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Front. Psychol. | doi: 10.3389/fpsyg.2018.01875

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

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

The performance of the limited-information statistic M2 for diagnostic classification models (DCMs) is under-investigated in the current literature. Specifically, the investigations of M2 for specific DCMs rather than general modeling frameworks are needed. This article aims to demonstrate the usefulness of M2 in hierarchical diagnostic classification models (HDCMs). The performance of M2 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 M2 under different simulation conditions, respectively. The findings suggest acceptable Type I error rates control of M2 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 M2 in practice.

Keywords: diagnostic classification models, Attribute hierarchies, absolute fit test, limited-information test statistics, goodness-of-fit

Received: 01 Aug 2017; Accepted: 13 Sep 2018.

Edited by:

Holmes Finch, Ball State University, United States

Reviewed by:

Ben Kelcey, University of Cincinnati, United States
Chanjin Zheng, Jiangxi Normal University, China
Scott Monroe, University of Massachusetts Amherst, United States  

Copyright: © 2018 Chen, Liu, Xin and Cui. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Prof. Tao Xin, Beijing Normal University, Collaborative Innovation Center of Assessment toward Basic Education Quality, Beijing, China, xintao@bnu.edu.cn