This article recognized uncertainty about some elements in the Q-matrix and proposed using a Bayesian extension of the deterministic input noisy (DINA) model to help recover the true Q-matrix. The study simulated eight conditions by manipulating the number of uncertain elements, the number of incorrectly specified elements, and a skill being completely uncertain for all items. Results showed that the Bayesian approach yielded correct recovery of elements when the matrix with uncertainty was accurately specified. However, when some elements of the Q-matrix were incorrectly specified, recovery was still good for uncertain elements, but not for the other elements. Also, it was poor when data have a higher order structure.
Due to my limited knowledge about CDM, I have problems in the determination of the precision of a Q-matrix. It seems that expert judgment determines the initial Q-matrix, introducing uncertain elements in the Q-matrix, which should be recognized and explored using statistical methods. However, how could we know the true elements in real data? In addition, the approach to validating (exploring might be more accurate) uncertain elements of a Q-matrix seems to be more like in an exploratory manner, not a confirmatory way. Therefore, empirical research needs other evidence to support the findings yielded by an approach.