Identifiability of Diagnostic Classification Models

Gongjun Xu, Stephanie Zhang

Research output: Contribution to journalArticlepeer-review

80 Scopus citations


Diagnostic classification models (DCMs) are important statistical tools in cognitive diagnosis. In this paper, we consider the issue of their identifiability. In particular, we focus on one basic and popular model, the DINA model. We propose sufficient and necessary conditions under which the model parameters are identifiable from the data. The consequences, in terms of the consistency of parameter estimates, of fulfilling or failing to fulfill these conditions are illustrated via simulation. The results can be easily extended to the DINO model through the duality of the DINA and DINO models. Moreover, the proposed theoretical framework could be applied to study the identifiability issue of other DCMs.

Original languageEnglish (US)
Pages (from-to)625-649
Number of pages25
Issue number3
StatePublished - Sep 1 2016


  • Q-matrix
  • diagnostic classification models
  • model identifiability
  • the DINA model


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