擬資料分析 48 第五章 兩變數情況下的母體理論值 60 第六章 結論與建議 65 參考文獻 66 zh_TW dc.format.extent 4020952 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0111354001 en_US dc.subject (關鍵詞) 多元線性迴歸 zh_TW dc.subject (關鍵詞) 相對重要性 zh_TW dc.subject (關鍵詞) LMG 指標 zh_TW dc.subject (關鍵詞) 比例邊際變異分解指標 zh_TW dc.subject (關鍵詞) Epsilon 指標 zh_TW dc.subject (關鍵詞) 優勢分析 zh_TW dc.subject (關鍵詞) 偏F 檢定 zh_TW dc.subject (關鍵詞) 熱圖 zh_TW dc.subject (關鍵詞) 拔靴法 zh_TW dc.subject (關鍵詞) 馬可夫鏈排序 zh_TW dc.title (題名) 比較與衡量線性迴歸模型中解釋變數的相對重要性指標 zh_TW dc.title (題名) Compare and evaluate the relative importance metrics for explanatory variables in the linear regression model en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 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 analysis (Vol. 4). Scott, Foresman Glenview, IL. 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 Engineering & System Safety, 142, 399–432. Weisberg, S. (2005). Applied linear regression (Vol. 528). John Wiley & Sons. zh_TW
