다차원 IRT 모형 적합 혼합형 검사를 위한 공통문항 척도 연계 방법

Abstract

Under the context of the common-item nonequivalent groups design, item response theory (IRT) scale
 linking methods have been presented for each of the multidimensional extensions of the three-parameter
 logistic (M3PL), graded response (MGR), generalized partial credit (MGPC), and nominal response (MNR)
 models. The common-item multidimensional IRT (MIRT) linking methods that have been proved effective
 for single-format tests include the direct least squares (DLS), item category response function (ICRF), and
 test response function (TRF) methods. This paper extends the three MIRT linking methods to any mixture
 of the exploratory M3PL, MGR, MGPC, and MNR models for mixed-format tests. Each linking method
 extended attempts to find the linking coefficients in the rotation matrix and translation vector that
 constitute a linear transformation between two multidimensional ability scales. Simulations are conducted to
 investigate the performance of the three linking methods under various linking conditions. The results
 indicated that overall, the ICRF method performed best in estimating the rotation matrix and translation
 vector of the linear transformation between the new and true simulation scales. In not a few conditions, the
 DLS method resulted in the second best linking solutions. The TRF method tended to estimate the rotation
 matrix well but the translation vector poorly and thus showed the worst performance among the linking
 methods in some conditions.