Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design - Cai, Yan; Tu, Dongbo; Ding, Shuliang (Frontiers in Psychology, 2018)
The design of test Q matrix can directly influence the classification accuracy for a cognitive diagnostic assessment. In this paper, we focus on the Q matrix design when attribute hierarchies are known before test development. A complete Q matrix design is proposed and theorems are presented to show that it is a necessary and sufficient condition to guarantee the identifiability of ideal response pattern. The proposed Q matrix design turns out to be the key condition to guarantee the classification accuracy for a family of conjunctive diagnostic models. The proposed procedures for a complete Q matrix design with attribute hierarchies can serve as guidelines for test blueprint development before item writing in a cognitive diagnostic assessment.