The Optimal Design of Bifactor Multidimensional Computerized Adaptive Testing with Mixed-format Items

Abstract

Multidimensional computerized adaptive testing (MCAT) using mixed-format items holds great potential for the next-generation assessments. Two critical factors in the mixed-format test design (i.e., the order and proportion of polytomous items) and item selection were addressed in the context of mixed-format bifactor MCAT. For item selection, this article presents the derivation of the Fisher information matrix of the bifactor graded response model and the application of the bifactor dimension reduction method to simplify the computation of the mutual information (MI) item selection method. In a simulation study, different MCAT designs were compared with varying proportions of polytomous items (0.2–0.6, 1), different item-delivering formats (DPmix: delivering polytomous items at the final stage; RPmix: random delivering), three bifactor patterns (low, middle, and high), and two item selection methods (Bayesian D-optimality and MI). Simulation results suggested that a) the overall estimation precision increased with a higher bifactor pattern; b) the two item selection methods did not show substantial differences in estimation precision; and c) the RPmix format always led to more precise interim and final estimates than the DPmix format. The proportions of 0.3 and 0.4 were recommended for the RPmix and DPmix formats, respectively.