IRT vs. Factor Analysis Approaches in Analyzing Multigroup Multidimensional Binary Data: The Effect of Structural Orthogonality, and the Equivalence in Test Structure, Item Difficulty, & Examinee Groups

Abstract

The purpose of this study was to investigate the performance of different approaches in analyzing multigroup multidimensional binary data under different conditions. Two multidimensional Item Response Theory (MIRT) methods (concurrent MIRT calibration and separate MIRT calibration with linking) and one factor analysis method (concurrent factor analysis calibration) were examined. The performance of the unidimensional IRT method compared to its multidimensional counterparts was also investigated.

The study was based on simulated data. Common-item nonequivalent groups design was employed with the manipulation of four factors: the structural orthogonality, the equivalence of test structure, the equivalence of item difficulty, and the equivalence of examinee groups. The performance of the methods was evaluated based on the recovery of the item parameters and the estimation of the true score of the examinees.

The results indicated that, in general, the concurrent factor analysis method performed as well as, sometimes even better than, the two MIRT methods in recovering the item parameters. However, in estimating the true score of examinees,

the concurrent MIRT method usually performed better than the concurrent factor analysis method. The results also indicated that the unidimensional IRT method was quite robust to the violation of unidimensionality assumption.