Statistical Analysis of Q-Matrix Based Diagnostic Classification Models

Yunxiao Chen, Jingchen Liu, Gongjun Xu, Zhiliang Ying

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


Diagnostic classification models (DMCs) have recently gained prominence in educational assessment, psychiatric evaluation, and many other disciplines. Central to the model specification is the so-called Q-matrix that provides a qualitative specification of the item-attribute relationship. In this article, we develop theories on the identifiability for the Q-matrix under the DINA and the DINO models. We further propose an estimation procedure for the Q-matrix through the regularized maximum likelihood. The applicability of this procedure is not limited to the DINA or the DINO model and it can be applied to essentially all Q-matrix based DMCs. Simulation studies show that the proposed method admits high probability recovering the true Q-matrix. Furthermore, two case studies are presented. The first case is a dataset on fraction subtraction (educational application) and the second case is a subsample of the National Epidemiological Survey on Alcohol and Related Conditions concerning the social anxiety disorder (psychiatric application).

Original languageEnglish (US)
Pages (from-to)850-866
Number of pages17
JournalJournal of the American Statistical Association
Issue number510
StatePublished - Apr 3 2015

Bibliographical note

Publisher Copyright:
© 2015 American Statistical Association.


  • Diagnostic classification models
  • Identifiability
  • Latent variable selection


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