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

Yuqi Gu () and Gongjun Xu ()
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Yuqi Gu: University of Michigan
Gongjun Xu: University of Michigan

Psychometrika, 2019, vol. 84, issue 2, No 7, 468-483

Abstract: 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 models; identifiability; estimability; Q-matrix (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (16)

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DOI: 10.1007/s11336-018-9619-8

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