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題名 含遺失值之列聯表最大概似估計量及模式的探討
Maximum Likelihood Estimation in Contingency Tables with Missing Data作者 黃珮菁
Huang, Pei-Ching貢獻者 江振東
Chiang, Jeng-Tung
黃珮菁
Huang, Pei-Ching關鍵詞 遺失值
完全及部分列聯表分析
單樣本方法
多樣本方法
概似方程式因式分解法
EM演算法
Missing data
Completely and partially cross-classified data
Single-sample method
Multiple-sample method
Factorization of the likelihood method
EM algorithm日期 2000 上傳時間 31-Mar-2016 14:44:42 (UTC+8) 摘要 在處理具遺失值之類別資料時，傳統的方法是將資料捨棄，但是這通常不是明智之舉，這些遺失某些分類訊息的資料通常還是可以提供其它重要的訊息，尤其當這類型資料的個數佔大多數時，將其捨棄可能使得估計的變異數增加，甚至影響最後的決策。如何將這些遺失某些訊息的資料納入考慮，作出完整的分析是最近幾十年間頗為重要的課題。本文主要整理了五種分析這類型資料的方法，分別為單樣本方法、多樣本方法、概似方程式因式分解法、EM演算法，以上四種方法可使用在資料遺失呈隨機分佈的條件成立下來進行分析。第五種則為樣本遺失不呈隨機分佈之分析方法。
Traditionally, the simple way to deal with observations for which some of the variables are missing so that they cannot cross-classified into a contingency table simply excludes them from any analysis. However, it is generally agreed that such a practice would usually affect both the accuracy and the precision of the results. The purpose of the study is to bring together some of the sound alternatives available in the literature, and provide a comprehensive review. Four methods for handling data missing at random are discussed, they are single-sample method, multiple-sample method, factorization of the likelihood method, and EM algorithm. In addition, one way of handling data missing not at random is also reviewed.參考文獻 Agresti, A. (1990). Categorical Data Analysis. New York：Wiley.Agresti, A. (1996). An Introduction to Categorical Data Analysis. New York：Wiley.Anderson, T.W. (1964). Maximum likelihood estimates for the multivariate normal distribution when some observations are missing. Journal of the American Statistical Association, 52, 200-203.Blumenthal, S. (1968). Multinomial sampling with partially categorized data. Journal of the American Statistical Association, 63, 542-551.Chen, T., and S. E. Fienberg (1974). Two-dimensional contingency tables with both completely and partially cross-classified data. Biometrics, 30, 629-642.Chen, T., and S. E. Fienberg (1976). The analysis of contingency tables with incompletely classified data. Biometrics, 32, 133-144.Choi, S.C., and D.M. Stablein (1988). Comparing incomplete paired binomial data under non-random mechanisms. Statistics in Medicine, 7, 929-939.Clogg, C. C., and E. S. Shihadeh (1994). Statistical Models for Ordinal Variables. SAGE PUBLICATION.Fuchs, C. (1982). Maximum likelihood estimation and model selection in contingency tables with missing data. Journal of the American Statistical Association, 77, 270-278.Haber, M., and G. D. Williamson (1994). Models for three-dimensional contingency tables with completely and partially cross-classified data. Biometrics, 49, 194-203.Haber, M., C. C.H. Chen, and G. D. Williamson (1991). Analysis of repeated categorical responses from fully and partially cross-classified data. Communications in statistics, 20, 3293-3313.Hocking, R.R., and H.H. Oxspring (1971). Maximum likelihood estimation with incomplete multinomial data. Journal of the American Statistical Association, 66, 65-70.Hocking, R.R., and H.H. Oxspring (1974). The analysis of partially categorized contingency data. Biometrics, 60, 469-483.Laird, N. M. (1988). Missing data in longitudinal studies. Statistics in Medicine, 7, 305-315.Lipsitz, S. R., J. G. Ibrahim, and G. M. Fitzmaurice (1999). Likelihood methods for incomplete longitudinal binary responses with incomplete categorical covariates. Biometrics, 55, 214-223.Little, R. J.A. (1982). Models for nonresponse in sample surveys. Journal of the American Statistical Association, 77, 237-250.Little, R. J.A., and D. B. Rubin (1987). Statistical Analysis with Missing Data. New York：Wiley.Nordheim, E. V. (1984). Inference from nonrandomly missing categorical data: an example from a genetic study on Turner’s syndrome. Journal of the American Statistical Association, 79, 772-780.Rubin, D. B. (1976). Inference and missing data. Biometrics, 63, 581-592. 描述 碩士
國立政治大學
統計學系
87354014資料來源 http://thesis.lib.nccu.edu.tw/record/#A2002001939 資料類型 thesis dc.contributor.advisor 江振東 zh_TW dc.contributor.advisor Chiang, Jeng-Tung en_US dc.contributor.author (Authors) 黃珮菁 zh_TW dc.contributor.author (Authors) Huang, Pei-Ching en_US dc.creator (作者) 黃珮菁 zh_TW dc.creator (作者) Huang, Pei-Ching en_US dc.date (日期) 2000 en_US dc.date.accessioned 31-Mar-2016 14:44:42 (UTC+8) - dc.date.available 31-Mar-2016 14:44:42 (UTC+8) - dc.date.issued (上傳時間) 31-Mar-2016 14:44:42 (UTC+8) - dc.identifier (Other Identifiers) A2002001939 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/83245 - 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) 87354014 zh_TW dc.description.abstract (摘要) 在處理具遺失值之類別資料時，傳統的方法是將資料捨棄，但是這通常不是明智之舉，這些遺失某些分類訊息的資料通常還是可以提供其它重要的訊息，尤其當這類型資料的個數佔大多數時，將其捨棄可能使得估計的變異數增加，甚至影響最後的決策。如何將這些遺失某些訊息的資料納入考慮，作出完整的分析是最近幾十年間頗為重要的課題。本文主要整理了五種分析這類型資料的方法，分別為單樣本方法、多樣本方法、概似方程式因式分解法、EM演算法，以上四種方法可使用在資料遺失呈隨機分佈的條件成立下來進行分析。第五種則為樣本遺失不呈隨機分佈之分析方法。 zh_TW dc.description.abstract (摘要) Traditionally, the simple way to deal with observations for which some of the variables are missing so that they cannot cross-classified into a contingency table simply excludes them from any analysis. However, it is generally agreed that such a practice would usually affect both the accuracy and the precision of the results. The purpose of the study is to bring together some of the sound alternatives available in the literature, and provide a comprehensive review. Four methods for handling data missing at random are discussed, they are single-sample method, multiple-sample method, factorization of the likelihood method, and EM algorithm. In addition, one way of handling data missing not at random is also reviewed. en_US dc.description.tableofcontents 封面頁證明書目錄表目錄圖目錄致謝詞論文摘要第一章 緒論1.1 研究動機與目的1.2 資料架構第二章 單樣本方法2.1 二維度完全列聯表和部分列聯表分析2.1.1 符號介紹2.1.2 樣本來自卜瓦松分配之最大概似估計值2.1.3 參數之估計2.1.4 參數之估計2.1.5 樣本來自多項分配之最大概似估計值2.1.6 實例2.2 三維度之完全列聯表和部分列聯表分析2.2.1 符號介紹2.2.2 樣本來自多項分配下之最大概似估計值2.2.3 參數之估計2.2.4 參數之估計2.3 適合度檢定第三章 多樣本方法3.1 二維度之完全列聯表和部分列聯表分析3.2 三維度之完全列聯表和部分列聯表分析3.3 與單樣本方法之比較3.4 實例第四章 概似方程式因式分解法4.1 巢狀型態資料4.2 概似方程式因式分解法4.2.1 符號介紹4.2.2 最大概似估計量4.3 應用與限制4.4 實例第五章 EM演算法5.1 EM演算法5.1.1 符號介紹5.1.2 最大概似估計量5.2 應用與限制5.3 範例一分析結果比較第六章 樣本遺失不呈隨機分佈之分析方法6.1 引言6.2 最大概似估計量第七章 結論文獻參考 zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#A2002001939 en_US dc.subject (關鍵詞) 遺失值 zh_TW dc.subject (關鍵詞) 完全及部分列聯表分析 zh_TW dc.subject (關鍵詞) 單樣本方法 zh_TW dc.subject (關鍵詞) 多樣本方法 zh_TW dc.subject (關鍵詞) 概似方程式因式分解法 zh_TW dc.subject (關鍵詞) EM演算法 zh_TW dc.subject (關鍵詞) Missing data en_US dc.subject (關鍵詞) Completely and partially cross-classified data en_US dc.subject (關鍵詞) Single-sample method en_US dc.subject (關鍵詞) Multiple-sample method en_US dc.subject (關鍵詞) Factorization of the likelihood method en_US dc.subject (關鍵詞) EM algorithm en_US dc.title (題名) 含遺失值之列聯表最大概似估計量及模式的探討 zh_TW dc.title (題名) Maximum Likelihood Estimation in Contingency Tables with Missing Data en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Agresti, A. (1990). Categorical Data Analysis. New York：Wiley.Agresti, A. (1996). An Introduction to Categorical Data Analysis. New York：Wiley.Anderson, T.W. (1964). Maximum likelihood estimates for the multivariate normal distribution when some observations are missing. Journal of the American Statistical Association, 52, 200-203.Blumenthal, S. (1968). Multinomial sampling with partially categorized data. Journal of the American Statistical Association, 63, 542-551.Chen, T., and S. E. Fienberg (1974). Two-dimensional contingency tables with both completely and partially cross-classified data. Biometrics, 30, 629-642.Chen, T., and S. E. Fienberg (1976). The analysis of contingency tables with incompletely classified data. Biometrics, 32, 133-144.Choi, S.C., and D.M. Stablein (1988). Comparing incomplete paired binomial data under non-random mechanisms. Statistics in Medicine, 7, 929-939.Clogg, C. C., and E. S. Shihadeh (1994). Statistical Models for Ordinal Variables. SAGE PUBLICATION.Fuchs, C. (1982). Maximum likelihood estimation and model selection in contingency tables with missing data. Journal of the American Statistical Association, 77, 270-278.Haber, M., and G. D. Williamson (1994). Models for three-dimensional contingency tables with completely and partially cross-classified data. Biometrics, 49, 194-203.Haber, M., C. C.H. Chen, and G. D. Williamson (1991). Analysis of repeated categorical responses from fully and partially cross-classified data. Communications in statistics, 20, 3293-3313.Hocking, R.R., and H.H. Oxspring (1971). Maximum likelihood estimation with incomplete multinomial data. Journal of the American Statistical Association, 66, 65-70.Hocking, R.R., and H.H. Oxspring (1974). The analysis of partially categorized contingency data. Biometrics, 60, 469-483.Laird, N. M. (1988). Missing data in longitudinal studies. Statistics in Medicine, 7, 305-315.Lipsitz, S. R., J. G. Ibrahim, and G. M. Fitzmaurice (1999). Likelihood methods for incomplete longitudinal binary responses with incomplete categorical covariates. Biometrics, 55, 214-223.Little, R. J.A. (1982). Models for nonresponse in sample surveys. Journal of the American Statistical Association, 77, 237-250.Little, R. J.A., and D. B. Rubin (1987). Statistical Analysis with Missing Data. New York：Wiley.Nordheim, E. V. (1984). Inference from nonrandomly missing categorical data: an example from a genetic study on Turner’s syndrome. Journal of the American Statistical Association, 79, 772-780.Rubin, D. B. (1976). Inference and missing data. Biometrics, 63, 581-592. zh_TW
