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題名 排名穩定度分析
Stability Analysis For Ranking作者 蔡詠丞
Tsai, Yung-Cheng貢獻者 鄭宗記
Cheng, Tsung-Chi
蔡詠丞
Tsai, Yung-Cheng關鍵詞 排序法
排名穩定度
ranking method
ranking stability日期 2020 上傳時間 3-Aug-2020 17:31:48 (UTC+8) 摘要 文獻中記載著許多關於資料排序的方法，在不同的排名結果之中，該如何決定最終的排名結果。本文將對不同的排名結果進行分析，觀察各個不同排名結果之間的相似處及相異處，透過相似處對排名結果進行假設，並將各個不同的排名結果進行調整，調整成新的排名結果。本文的研究目的為提供一種方式判別排名結果的穩定度，藉由比較各個排名結果的穩定度，進行排名結果的挑選。調整後依序對各個排名結果進行分析，首先抽出資料中部份的觀測對象，抽出後對這些觀測對象進行兩兩比較，比較的方式為觀察挑出的兩觀測對象中各個變數數值之間的差異及排名的差異，並假設排名的差異大小受各變數數值差異大小影響。透過以上假設將抽出的所有觀測對象進行兩兩相減，相減的方式為將兩觀測對象的各個變數數值與排名相減，此時即可得一筆新的資料，以下將此稱為排名差分資料。由於有部分觀測對象未被抽到，本文將剩下的觀測對象與所有其自身以外的觀測對象(包含以抽出的觀測對象)進行比較，比較方式稍有不同，此時只比較各變數數值的差異，並不比較排名之間的差異，接著將所有倆倆觀測對象的各變數數值進行相減，可得一筆新的資料，以下將此稱為差分資料。再來將排名差分資料視為訓練集，分別建立決策樹與複迴歸式，其中應變數為排名差。建立後對差分資料中每一筆資料進行預測，每一筆預測的結果即為該二觀測對象預測的排名差，接著將此預測的結果套入全美大學體育協會第一級男籃錦標賽（National Collegiate Athletic Association，NCAA）所使用的排序法對所有觀測對象進行重新排名，最後比較原排名結果與新排名結果的關係，本文將此關係稱為排名穩定度。
There are many methods for ranking in the literature. Among different ranking results, how to determine the final ranking result. This article will analyze the different ranking results, observe the similarities and differences between the different ranking results,we make assumptions about the ranking results through the similarities, and adjust the ranking results to the new ranking results. The research purpose of this article is to provide a way to judge the stability of the ranking results, and select the ranking results by comparing the stability of each ranking result.After adjustment, First, extract some of the observation objects in the data, and then compare these observation objects in pairs. The comparison method is to observe the value of each variable in the two observation objects selected. We assume that the ranking difference is affected by the difference in the value of each variable. Based on the above assumptions, all the extracted observation objects are subtracted in pairs. The method of subtraction is to subtract each variable value of the two observation objects and subtract ranking of the two observation objects. At this time, a new piece of data can be obtained, which is called the ranking difference data. Since some observation objects have not been selected, this article compares the remaining observation objects with all observation objects other than itself (including the extracted observation objects). The comparison method is slightly different. At this time, only the value of each variable is compared. The difference does not compare the difference between the rankings, and then subtract the variable values of all the two observation objects to obtain a new piece of data, which is called difference data.Then regard the ranking difference data as a training set, and establish a decision tree and a multiple regression formula, where the dependent variable is ranking difference. After establishment, a prediction is made for difference data, and the result of each prediction is the predicted ranking difference of the two observation objects. The prediction result is applied to the National Collegiate Athletic Basketball Championship. Association, NCAA) used the ranking method to re-rank all observation objects, and finally compare the relationship between the original ranking result and the new ranking result. This relationship is called ranking stability in this article.參考文獻 1.Barrett, B. E. & Barron, F. H. (1996). Decision Quality Using Ranked Attribute Weights. Management Science 42(11),1515-15232. Calculating College Basketball rankings using functional programming in R,Retrieved March 10 2018, from:https://dpmartin42.github.io/posts/r/college-basketball-rankings3. Dembczyński, K., Kotłowski, W. & Słowiński, R. (2008). A General Framework for Learning an Ensemble of Decision Rules. Local Patterns to Global Models, ECML/PKDD 2008 Workshop, Antwerp, Belgium, 17–36.4. Doyle, John R., Rodney H. Green &Paul A. Bottomley (1997). Judging Relative Importance: Direct Rating and Point Allocation Are Not Equivalent. Organizational Behavior and Human Decision Processes,70 (April), 65-72.5. Dyer, J. S., Fischer, G. W. & Jia, J. (1998), Attribute Weighting Methods and Decision Quality in the Presence of Response Error: A Simulation Study. Journal of Behavioral Decision Making, 11(2),85-1056. Edwards. W. & Barron. F. H. (1994). SMARTS and SMARTER: Improved simple methods for multiattribute utility measurement. Organizational Behavior and Human Decision Processes 60, 306-325.7. Etten, J., Firth, D. J., Kosmidis, I. & Turner, H. L. (2019). Modelling rankings in R: the PlackettLuce package. Computational Statistics.8. Fürnkranz, J. & Hüllermeier, E. (2010). Preference Learning. In: Sammut C., Webb G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA529. Goodwin, P. & Roberts, R. (2002). Weight Approximations in Multi-Attribute Decision Models. Journal of Multi-Criteria Decision Analysis, 291-30310. Jaccard, J., Brinberg, D., & Ackerman, L. (1986). Assessing attribute importance: A comparison of six methods. Journal of Consumer Research, 12, 463-468.11. Leskinen P. & Kangas. J. (2005). Rank reversals in multi-criteria decision analysis with statistical modelling of ratio-scale pairwise comparisons. Journal of the Operational Research Society 56, 855-861.12. Massey K. (1997). Statistical Models Applied to the Rating of Sports Teams. Bluefield College. Master’s thesis Google Scholar13. Nardo, M., Saisana, M., Saltelli, A. & Tarantola, S. (2005). Tools for Composite Indicators Building. European Commission, report EUR 21682 EN. Joint Research Centre, Ispra, Italy14. Nardo, M., Saisana, M., Saltelli, A., Tarantola, S., Hoffmann, A. & Giovannini, E. (2008). Handbook on Constructing Composite Indicators: Methodology and User Guide. Location: OECD publishing,106-109.15. Qian, Z. & Yu, P. L.H. (2019). Weighted Distance-Based Models for Ranking Data Using the R Package Rankdist. J. Stat. Softw. 90(5):1–31.16. Timofeev, R. (2004). Classification and regression trees (cart) theory and applications. Master’s thesis, Humboldt University Berlin. 描述 碩士
國立政治大學
統計學系
107354016資料來源 http://thesis.lib.nccu.edu.tw/record/#G0107354016 資料類型 thesis dc.contributor.advisor 鄭宗記 zh_TW dc.contributor.advisor Cheng, Tsung-Chi en_US dc.contributor.author (Authors) 蔡詠丞 zh_TW dc.contributor.author (Authors) Tsai, Yung-Cheng en_US dc.creator (作者) 蔡詠丞 zh_TW dc.creator (作者) Tsai, Yung-Cheng en_US dc.date (日期) 2020 en_US dc.date.accessioned 3-Aug-2020 17:31:48 (UTC+8) - dc.date.available 3-Aug-2020 17:31:48 (UTC+8) - dc.date.issued (上傳時間) 3-Aug-2020 17:31:48 (UTC+8) - dc.identifier (Other Identifiers) G0107354016 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/130958 - 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) 107354016 zh_TW dc.description.abstract (摘要) 文獻中記載著許多關於資料排序的方法，在不同的排名結果之中，該如何決定最終的排名結果。本文將對不同的排名結果進行分析，觀察各個不同排名結果之間的相似處及相異處，透過相似處對排名結果進行假設，並將各個不同的排名結果進行調整，調整成新的排名結果。本文的研究目的為提供一種方式判別排名結果的穩定度，藉由比較各個排名結果的穩定度，進行排名結果的挑選。調整後依序對各個排名結果進行分析，首先抽出資料中部份的觀測對象，抽出後對這些觀測對象進行兩兩比較，比較的方式為觀察挑出的兩觀測對象中各個變數數值之間的差異及排名的差異，並假設排名的差異大小受各變數數值差異大小影響。透過以上假設將抽出的所有觀測對象進行兩兩相減，相減的方式為將兩觀測對象的各個變數數值與排名相減，此時即可得一筆新的資料，以下將此稱為排名差分資料。由於有部分觀測對象未被抽到，本文將剩下的觀測對象與所有其自身以外的觀測對象(包含以抽出的觀測對象)進行比較，比較方式稍有不同，此時只比較各變數數值的差異，並不比較排名之間的差異，接著將所有倆倆觀測對象的各變數數值進行相減，可得一筆新的資料，以下將此稱為差分資料。再來將排名差分資料視為訓練集，分別建立決策樹與複迴歸式，其中應變數為排名差。建立後對差分資料中每一筆資料進行預測，每一筆預測的結果即為該二觀測對象預測的排名差，接著將此預測的結果套入全美大學體育協會第一級男籃錦標賽（National Collegiate Athletic Association，NCAA）所使用的排序法對所有觀測對象進行重新排名，最後比較原排名結果與新排名結果的關係，本文將此關係稱為排名穩定度。 zh_TW dc.description.abstract (摘要) There are many methods for ranking in the literature. Among different ranking results, how to determine the final ranking result. This article will analyze the different ranking results, observe the similarities and differences between the different ranking results,we make assumptions about the ranking results through the similarities, and adjust the ranking results to the new ranking results. The research purpose of this article is to provide a way to judge the stability of the ranking results, and select the ranking results by comparing the stability of each ranking result.After adjustment, First, extract some of the observation objects in the data, and then compare these observation objects in pairs. The comparison method is to observe the value of each variable in the two observation objects selected. We assume that the ranking difference is affected by the difference in the value of each variable. Based on the above assumptions, all the extracted observation objects are subtracted in pairs. The method of subtraction is to subtract each variable value of the two observation objects and subtract ranking of the two observation objects. At this time, a new piece of data can be obtained, which is called the ranking difference data. Since some observation objects have not been selected, this article compares the remaining observation objects with all observation objects other than itself (including the extracted observation objects). The comparison method is slightly different. At this time, only the value of each variable is compared. The difference does not compare the difference between the rankings, and then subtract the variable values of all the two observation objects to obtain a new piece of data, which is called difference data.Then regard the ranking difference data as a training set, and establish a decision tree and a multiple regression formula, where the dependent variable is ranking difference. After establishment, a prediction is made for difference data, and the result of each prediction is the predicted ranking difference of the two observation objects. The prediction result is applied to the National Collegiate Athletic Basketball Championship. Association, NCAA) used the ranking method to re-rank all observation objects, and finally compare the relationship between the original ranking result and the new ranking result. This relationship is called ranking stability in this article. en_US dc.description.tableofcontents 第壹章 緒論 ……………………………………………………………………………7第一節 研究動機 ………………………………………………………………………7第二節 研究目的 ………………………………………………………………………7第貳章 文獻回顧 ………………………………………………………………………9第一節 排序法 …………………………………………………………………………9第二節 NCAA排名法 …………………………………………………………………13第三節 CART決策樹…………………………………………………………………15第四節 王道永續指標………………………………………………………………17第參章 排名穩定度 …………………………………………………………………24第一節 分段個數與級距排名…………………………………………………………24第二節 分段抽樣與重新排名…………………………………………………………26第三節 王道資料………………………………………………………………………28第肆章 模擬 …………………………………………………………………………39第一節 成績資料 ……………………………………………………………………39第二節 級距成績資料 ………………………………………………………………44第三節 王道資料排序法比較 ………………………………………………………48第伍章 結論與建議…………………………………………………………………50第一節 結論…………………………………………………………………………50第二節 研究限制與未來方向………………………………………………………50參考文獻……………………………………………………………………………51 zh_TW dc.format.extent 2344398 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0107354016 en_US dc.subject (關鍵詞) 排序法 zh_TW dc.subject (關鍵詞) 排名穩定度 zh_TW dc.subject (關鍵詞) ranking method en_US dc.subject (關鍵詞) ranking stability en_US dc.title (題名) 排名穩定度分析 zh_TW dc.title (題名) Stability Analysis For Ranking en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 1.Barrett, B. E. & Barron, F. H. (1996). Decision Quality Using Ranked Attribute Weights. Management Science 42(11),1515-15232. Calculating College Basketball rankings using functional programming in R,Retrieved March 10 2018, from:https://dpmartin42.github.io/posts/r/college-basketball-rankings3. Dembczyński, K., Kotłowski, W. & Słowiński, R. (2008). A General Framework for Learning an Ensemble of Decision Rules. Local Patterns to Global Models, ECML/PKDD 2008 Workshop, Antwerp, Belgium, 17–36.4. Doyle, John R., Rodney H. Green &Paul A. Bottomley (1997). Judging Relative Importance: Direct Rating and Point Allocation Are Not Equivalent. Organizational Behavior and Human Decision Processes,70 (April), 65-72.5. Dyer, J. S., Fischer, G. W. & Jia, J. (1998), Attribute Weighting Methods and Decision Quality in the Presence of Response Error: A Simulation Study. Journal of Behavioral Decision Making, 11(2),85-1056. Edwards. W. & Barron. F. H. (1994). SMARTS and SMARTER: Improved simple methods for multiattribute utility measurement. Organizational Behavior and Human Decision Processes 60, 306-325.7. Etten, J., Firth, D. J., Kosmidis, I. & Turner, H. L. (2019). Modelling rankings in R: the PlackettLuce package. Computational Statistics.8. Fürnkranz, J. & Hüllermeier, E. (2010). Preference Learning. In: Sammut C., Webb G.I. (eds) Encyclopedia of Machine Learning. Springer, Boston, MA529. Goodwin, P. & Roberts, R. (2002). Weight Approximations in Multi-Attribute Decision Models. Journal of Multi-Criteria Decision Analysis, 291-30310. Jaccard, J., Brinberg, D., & Ackerman, L. (1986). Assessing attribute importance: A comparison of six methods. Journal of Consumer Research, 12, 463-468.11. Leskinen P. & Kangas. J. (2005). Rank reversals in multi-criteria decision analysis with statistical modelling of ratio-scale pairwise comparisons. Journal of the Operational Research Society 56, 855-861.12. Massey K. (1997). Statistical Models Applied to the Rating of Sports Teams. Bluefield College. Master’s thesis Google Scholar13. Nardo, M., Saisana, M., Saltelli, A. & Tarantola, S. (2005). Tools for Composite Indicators Building. European Commission, report EUR 21682 EN. Joint Research Centre, Ispra, Italy14. Nardo, M., Saisana, M., Saltelli, A., Tarantola, S., Hoffmann, A. & Giovannini, E. (2008). Handbook on Constructing Composite Indicators: Methodology and User Guide. Location: OECD publishing,106-109.15. Qian, Z. & Yu, P. L.H. (2019). Weighted Distance-Based Models for Ranking Data Using the R Package Rankdist. J. Stat. Softw. 90(5):1–31.16. Timofeev, R. (2004). Classification and regression trees (cart) theory and applications. Master’s thesis, Humboldt University Berlin. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202001040 en_US
