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1 results

  • The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model

  • Yuqi Gu, Gongjun Xu
  • Journal:
    Psychometrika / Volume 84 / Issue 2 / June 2019
    Published online by Cambridge University Press:
    01 January 2025, pp. 468-483

  • Cognitive diagnosis models (CDMs) are useful statistical tools in cognitive diagnosis assessment. However, as many other latent variable models, the CDMs often suffer from the non-identifiability issue. This work gives the sufficient and necessary condition for identifiability of the basic DINA model, which not only addresses the open problem in Xu and Zhang (Psychometrika 81:625–649, 2016) on the minimal requirement for identifiability, but also sheds light on the study of more general CDMs, which often cover DINA as a submodel. Moreover, we show the identifiability condition ensures the consistent estimation of the model parameters. From a practical perspective, the identifiability condition only depends on the Q-matrix structure and is easy to verify, which would provide a guideline for designing statistically valid and estimable cognitive diagnosis tests.