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

Fu Chen; Yanlou Liu; Tao Xin; Ying Cui

doi:10.3389/fpsyg.2018.01875

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

Front Psychol. 2018 Oct 9:9:1875. doi: 10.3389/fpsyg.2018.01875. eCollection 2018.

Authors

Fu Chen¹, Yanlou Liu², Tao Xin³, Ying Cui⁴

Affiliations

¹ Faculty of Psychology, Beijing Normal University, Beijing, China.
² China Academy of Big Data for Education, Qufu Normal University, Shandong, China.
³ Collaborative Innovation Center of Assessment toward Basic Education Quality, Beijing Normal University, Beijing, China.
⁴ Department of Educational Psychology, University of Alberta, Edmonton, AB, Canada.

Abstract

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.

Keywords: absolute fit test; attribute hierarchies; diagnostic classification models; goodness-of-fit; limited-information test statistics.