Application of Dimension Reduction to CAT Item Selection Under the Bifactor Model

Abstract

Multidimensional computerized adaptive testing (MCAT) based on the bifactor model is suitable for tests with multidimensional bifactor measurement structures. Several item selection methods that proved to be more advantageous than the maximum Fisher information method are not practical for bifactor MCAT due to time-consuming computations resulting from high dimensionality. To make them applicable in bifactor MCAT, dimension reduction is applied to four item selection methods, which are the posterior-weighted Fisher D-optimality (PDO) and three non-Fisher information-based methods—posterior expected Kullback–Leibler information (PKL), continuous entropy (CE), and mutual information (MI). They were compared with the Bayesian D-optimality (BDO) method in terms of estimation precision. When both the general and group factors are the measurement objectives, BDO, PDO, CE, and MI perform equally well and better than PKL. When the group factors represent nuisance dimensions, MI and CE perform the best in estimating the general factor, followed by the BDO, PDO, and PKL. How the bifactor pattern and test length affect estimation accuracy was also discussed.