A Comparative Study of Online Item Calibration Methods in Multidimensional Computerized Adaptive Testing

Calibration of new items online has been an important topic in item replenishment for multidimensional computerized adaptive testing (MCAT). Several online calibration methods have been proposed for MCAT, such as multidimensional "one expectation-maximization (EM) cycle" (M-OEM) and multidimensional "multiple EM cycles" (M-MEM). However, M-MEM often fails to converge when the correlations between dimensions are relatively high. To solve the nonconvergence issue and more accurately calibrate new items, this article combines Bayes modal estimation with M-OEM and M-MEM to make full use of the prior information from the item parameters of the new items. The obtained two new Bayesian methods were compared with the existing methods under several conditions, assuming the new items were assigned to examinees via random design or optimal Bayesian adaptive design. The simulation results showed that adding prior to the new item parameters was helpful to improve the calibration precision and efficiency of M-MEM but not so much for M-OEM, and the two online calibration designs exemplified very similar calibration precision.