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題名 具潛在因素之二元變數資料遺失值插補方法之研究
A Study on Missing Data Imputation Methods for Binary Variables with Underlying Latent Factors作者 丁家麒
Ting, Chia-Chi貢獻者 張育瑋
Chang, Yu-Wei
丁家麒
Ting, Chia-Chi關鍵詞 二元變數
分類與迴歸樹
試題反應理論模型
插補遺失值
binary variable
Classification And Regression Tree
Item Response Theory model
missing data imputation日期 2023 上傳時間 2-Aug-2023 13:03:22 (UTC+8) 摘要 二元變數是一種常見的資料型態，而試題反應理論 (Item Response Theory) 模型是一種常見用來描述可觀測的二元變數之潛在相關的模型，常用來分析測驗中受試者的答題狀況的數據或是問卷調查的數據。這類數據也會出現遺失值的現象，其常見的遺失值插補(imputation) 方法有 IN 法、PM 法、IM 法、TW 法、RF 法及 EM 法共 6 種方法。本研究進一步在Chen (2022) 以分類與迴歸樹 (Classification And Regression Tree; CART) 插補遺失值的研究基礎上，應用其中 5 種分類與迴歸樹插補遺失值的方法至試題反應理論模型下的二元變數遺失值之插補，並且控制不同的模型、不同的遺失機制 (Rubin, 1976) 等設定，以模擬研究比較上述 11 種方法的插補效果。最後將這些方法應用在性自我概念問卷 (Multidimensional Sexual Self-Concept Questionnaire; MSSCQ) 與立方體比較測試 (Cube Comparsion Test; CCT)兩筆實際資料，展現各種插補方法的差異。
Binary variable is a common data type. In the current study, we consider the type of correlation, underlying observed binary variables, that could be generated by latent factors in Item Response Theory (IRT) models, which are commonly used for data from tests or for data from questionnaires. Missing data are also issues for this type of data. In the literature, there are six popular imputation methods for binary variables with missing data: Treat missing responses as incorrect, Person Mean Imputation, Item Mean Imputation, Two-Way Imputation, Response Function Imputation, Expectation-Maximum Imputation. In the current study, we further apply the imputation methods in Chen (2022), imputation based on Classification And Regression Trees (CART) methods, to missing data imputation for binary data. We conduct simulation studies to compare the aforementioned imputation methods for missing binary data under missing mechanisms in (Rubin, 1976) and different data. Finally, these methods are applied to real data from the Multidimensional Sexual Self-Concept Questionnaire (MSSCQ) and Cube Comparsion Test (CCT) to illustrate the differences in imputation methods for binary missing data參考文獻 Ache, M. (2020). Kaggle Database.Multidimensional Sexual Self-Concept Questionnaire.https : / / www . kaggle . com / datasets / mathurinache / multidimensional - sexual - selfconcept-questionnaireBeaulac, C., & Rosenthal, J. S. (2020). Best: A decision tree algorithm that handles missing values.Computational Statistics, 35, 1001–1026.Bernaards, C. A., & Sijtsma, K. (2000). Influence of imputation and em methods on factor analysis when item nonresponse in questionnaire data is nonignorable. Multivariate Behavioral Research, 35, 321–364.Breiman, L., Friedman, J., Olshen, R., & Stone, C. (1984). Classification and regression trees. monterey, ca: Wadsworth & brooks.Chen, J.-Y. (2022). Missing Data Imputation with Classification and Regression Trees: A Simulation Study. (Unpublished master dissertation). National Cheng-Chi University, Taiwan, R.O.C.Dai, S., Wang, X., & Svetina, D. (2017). Testdataimputation: Missing item responses imputation for test and assessment data (r package version 2.3).Dempster, A. (1977). Maximum likelihood estimation from incomplete data via the em algorithm. Journal of the Royal Statistical Society, 39, 1–38.Finch, H. (2008). Estimation of item response theory parameters in the presence of missing data. Journal of Educational Measurement, 45, 225–245.Gareth, J., Daniela, W., Trevor, H., & Robert, T. (2013). An introduction to statistical learning: With applications in r. Spinger.Honaker, J., & King, G. (2010). What to do about missing values in time-series crosssection data. American journal of political science, 54, 561–581.Huisman, M. (2000). Imputation of missing item responses: Some simple techniques. Quality and Quantity, 34, 331–351.Janssen, A. B., & Geiser, C. (2010). On the relationship between solution strategies in two mental rotation tasks. Learning and Individual Differences, 20, 473–478.Kim, H., & Loh, W.-Y. (2001). Classification trees with unbiased multiway splits. Journal of the American Statistical Association, 96, 589–604.Loh, W.-Y., & Shih, Y.-S. (1997). Split selection methods for classification trees. Statistica sinica, 815–840.Mislevy, R. J., & Wu, P.-K. (1996). Missing responses and irt ability estimation: Omits, choice, time limits, and adaptive testing. ETS Research Report Series, 1996, i–36.Quinlan, J. R. (1993). C4. 5: Programming for machine learning. Morgan Kauffmann, 38, 49.Rahman, M. G., & Islam, M. Z. (2013). Missing value imputation using decision trees and decision forests by splitting and merging records: Two novel techniques.KnowledgeBased Systems, 53, 51–65.Rasch, G. (1961). On general laws and the meaning of measurement. Psychology, Proceedings of the Fourth Berkley Symposium on Mathematical Statistics and Probability; University of California Press: Oakland, CA, USA, 5, 321–333.Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581–592.Sijtsma, K., & van der Ark, L. A. (2003). Investigation and treatment of missing itemscores in test and questionnaire data. Multivariate Behavioral Research, 38, 505– 528.Tibshirani, R. J., & Efron, B. (1993). An introduction to the bootstrap. 描述 碩士
國立政治大學
統計學系
110354006資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110354006 資料類型 thesis dc.contributor.advisor 張育瑋 zh_TW dc.contributor.advisor Chang, Yu-Wei en_US dc.contributor.author (Authors) 丁家麒 zh_TW dc.contributor.author (Authors) Ting, Chia-Chi en_US dc.creator (作者) 丁家麒 zh_TW dc.creator (作者) Ting, Chia-Chi en_US dc.date (日期) 2023 en_US dc.date.accessioned 2-Aug-2023 13:03:22 (UTC+8) - dc.date.available 2-Aug-2023 13:03:22 (UTC+8) - dc.date.issued (上傳時間) 2-Aug-2023 13:03:22 (UTC+8) - dc.identifier (Other Identifiers) G0110354006 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/146303 - 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) 110354006 zh_TW dc.description.abstract (摘要) 二元變數是一種常見的資料型態，而試題反應理論 (Item Response Theory) 模型是一種常見用來描述可觀測的二元變數之潛在相關的模型，常用來分析測驗中受試者的答題狀況的數據或是問卷調查的數據。這類數據也會出現遺失值的現象，其常見的遺失值插補(imputation) 方法有 IN 法、PM 法、IM 法、TW 法、RF 法及 EM 法共 6 種方法。本研究進一步在Chen (2022) 以分類與迴歸樹 (Classification And Regression Tree; CART) 插補遺失值的研究基礎上，應用其中 5 種分類與迴歸樹插補遺失值的方法至試題反應理論模型下的二元變數遺失值之插補，並且控制不同的模型、不同的遺失機制 (Rubin, 1976) 等設定，以模擬研究比較上述 11 種方法的插補效果。最後將這些方法應用在性自我概念問卷 (Multidimensional Sexual Self-Concept Questionnaire; MSSCQ) 與立方體比較測試 (Cube Comparsion Test; CCT)兩筆實際資料，展現各種插補方法的差異。 zh_TW dc.description.abstract (摘要) Binary variable is a common data type. In the current study, we consider the type of correlation, underlying observed binary variables, that could be generated by latent factors in Item Response Theory (IRT) models, which are commonly used for data from tests or for data from questionnaires. Missing data are also issues for this type of data. In the literature, there are six popular imputation methods for binary variables with missing data: Treat missing responses as incorrect, Person Mean Imputation, Item Mean Imputation, Two-Way Imputation, Response Function Imputation, Expectation-Maximum Imputation. In the current study, we further apply the imputation methods in Chen (2022), imputation based on Classification And Regression Trees (CART) methods, to missing data imputation for binary data. We conduct simulation studies to compare the aforementioned imputation methods for missing binary data under missing mechanisms in (Rubin, 1976) and different data. Finally, these methods are applied to real data from the Multidimensional Sexual Self-Concept Questionnaire (MSSCQ) and Cube Comparsion Test (CCT) to illustrate the differences in imputation methods for binary missing data en_US dc.description.tableofcontents 第 一 章 緒 論 1第 二 章 背 景 知 識 32.1 遺 失 機 制 的 介 紹 32.2 模 型 介 紹 4第 三 章 填 補 遺 失 值 的 方 法 63.1 IN 法 63.2 PM 法 63.3 IM 法 73.4 TW 法 73.5 RF 法 73.6 EM 法 93.7 使 用 分 類 與 迴 歸 樹 進 行 插 補 10第 四 章 模 擬 研 究 184.1 模 擬 設 定 184.2 MNAR 254.3 MAR 36第 五 章 實 證 分 析 465.1 性 自 我 概 念 問 卷 之 資 料 分 析 465.2 立 方 體 比 較 測 驗 之 資 料 分 析 58第 六 章 結 論 與 建 議 61參 考 文 獻 63 zh_TW dc.format.extent 2153964 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110354006 en_US dc.subject (關鍵詞) 二元變數 zh_TW dc.subject (關鍵詞) 分類與迴歸樹 zh_TW dc.subject (關鍵詞) 試題反應理論模型 zh_TW dc.subject (關鍵詞) 插補遺失值 zh_TW dc.subject (關鍵詞) binary variable en_US dc.subject (關鍵詞) Classification And Regression Tree en_US dc.subject (關鍵詞) Item Response Theory model en_US dc.subject (關鍵詞) missing data imputation en_US dc.title (題名) 具潛在因素之二元變數資料遺失值插補方法之研究 zh_TW dc.title (題名) A Study on Missing Data Imputation Methods for Binary Variables with Underlying Latent Factors en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Ache, M. (2020). Kaggle Database.Multidimensional Sexual Self-Concept Questionnaire.https : / / www . kaggle . com / datasets / mathurinache / multidimensional - sexual - selfconcept-questionnaireBeaulac, C., & Rosenthal, J. S. (2020). Best: A decision tree algorithm that handles missing values.Computational Statistics, 35, 1001–1026.Bernaards, C. A., & Sijtsma, K. (2000). Influence of imputation and em methods on factor analysis when item nonresponse in questionnaire data is nonignorable. Multivariate Behavioral Research, 35, 321–364.Breiman, L., Friedman, J., Olshen, R., & Stone, C. (1984). Classification and regression trees. monterey, ca: Wadsworth & brooks.Chen, J.-Y. (2022). Missing Data Imputation with Classification and Regression Trees: A Simulation Study. (Unpublished master dissertation). National Cheng-Chi University, Taiwan, R.O.C.Dai, S., Wang, X., & Svetina, D. (2017). Testdataimputation: Missing item responses imputation for test and assessment data (r package version 2.3).Dempster, A. (1977). Maximum likelihood estimation from incomplete data via the em algorithm. Journal of the Royal Statistical Society, 39, 1–38.Finch, H. (2008). Estimation of item response theory parameters in the presence of missing data. Journal of Educational Measurement, 45, 225–245.Gareth, J., Daniela, W., Trevor, H., & Robert, T. (2013). An introduction to statistical learning: With applications in r. Spinger.Honaker, J., & King, G. (2010). What to do about missing values in time-series crosssection data. American journal of political science, 54, 561–581.Huisman, M. (2000). Imputation of missing item responses: Some simple techniques. Quality and Quantity, 34, 331–351.Janssen, A. B., & Geiser, C. (2010). On the relationship between solution strategies in two mental rotation tasks. Learning and Individual Differences, 20, 473–478.Kim, H., & Loh, W.-Y. (2001). Classification trees with unbiased multiway splits. Journal of the American Statistical Association, 96, 589–604.Loh, W.-Y., & Shih, Y.-S. (1997). Split selection methods for classification trees. Statistica sinica, 815–840.Mislevy, R. J., & Wu, P.-K. (1996). Missing responses and irt ability estimation: Omits, choice, time limits, and adaptive testing. ETS Research Report Series, 1996, i–36.Quinlan, J. R. (1993). C4. 5: Programming for machine learning. Morgan Kauffmann, 38, 49.Rahman, M. G., & Islam, M. Z. (2013). Missing value imputation using decision trees and decision forests by splitting and merging records: Two novel techniques.KnowledgeBased Systems, 53, 51–65.Rasch, G. (1961). On general laws and the meaning of measurement. Psychology, Proceedings of the Fourth Berkley Symposium on Mathematical Statistics and Probability; University of California Press: Oakland, CA, USA, 5, 321–333.Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581–592.Sijtsma, K., & van der Ark, L. A. (2003). Investigation and treatment of missing itemscores in test and questionnaire data. Multivariate Behavioral Research, 38, 505– 528.Tibshirani, R. J., & Efron, B. (1993). An introduction to the bootstrap. zh_TW
