Applying the M(2) Statistic to Evaluate the Fit of Diagnostic Classification Models in the Presence of Attribute Hierarchies

The performance of the limited-information statistic M(2) for diagnostic classification models (DCMs) is under-investigated in the current literature. Specifically, the investigations of M(2) for specific DCMs rather than general modeling frameworks are needed. This article aims to demonstrate the usefulness of M(2) in hierarchical diagnostic classification models (HDCMs). The performance of M(2) in evaluating the fit of HDCMs was investigated in the presence of four types of attribute hierarchies. Two simulation studies were conducted to examine Type I error rates and statistical power of M(2) under different simulation conditions, respectively. The findings suggest acceptable Type I error rates control of M(2) as well as high statistical power under the conditions of a Q-matrix misspecification and the DINA model misspecification. The data of Examination for the Certificate of Proficiency in English (ECPE) were used to empirically illustrate the suitability of M(2) in practice.