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

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