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題名 兩組資料集間之相關性研究
The study about correlations between two data sets
作者 紀穎澤
Che, Kee Ying
貢獻者 鄭宗記
紀穎澤
Kee Ying Che
關鍵詞 Mantel 檢定
距離共變異數檢定
RV係數
PROTEST
典型相關係數分析
歐氏離氏
馬氏距離
曼哈頓距離
明氏距離
Mantel test
distance covariance test
RV coefficient
PROTEST
canonical correlation coefficient analysis
Euclidean distance
Mahalanobis distance
Manhattan distance
Minkowski distance
日期 2024
上傳時間 5-Aug-2024 13:58:42 (UTC+8)
摘要 評估兩組資料集相關性是需要去探討的。其中去觀察兩組資料集相關性的統計方法除了Mantel 檢定，距離共變異數檢定，PROTEST，RV係數，典型相關係數分析等方法，去比較這幾種方法下在不同的資料形態下的好。Mantel檢定與距離共變異數檢定都是通過距離去觀察資料集的相關性，本論文除了使用歐式距離外，也有使用馬氏距離，曼哈頓距離以及明氏距離，並去比較不同距離方法對檢定結果有何影響。我們通過電腦模擬一般多元常態分配以及多變量t分配資料，針對每個模型分配去變更資料變數的變異數，資料的樣本數，資料的維度等，並根據檢定力(power)與檢定力圖來比較每個檢定的結果，最後利用實證資料觀察各檢定的檢定結果。
Across various statistical studies, assessing the correlation between two sets of data is an issue that needs to be discussed in most topics. There are countless statistical methods for observing correlations between two sets of data. The methods used include Mantel test, distance covariance test, PROTEST, RV coefficient, canonical correlation coefficient analysis, then we compare the performance and pros & cons of different data forms under these methods. The Mantel test and the distance covariance test both use distance to observe the correlation of data sets. In addition to using Euclidean distance, this article also uses Mahalanobis distance, Manhattan distance and Minkowski distance to compare the test results of different distance methods. What impact does it have. Then we use computer simulations to simulate general multivariate normal distribution and multivariate t-distribution data, changing the variation of data variables of each model distribution, the number of data samples, the dimensions of the data, etc., and based on the test power and test power diagram to compare the results of each test.
參考文獻 Abdi, H. (2011). Congruence: Congruence coefficient, RV-coefficient, and Mantel coefficient. pp. 1-15. Arslan, O. (2004). Family of multivariate generalized t distributions. Journal of Multivariate Analysis, 89(2), pp. 329-337. Canty, A.J., & Ripley, B.D. (2022). Bootstrap Functions. R package version 1.3-28.1., pp.1-117. Davison, A.C., & Kuonen, D. (2002). An introduction to the bootstrap with applications in R. Statistical Computing and Graphics Newsletter, 13(1), pp. 6-11. Diniz-FilhoI, J.A.F., Soares, T.N., & Lima, J.S. (2013). Mantel test in population genetics. Genetics and molecular biology, 36(4), pp. 475-485. Dutilleul, P., Stockwell, J.D., Frigon, D., & Legendre, P. ( 2000). The Mantel test versus Pearson's correlation analysis: Assessment of the differences for biological and environmental studies, pp. 131-150. Escoufier, Y. (1973). Le traitement des variables vectorielles. Biometrics, 29, pp. 751-760. Flury, B.K., & Riedwyl, H. (1986). Standard distance in univariate and multivariate analysis. The American Statistician. pp. 249-251. Ghorbani, H.R. (2019). Mahalanobis distance and its application for detecting multivariate outliers. Facta Universitatis Series Mathematics and Informatics, 34(3), pp. 583-595. González, I., Déjean, S., Martin, P. G. P., & Baccini, A. (2008). CCA: An R package to extend canonical correlation analysis. Journal of Statistical Software, 23(12), pp. 1-14. Hotelling, H. (1935). Demand functions with limited budgets. Journal of Educational Psychology, 26, pp. 139-142. Husson, F., Josse J. (2007). FactoMineR: Multivariate Analysis with the FactoMineR package Jackson, D.A. (1995). PROTEST: a PROcrustean randomization TEST of community environment concordance. Ecoscience, 2(3), pp. 297-303. Kibria, B.M.G., & Joarder A.H. (2006). A short review of multivariate t-distribution. Journal of Statistical research, 40(1), pp. 59-72. Leduc, G. (1992). A framework based on implementation relations for implementing LOTOS specifications. Legendre, P. (2000). Comparison of permutation methods for the partial correlation and partial Mantel tests, Journal of statistical computation and simulation, pp. 37-73. Legendre, P. & Fortin, M.J. (2010). Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data. Molecular ecology resources, 10(5), pp. 831-844. Mahalanobis, P.C. (1936). A note on the statistical and biometric writings of Karl Pearson. The Indian Journal of Statistics, 2(4), pp. 411-422. Mantel N. (1967). The detection of disease clustering and a generalized regression approach. Cancer research, 27(2), pp. 209-220. Peres-Neto, P.R. & Jackson, D.A., (2001). How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test. Oecologia, 129(2), pp. 169-178. Robert ,P., & Escoufier , Y. (1976). A Unifying Tool for Linear Multivariate Statistical Methods: The RV-Coefficient. Journal of the Royal Statistical Society Series C: Applied Statistics, 25(3), pp. 257-265. Silva, A., Dias, C.T., Cecon, P., & Rego, E. (2015). An alternative procedure for performing a power analysis of Mantel’s test. Journal of Applied Statistics, 42(9), pp. 1984-1992. Sto ̈ckl, S., & Hanke, M. (2014). Financial Applications of the Mahalanobis Distance. Applied Economics and Finance, 1(2), pp. 78-84. Székely, G.J., Rizzo, M.L. & Bakirov, N.K. (2007). Measuring and testing dependence by correlation of distances. The annals of statistics, 35, pp. 2769-2794.
描述 碩士
國立政治大學
統計學系
110354031
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110354031
資料類型 thesis
dc.contributor.advisor 鄭宗記zh_TW
dc.contributor.author (Authors) 紀穎澤zh_TW
dc.contributor.author (Authors) Kee Ying Cheen_US
dc.creator (作者) 紀穎澤zh_TW
dc.creator (作者) Che, Kee Yingen_US
dc.date (日期) 2024en_US
dc.date.accessioned 5-Aug-2024 13:58:42 (UTC+8)-
dc.date.available 5-Aug-2024 13:58:42 (UTC+8)-
dc.date.issued (上傳時間) 5-Aug-2024 13:58:42 (UTC+8)-
dc.identifier (Other Identifiers) G0110354031en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/152772-
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) 110354031zh_TW
dc.description.abstract (摘要) 評估兩組資料集相關性是需要去探討的。其中去觀察兩組資料集相關性的統計方法除了Mantel 檢定，距離共變異數檢定，PROTEST，RV係數，典型相關係數分析等方法，去比較這幾種方法下在不同的資料形態下的好。Mantel檢定與距離共變異數檢定都是通過距離去觀察資料集的相關性，本論文除了使用歐式距離外，也有使用馬氏距離，曼哈頓距離以及明氏距離，並去比較不同距離方法對檢定結果有何影響。我們通過電腦模擬一般多元常態分配以及多變量t分配資料，針對每個模型分配去變更資料變數的變異數，資料的樣本數，資料的維度等，並根據檢定力(power)與檢定力圖來比較每個檢定的結果，最後利用實證資料觀察各檢定的檢定結果。zh_TW
dc.description.abstract (摘要) Across various statistical studies, assessing the correlation between two sets of data is an issue that needs to be discussed in most topics. There are countless statistical methods for observing correlations between two sets of data. The methods used include Mantel test, distance covariance test, PROTEST, RV coefficient, canonical correlation coefficient analysis, then we compare the performance and pros & cons of different data forms under these methods. The Mantel test and the distance covariance test both use distance to observe the correlation of data sets. In addition to using Euclidean distance, this article also uses Mahalanobis distance, Manhattan distance and Minkowski distance to compare the test results of different distance methods. What impact does it have. Then we use computer simulations to simulate general multivariate normal distribution and multivariate t-distribution data, changing the variation of data variables of each model distribution, the number of data samples, the dimensions of the data, etc., and based on the test power and test power diagram to compare the results of each test.en_US
dc.description.tableofcontents 第一章 緒論 1 第一節 研究目的與動機 1 第二節 研究架構 2 第二章 研究方法 3 第一節 距離矩陣 3 第二節 歐氏距離(Euclidean distance) 3 第三節 馬氏距離(Mahalanobis distance) 4 第四節 曼哈頓距離(Manhanttan distance) 4 第五節 明氏距離(Minkowski distance) 4 第六節 Mantel檢定 5 第七節 距離共變異數檢定 6 第八節 普魯克隨機化檢定(PROTEST) 6 第九節 典型相關分析(CCA) 7 第十節 RV係數(Raoult-Verdet coefficient) 8 第三章 模擬分析 10 第一節 模擬設計 10 3.1.1多元常態分配 10 3.1.2多元T分配 14 第二節 模擬結果 16 3.2.1 多元常態分配 16 3.2.2多元T分配 81 第四章 實證資料分析 132 第一節 自身生活形態與現實社會基層壓力 132 第五章 結論 137 參考文獻 141zh_TW
dc.format.extent 13623243 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110354031en_US
dc.subject (關鍵詞) Mantel 檢定zh_TW
dc.subject (關鍵詞) 距離共變異數檢定zh_TW
dc.subject (關鍵詞) RV係數zh_TW
dc.subject (關鍵詞) PROTESTzh_TW
dc.subject (關鍵詞) 典型相關係數分析zh_TW
dc.subject (關鍵詞) 歐氏離氏zh_TW
dc.subject (關鍵詞) 馬氏距離zh_TW
dc.subject (關鍵詞) 曼哈頓距離zh_TW
dc.subject (關鍵詞) 明氏距離zh_TW
dc.subject (關鍵詞) Mantel testen_US
dc.subject (關鍵詞) distance covariance testen_US
dc.subject (關鍵詞) RV coefficienten_US
dc.subject (關鍵詞) PROTESTen_US
dc.subject (關鍵詞) canonical correlation coefficient analysisen_US
dc.subject (關鍵詞) Euclidean distanceen_US
dc.subject (關鍵詞) Mahalanobis distanceen_US
dc.subject (關鍵詞) Manhattan distanceen_US
dc.subject (關鍵詞) Minkowski distanceen_US
dc.title (題名) 兩組資料集間之相關性研究zh_TW
dc.title (題名) The study about correlations between two data setsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Abdi, H. (2011). Congruence: Congruence coefficient, RV-coefficient, and Mantel coefficient. pp. 1-15. Arslan, O. (2004). Family of multivariate generalized t distributions. Journal of Multivariate Analysis, 89(2), pp. 329-337. Canty, A.J., & Ripley, B.D. (2022). Bootstrap Functions. R package version 1.3-28.1., pp.1-117. Davison, A.C., & Kuonen, D. (2002). An introduction to the bootstrap with applications in R. Statistical Computing and Graphics Newsletter, 13(1), pp. 6-11. Diniz-FilhoI, J.A.F., Soares, T.N., & Lima, J.S. (2013). Mantel test in population genetics. Genetics and molecular biology, 36(4), pp. 475-485. Dutilleul, P., Stockwell, J.D., Frigon, D., & Legendre, P. ( 2000). The Mantel test versus Pearson's correlation analysis: Assessment of the differences for biological and environmental studies, pp. 131-150. Escoufier, Y. (1973). Le traitement des variables vectorielles. Biometrics, 29, pp. 751-760. Flury, B.K., & Riedwyl, H. (1986). Standard distance in univariate and multivariate analysis. The American Statistician. pp. 249-251. Ghorbani, H.R. (2019). Mahalanobis distance and its application for detecting multivariate outliers. Facta Universitatis Series Mathematics and Informatics, 34(3), pp. 583-595. González, I., Déjean, S., Martin, P. G. P., & Baccini, A. (2008). CCA: An R package to extend canonical correlation analysis. Journal of Statistical Software, 23(12), pp. 1-14. Hotelling, H. (1935). Demand functions with limited budgets. Journal of Educational Psychology, 26, pp. 139-142. Husson, F., Josse J. (2007). FactoMineR: Multivariate Analysis with the FactoMineR package Jackson, D.A. (1995). PROTEST: a PROcrustean randomization TEST of community environment concordance. Ecoscience, 2(3), pp. 297-303. Kibria, B.M.G., & Joarder A.H. (2006). A short review of multivariate t-distribution. Journal of Statistical research, 40(1), pp. 59-72. Leduc, G. (1992). A framework based on implementation relations for implementing LOTOS specifications. Legendre, P. (2000). Comparison of permutation methods for the partial correlation and partial Mantel tests, Journal of statistical computation and simulation, pp. 37-73. Legendre, P. & Fortin, M.J. (2010). Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data. Molecular ecology resources, 10(5), pp. 831-844. Mahalanobis, P.C. (1936). A note on the statistical and biometric writings of Karl Pearson. The Indian Journal of Statistics, 2(4), pp. 411-422. Mantel N. (1967). The detection of disease clustering and a generalized regression approach. Cancer research, 27(2), pp. 209-220. Peres-Neto, P.R. & Jackson, D.A., (2001). How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test. Oecologia, 129(2), pp. 169-178. Robert ,P., & Escoufier , Y. (1976). A Unifying Tool for Linear Multivariate Statistical Methods: The RV-Coefficient. Journal of the Royal Statistical Society Series C: Applied Statistics, 25(3), pp. 257-265. Silva, A., Dias, C.T., Cecon, P., & Rego, E. (2015). An alternative procedure for performing a power analysis of Mantel’s test. Journal of Applied Statistics, 42(9), pp. 1984-1992. Sto ̈ckl, S., & Hanke, M. (2014). Financial Applications of the Mahalanobis Distance. Applied Economics and Finance, 1(2), pp. 78-84. Székely, G.J., Rizzo, M.L. & Bakirov, N.K. (2007). Measuring and testing dependence by correlation of distances. The annals of statistics, 35, pp. 2769-2794.zh_TW