Methods for online calibration of Q-matrix and item parameters for polytomous responses in cognitive diagnostic computerized adaptive testing

The ability to rapidly provide examinees with detailed and effective diagnostic information is a critical topic in psychology. Knowing what diagnostic criteria the examinees have met enables the practitioner to seek the solution to help them in a timely manner, and this can be achieved by cognitive diagnostic computerized adaptive testing (CD-CAT). However, the pervasive challenge of replenishing items in the CD-CAT item bank limits its practical application. Online calibration is a means to address item replenishment, but in CD-CAT, most existing online calibration methods that jointly calibrate the Q-matrix and item parameters of the new items are developed only for dichotomous responses and are time-consuming. Notably, previous studies pay no attention to polytomously scored items that are frequently observed in testing, even though they can offer additional evidence for the examinees' diagnosis. To fill this gap, we propose a SCAD-based method (SCAD-EM) to calibrate the Q-matrix and item parameters of the new items with polytomous response data in order to promote the application of CD-CAT in practice. The performance of the SCAD-EM was investigated in two comprehensive simulation studies and compared against the revised single-item estimation method (SIE-BIC). Results indicated that the SCAD-EM produces a higher calibration accuracy for the category-level Q-matrix and is computationally more efficient across all conditions, but it produces a lower calibration accuracy for the item-level Q-matrix. An empirical study further demonstrated the utility of the SCAD-EM and the SIE-BIC methods in calibrating new items with a real dataset. The advantages of the proposed method, its limitations, and possible future research directions are offered at the end.