Making up the Complete Matrix from the Incomplete Matrix Using the EM-type IRT and Its Application

作村 建紀、徳永 正和、廣瀬 英雄
Takenori Sakumura, Masakazu Tokunaga, Hideo Hirose


情報処理学会論文誌, 数理モデル化と応用 Vol.7 , No.2 , pp.17-26 (2014.11)

IPSJ (TOM), (TOM) 7(2), 17-26, 2014-11-27



The item response theory (IRT) gives us the valuable information about the difficulties of problems as well as the abilities of students. Although, the IRT covers the complete matrix, the EM-type IRT can be applied to also the incomplete matrix. This method predicts the values of the vacant elements using the observed values in the incomplete matrix. The matrix decomposition method is another choice to make up a complete matrix from the incomplete matrix. When the characteristics of users dominate in the matrix, the EM-type IRT has a possibility to work more effective than does the matrix decomposition method. In this paper, we compare the prediction results between the EM-type IRT and the matrix decomposition method using the real case of the incomplete matrix. In addition, we show the results of the convergence for the EM-type IRT.

Key Words
item response theory, incomplete matrix, EM-type IRT, adaptive test, matrix decomposition method, calibration



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