AUTHOR=Cai Yan , Tu Dongbo , Ding Shuliang TITLE=Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design JOURNAL=Frontiers in Psychology VOLUME=9 YEAR=2018 URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2018.01413 DOI=10.3389/fpsyg.2018.01413 ISSN=1664-1078 ABSTRACT=

The design of test Q matrix can directly influence the classification accuracy of a cognitive diagnostic assessment. In this paper, we focus on Q matrix design when attribute hierarchies are known prior to test development. A complete Q matrix design is proposed and theorems are presented to demonstrate that it is a necessary and sufficient condition to guarantee the identifiability of ideal response patterns. A simulation study is also conducted to detect the effects of the proposed design on a family of conjunctive diagnostic models. The results revealed that the proposed Q matrix design is the key condition for guaranteeing classification accuracy. When only one type of item pattern in R matrix is missing from the associated test Q matrix, the related attribute-wise agreement rate will decrease dramatically. When the entire R matrix is missing, both the pattern-wise and attribute-wise agreement rates will decrease sharply. This indicates that the proposed procedures for complete Q matrix design with attribute hierarchies can serve as guidelines for test blueprint development prior to item writing in a cognitive diagnostic assessment.