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Title: Equating multidimensional IRT parameters when both common items and common persons are available Authors:  Yoshinori Oki - Tokyo Institute of Technology (Japan) [presenting]
Shin-ichi Mayekawa - Tokyo Institute of Technology (Japan)
Abstract: Item Response Theory (IRT) is a set of stochastic models for psychological and educational tests. IRT is based on the idea that the probability of a correct response to an item is represented by a mathematical function of item and person parameters. In the application of IRT, calibrating the parameters of two or more tests is a critical issue, because it allows for comparisons between test scores, and common item design or common person design is often used for the equating. Multidimensional IRT (MIRT) is a sub-model of IRT; in MIRT it is assumed that more than two abilities have effects on the probability of a correct answer. MIRT has indeterminacy between item and person parameters same as factor analysis, and one can use equating methods for rotation of parameter matrixes. There is a case that both common item and common person design are available in MIRT. However, few studies have been conducted corresponding to the case. We propose the integration of common item and common person criteria, and utilize a rotation method in factor analysis focusing on both factor scores and factor loadings as a method for equating in MIRT.