Validating Attribute Hierarchies in Cognitive Diagnosis Models

Xueqin Zhang ¹ Yu Jiang ² Tao Xin ^1* Yanlou Liu ³

• ¹ Collaborative Innovation Center of Assessment for Basic Education Quality, Beijing Normal University, Beijing, Beijing, China
• ² Joint Logistics College, National Defense University, Beijing, China
• ³ China Academy of Education Big Data, Qufu Normal University, Qufu, Shandong Province, China

Cognitive diagnosis models (CDMs) are restricted latent class models that are widely used in educational and psychological fields. Attribute hierarchy, as an important structural feature of the CDM, can provide critical information for inferring examinees' attribute mastery patterns. Previous studies usually formulate likelihood ratio (LR) tests for full models and hierarchical models to validate attribute hierarchies, but their asymptotic distributions tend to become non-standard, resulting in test failures. This study proposes the Wald statistic to statistically test the a priori defined attribute hierarchy. Specifically, two covariance matrix estimators, empirical cross-product information matrix (XPD), and observed information matrix (Obs), are considered to compute the Wald statistic, referred to as Wald-XPD and Wald-Obs, respectively.Simulation studies with various factors were conducted to investigate the performance of the new methods. The results show that Wald-XPD has an acceptable empirical performance with high or low quality items and a higher test efficiency. Real datasets were also analyzed for illustrative purpose.