AUTHOR=Chen Fu , Liu Yanlou , Xin Tao , Cui Ying 

TITLE=Applying the M2 Statistic to Evaluate the Fit of Diagnostic Classification Models in the Presence of Attribute Hierarchies

JOURNAL=Frontiers in Psychology

VOLUME=9

YEAR=2018

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2018.01875

DOI=10.3389/fpsyg.2018.01875

ISSN=1664-1078

ABSTRACT=<p>The performance of the limited-information statistic <italic>M</italic><sub><italic>2</italic></sub> for diagnostic classification models (DCMs) is under-investigated in the current literature. Specifically, the investigations of <italic>M</italic><sub><italic>2</italic></sub> for specific DCMs rather than general modeling frameworks are needed. This article aims to demonstrate the usefulness of <italic>M</italic><sub><italic>2</italic></sub> in hierarchical diagnostic classification models (HDCMs). The performance of <italic>M</italic><sub><italic>2</italic></sub> 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 <italic>M</italic><sub><italic>2</italic></sub> under different simulation conditions, respectively. The findings suggest acceptable Type I error rates control of <italic>M</italic><sub><italic>2</italic></sub> 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 <italic>M</italic><sub><italic>2</italic></sub> in practice.</p>