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題名 具遺漏值之連續與順序變數混合資料的馬氏距離估計
Estimating of Mahalanobis distances for mixed continuous and ordinal data with missing values
作者 黃品勝
貢獻者 鄭宗記
黃品勝
關鍵詞 馬氏距離
遺漏值
混合資料
多重插補
Mahalanobis distances
missing value
mixed data
multiple imputation
日期 2016
上傳時間 20-Jul-2016 16:52:21 (UTC+8)
摘要 Bedrick, Lapodus和Powell(2000)提出利用常態潛在變數模型(normal latent variable model)，估計連續與順序變數混合型資料(mixed data)馬氏距離(Mahalanobis Distance)的方法，在本論文中沿用相同方法來估計具遺漏值混合型資料馬氏距離，利用一般位置模型(general location model)進行多重插補(multiple imputation)的方法，藉由模擬資料與實例分析，來評估此方法用於處理估計具遺漏值混合型資料馬氏距離。
Bedrick, Lapodus, and Powell(2000) apply the normal latent variable model to estimate the Mahalanobis distances for mixed continuous and ordinal data. In this thesis, we extend the similar idea by applying general location model and multiple imputation to estimate the Mahalanobis distances for mixed countinuous and ordinal data with missing value. Simulation and real data are used to evaluate the proposed method.
參考文獻 Bar-Hen, A. and Daudin, J. J. (1995). Generalization of the Mahalanobis Distance in
      The Mixed Case. Journal of Multivariate Analysis, 53, 332-342
     
     Bedrick, E. J., Lapidus, J. and Powell, J. F. (2000). Estimating the Mahalanobis Dista-
      Nce from Mixed Continuous and Discrete Data. Biometric 56, 394-401.
     
     Byar, D. P., Green S. B. (1980). The choice of treatment for patients based on covari-
      ate information: application to prostate cancer. Bull du Cancer 67,477-490
     
     Dempster, A. P., Laird, M., Rubin, D. B. (1977). Maximum likelihood from incompl-
      Ete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B 39, 1-38
     
     De Maesschalck, R., Jouan-Rimbaud, D. and Massart, D. L. (2000). The Mahalanobis
      Distance, Chemometrics and Intelligent Laboratory Systems 50, 1-18
     
     Hunt L. and Jorgensen M. (1999). Mixture model clustering using the multimix progr-
      am. Australia and New Zealand Journal of Statistics 41,153-171
     
     Schafer J. L. (1977). Analysis of Incomplete Multivariate Data, CHAPMAN and HA-
      LL
     
     Kullback, S. (1959). Information Theory and Statistical. New-York: Dover.
     
     Krzanowski, W. J. (1983). Distance between population using mixed continuous and
      categorical variable. Biometrika 70, 235-243
     
     Kenne Pagiui, E. C. and Canale, A. (2014). Pairwise likelihood inference for multiva-
      Riate categorical responses. Technical Report, Department of Statistics, Univers-
      ity of Padua
     
     Little, R. J. A. and Rubin, D. B. (1989). The analysis of social science data with miss-
      ing values. Sociological Methods and Research, 18, pp. 292-326
     
     Many, B. F. J. (1994). Multivariate Statistical Method: A Prime, 2nd edition. New Yo-
      rk : Chapman amd Hall.
     
     Mahalanobis, P. C.(1936). On the generalized distance in statistics, Proceedings of
      the National Institute of Science India, 2, 49–55.
     
     McParland,D.and Gormley,I.C. (2014). Model base clustering for mixed data:cluster-
      MD.Technical,University College Dublin.
     
     Olkin, I. and Tate, R. F. (1961). Multivariate correlation models with mixed discrete
      and continuous variables. Annals of Mathematical Statistics 32,448-465
     
     Poon, W. Y. and Lee, S. Y. (1987). Maximum likelihood estimation of multivariate
      polychoric correlation coefficients. Psychometrika 52, 409-430.
     
     Rao, C. R (1973). Linear Statistic Inference and Its Applications, 2nd edition. New
      York :Wiley.
     
     Rubin, D. B. (1976). Inference and missing data. Biometrika 63, 581-592
     
     Rubin, D. B. (1987). Multiple Imputations for Nonresponse in Surveys. Wiley, New
      York
     
     Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance Components. New
      York: Wiley.
     
     Scafer,J.L(1999). Multiple imputation: a primer. Statiscal methods in medical resear-
      ch, 8(1), 3-15
描述 碩士
國立政治大學
統計學系
103354017
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0103354017
資料類型 thesis
dc.contributor.advisor 鄭宗記zh_TW
dc.contributor.author (Authors) 黃品勝zh_TW
dc.creator (作者) 黃品勝zh_TW
dc.date (日期) 2016en_US
dc.date.accessioned 20-Jul-2016 16:52:21 (UTC+8)-
dc.date.available 20-Jul-2016 16:52:21 (UTC+8)-
dc.date.issued (上傳時間) 20-Jul-2016 16:52:21 (UTC+8)-
dc.identifier (Other Identifiers) G0103354017en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/99311-
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) 103354017zh_TW
dc.description.abstract (摘要) Bedrick, Lapodus和Powell(2000)提出利用常態潛在變數模型(normal latent variable model)，估計連續與順序變數混合型資料(mixed data)馬氏距離(Mahalanobis Distance)的方法，在本論文中沿用相同方法來估計具遺漏值混合型資料馬氏距離，利用一般位置模型(general location model)進行多重插補(multiple imputation)的方法，藉由模擬資料與實例分析，來評估此方法用於處理估計具遺漏值混合型資料馬氏距離。zh_TW
dc.description.abstract (摘要) Bedrick, Lapodus, and Powell(2000) apply the normal latent variable model to estimate the Mahalanobis distances for mixed continuous and ordinal data. In this thesis, we extend the similar idea by applying general location model and multiple imputation to estimate the Mahalanobis distances for mixed countinuous and ordinal data with missing value. Simulation and real data are used to evaluate the proposed method.en_US
dc.description.tableofcontents 第一章 緒論1
     1.1研究背景與動機………………………………………………………1
     1.2研究目的………………………………………………………………2
     1.3論文架構………………………………………………………………3
     第二章 一般位置模型與多重插補4
     2.1一般位置模型(general location model)與最大概似估量……………4
     2.2 EM演算法……………………………………………………………5
      2.2.1預測機率函數…………………………………………………6
      2.2.2一般位置模型下EM演算法…………………………………8
     2.3多重插補(multiple imputation)…………………………………………9
      2.3.1多重插補統計推論……………………………………………9
     第三章 估計混合型資料馬氏距離11
     3.1混合型資料馬氏距(Mahalanobis distances)………………………11
     3.2估計混合型資料馬氏距離……………………………………………13
     3.3馬氏距離估計量統計推論……………………………………………15
     第四章 估計具遺漏值混合型資料馬氏距離與模擬分析17
     4.1具遺漏值時一般位置模型下多重插補的馬氏距離估計……………17
     4.2模擬分析………………………………………………………………22
     第五章 實例分析………………………………………………………………….29
     第六章 結論與後續研究………………………………………………………….36
     參考文獻…………………………………………………………………………37		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0103354017en_US
dc.subject (關鍵詞) 馬氏距離zh_TW
dc.subject (關鍵詞) 遺漏值zh_TW
dc.subject (關鍵詞) 混合資料zh_TW
dc.subject (關鍵詞) 多重插補zh_TW
dc.subject (關鍵詞) Mahalanobis distancesen_US
dc.subject (關鍵詞) missing valueen_US
dc.subject (關鍵詞) mixed dataen_US
dc.subject (關鍵詞) multiple imputationen_US
dc.title (題名) 具遺漏值之連續與順序變數混合資料的馬氏距離估計zh_TW
dc.title (題名) Estimating of Mahalanobis distances for mixed continuous and ordinal data with missing valuesen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Bar-Hen, A. and Daudin, J. J. (1995). Generalization of the Mahalanobis Distance in
      The Mixed Case. Journal of Multivariate Analysis, 53, 332-342
     
     Bedrick, E. J., Lapidus, J. and Powell, J. F. (2000). Estimating the Mahalanobis Dista-
      Nce from Mixed Continuous and Discrete Data. Biometric 56, 394-401.
     
     Byar, D. P., Green S. B. (1980). The choice of treatment for patients based on covari-
      ate information: application to prostate cancer. Bull du Cancer 67,477-490
     
     Dempster, A. P., Laird, M., Rubin, D. B. (1977). Maximum likelihood from incompl-
      Ete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B 39, 1-38
     
     De Maesschalck, R., Jouan-Rimbaud, D. and Massart, D. L. (2000). The Mahalanobis
      Distance, Chemometrics and Intelligent Laboratory Systems 50, 1-18
     
     Hunt L. and Jorgensen M. (1999). Mixture model clustering using the multimix progr-
      am. Australia and New Zealand Journal of Statistics 41,153-171
     
     Schafer J. L. (1977). Analysis of Incomplete Multivariate Data, CHAPMAN and HA-
      LL
     
     Kullback, S. (1959). Information Theory and Statistical. New-York: Dover.
     
     Krzanowski, W. J. (1983). Distance between population using mixed continuous and
      categorical variable. Biometrika 70, 235-243
     
     Kenne Pagiui, E. C. and Canale, A. (2014). Pairwise likelihood inference for multiva-
      Riate categorical responses. Technical Report, Department of Statistics, Univers-
      ity of Padua
     
     Little, R. J. A. and Rubin, D. B. (1989). The analysis of social science data with miss-
      ing values. Sociological Methods and Research, 18, pp. 292-326
     
     Many, B. F. J. (1994). Multivariate Statistical Method: A Prime, 2nd edition. New Yo-
      rk : Chapman amd Hall.
     
     Mahalanobis, P. C.(1936). On the generalized distance in statistics, Proceedings of
      the National Institute of Science India, 2, 49–55.
     
     McParland,D.and Gormley,I.C. (2014). Model base clustering for mixed data:cluster-
      MD.Technical,University College Dublin.
     
     Olkin, I. and Tate, R. F. (1961). Multivariate correlation models with mixed discrete
      and continuous variables. Annals of Mathematical Statistics 32,448-465
     
     Poon, W. Y. and Lee, S. Y. (1987). Maximum likelihood estimation of multivariate
      polychoric correlation coefficients. Psychometrika 52, 409-430.
     
     Rao, C. R (1973). Linear Statistic Inference and Its Applications, 2nd edition. New
      York :Wiley.
     
     Rubin, D. B. (1976). Inference and missing data. Biometrika 63, 581-592
     
     Rubin, D. B. (1987). Multiple Imputations for Nonresponse in Surveys. Wiley, New
      York
     
     Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance Components. New
      York: Wiley.
     
     Scafer,J.L(1999). Multiple imputation: a primer. Statiscal methods in medical resear-
      ch, 8(1), 3-15		zh_TW