The Impact of Item Calibration Error on Variable-Length Cognitive Diagnostic Computerized Adaptive Testing

Robustness of Adaptive Measurement of Change to Item Parameter Estimation Error

Adaptive measurement of change (AMC) is a psychometric method for measuring intra-individual change on one or more latent traits across testing occasions. Three hypothesis tests-a Z test, likelihood ratio test, and score ratio index-have demonstrated desirable statistical properties in this context, including low false positive rates and high true positive rates. However, the extant AMC research has assumed that the item parameter values in the simulated item banks were devoid of estimation error. This assumption is unrealistic for applied testing settings, where item parameters are estimated from a calibration sample before test administration. Using Monte Carlo simulation, this study evaluated the robustness of the common AMC hypothesis tests to the presence of item parameter estimation error when measuring omnibus change across four testing occasions. Results indicated that item parameter estimation error had at most a small effect on false positive rates and latent trait change recovery, and these effects were largely explained by the computerized adaptive testing item bank information functions. Differences in AMC performance as a function of item parameter estimation error and choice of hypothesis test were generally limited to simulees with particularly low or high latent trait values, where the item bank provided relatively lower information. These simulations highlight how AMC can accurately measure intra-individual change in the presence of item parameter estimation error when paired with an informative item bank. Limitations and future directions for AMC research are discussed.

An Adaptive Design for Item Parameter Online Estimation and Q-Matrix Online Calibration in CD-CAT

The implementation of cognitive diagnostic computerized adaptive testing often depends on a high-quality item bank. How to online estimate the item parameters and calibrate the Q-matrix required by items becomes an important problem in the construction of the high-quality item bank for personalized adaptive learning. The related previous research mainly focused on the calibration method with the random design in which the new items were randomly assigned to examinees. Although the way of randomly assigning new items can ensure the randomness of data sampling, some examinees cannot provide enough information about item parameter estimation or Q-matrix calibration for the new items. In order to increase design efficiency, we investigated three adaptive designs under different practical situations: (a) because the non-parametric classification method needs calibrated item attribute vectors, but not item parameters, the first study focused on an optimal design for the calibration of the Q-matrix of the new items based on Shannon entropy; (b) if the Q-matrix of the new items was specified by subject experts, an optimal design was designed for the estimation of item parameters based on Fisher information; and (c) if the Q-matrix and item parameters are unknown for the new items, we developed a hybrid optimal design for simultaneously estimating them. The simulation results showed that, the adaptive designs are better than the random design with a limited number of examinees in terms of the correct recovery rate of attribute vectors and the precision of item parameters.

Binary Restrictive Threshold Method for Item Exposure Control in Cognitive Diagnostic Computerized Adaptive Testing

Although classification accuracy is a critical issue in cognitive diagnostic computerized adaptive testing, attention has increasingly shifted to item exposure control to ensure test security. In this study, we developed the binary restrictive threshold (BRT) method to balance measurement accuracy and item exposure. In addition, a simulation study was conducted to evaluate its performance. The results indicated that the BRT method performed better than the restrictive progressive (RP) and stratified dynamic binary searching (SDBS) approaches but worse than the restrictive threshold (RT) method in terms of classification accuracy. With respect to item exposure control, the BRT method exhibited noticeably stronger performance compared with the RT method, even though its performance was not as high as that of the RP and SDBS methods.