Optimal Online Calibration Designs for Item Replenishment in Adaptive Testing

The maintenance of item bank is essential for continuously implementing adaptive tests. Calibration of new items online provides an opportunity to efficiently replenish items for the operational item bank. In this study, a new optimal design for online calibration (referred to as D-c) is proposed by incorporating the idea of original D-optimal design into the reformed D-optimal design proposed by van der Linden and Ren (Psychometrika 80:263-288, 2015) (denoted as D-VR design). To deal with the dependence of design criteria on the unknown item parameters of new items, Bayesian versions of the locally optimal designs (e.g., D-c and D-VR) are put forward by adding prior information to the new items. In the simulation implementation of the locally optimal designs, five calibration sample sizes were used to obtain different levels of estimation precision for the initial item parameters, and two approaches were used to obtain the prior distributions in Bayesian optimal designs. Results showed that the D-c design performed well and retired smaller number of new items than the D-VR design at almost all levels of examinee sample size; the Bayesian version of D-c using the prior obtained from the operational items worked better than that using the default priors in BILOG-MG and PARSCALE; and Bayesian optimal designs generally outperformed locally optimal designs when the initial item parameters of the new items were poorly estimated.