모수 복원 상황에서 MIRT 척도연계 방법의 기능 진단

초록

In multidimensional item response theory (MIRT), scale linking methods, developed under the anchor-item or common-examinee design, attempt to estimate the rotation matrix and location vector of the linking function that connects two multidimensional ability scales (i.e., coordinate systems). In MIRT applications, the need for scale linking typically occurs when the recovery of parameters is being investigated and the parameters that are expressed on an arbitrary “0-I” scale should be placed onto the true simulation scale. Assuming such a parameter-recovery situation, the present study investigated the characteristics and performances of the three “common-item” based MIRT linking methods, Direct, TCF, and LLM. A critical study factor was the population two-dimensional ability distribution, whose means, variances and covariance were varied so that the characteristics and performances of the three methods might be clearly revealed. The major results were as follows. First, all three methods performed “non-symmetric” scale linking. Second, in the recovery of item parameters and ability distributions on the simulation scale, the Direct and TCF methods performed well because they estimated “oblique” rotation matrices. On the other hand, the LLM method recovered poorly the parameters except when the population covariance was zero, because it estimated “pseudo-orthogonal” rotation matrices. Third, it was observed for all the linking methods that the dimension-matching between two multidimensional scales was determined entirely by mathematics and thus the order of dimensions in the ability scale prior to scale linking could be changed after scale linking.

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