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Statistical analysis of Q-matrix based diagnostic classification models

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  • Chen, Yunxiao
  • Liu, Jingchen
  • Xu, Gongjun
  • Ying, Zhiliang

Abstract

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).

Suggested Citation

  • Chen, Yunxiao & Liu, Jingchen & Xu, Gongjun & Ying, Zhiliang, 2015. "Statistical analysis of Q-matrix based diagnostic classification models," LSE Research Online Documents on Economics 103183, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:103183
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    References listed on IDEAS

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    More about this item

    Keywords

    diagnostic classification models; identifiability; latent variable selection;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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