Online Item Calibration for Q-matrix in CD-CAT

Item replenishment is important to maintaining a large scale item bank. In this paper we consider calibrating new items based on pre-calibrated operational items under the DINA model, the specification of which includes the so-called Q-matrix, as well as the slipping and guessing parameters. Making use of the maximum likelihood and Bayesian estimators for the latent knowledge states, we propose two methods for the calibration. These methods are applicable to both traditional paper-pencil based tests, for which the selection of operational items is prefixed, and computerized adaptive tests, for which the selection of operational items is sequential and random. Extensive simulations are done to assess and to compare the performance of these approaches. Extensions to other diagnostic classification models are also discussed.