An iterative two-step method for online item calibration in CD-CAT

The development and maintenance of the item bank is a critical element to a CD-CAT (cognitive diagnostic computerized adaptive testing; Cheng, 2009) system. For continuous testing, it is important to replenish the item bank with new items that have been calibrated. This requires pretesting to estimate the parameters of the new items. For CD-CAT, the structural parameters that need to be estimated include both item parameters and attribute vectors. In this paper, we propose three residual-statistic-based methods: RMA, ROEM, and RMEM, to estimate the attribute vectors and item parameters all together for new items. An iterative two-step online calibration procedure is developed to estimate the attribute vectors for the new items in the first step, and estimate the item parameters in the second step, then proceed iteratively until convergence is reached. An extensive simulation study was conducted to evaluate the performance of the three proposed methods and compare them with two existing methods, namely the Joint Estimation Algorithm (JEA; Chen & Xin, 2011) and Single Item Estimation (SIE; Chen et al., 2015) methods. In terms of the estimation of the attribute vector, the RMEM method performs the best in most of the cases. In terms of item parameter estimation, RMEM still has some advantages, and RMA outperforms JEA and SIE. Taken together, results suggest that the RMEM is superior to the other methods, especially when sample size is relatively small. A real-data example is provided to illustrate the application of RMEM in practice.