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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-Tungen_US
dc.contributor.author (Authors) 黃珮菁zh_TW
dc.contributor.author (Authors) Huang, Pei-Chingen_US
dc.creator (作者) 黃珮菁zh_TW
dc.creator (作者) Huang, Pei-Chingen_US
dc.date (日期) 2000en_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) A2002001939en_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) 87354014zh_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/#A2002001939en_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 dataen_US
dc.subject (關鍵詞) Completely and partially cross-classified dataen_US
dc.subject (關鍵詞) Single-sample methoden_US
dc.subject (關鍵詞) Multiple-sample methoden_US
dc.subject (關鍵詞) Factorization of the likelihood methoden_US
dc.subject (關鍵詞) EM algorithmen_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 Dataen_US
dc.type (資料類型) thesisen_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