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

Published online by Cambridge University Press:  01 January 2025

Yuqi Gu  and
Gongjun Xu
Yuqi Gu
Affiliation:
University of Michigan
Gongjun Xu*
Affiliation:
University of Michigan
*
Correspondence should be made to Gongjun Xu, Department of Statistics, University of Michigan, 456 West Hall, 1085 South University, Ann Arbor, MI 48109, USA. Email: gongjun@umich.edu
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Abstract

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.

Keywords

cognitive diagnosis modelsidentifiabilityestimabilityQ-matrix
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 2 , June 2019 , pp. 468 - 483
Copyright
Copyright © 2018 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (https://doi.org/10.1007/s11336-018-9619-8) contains supplementary material, which is available to authorized users.

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