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

Yuqi Gu · Gongjun Xu

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Educational Technology and Assessment

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.

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References

1974Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models 2001Cognitive Assessment Models with Few Assumptions, and Connections with Nonparametric Item Response Theory 1983RULE SPACE: AN APPROACH FOR DEALING WITH MISCONCEPTIONS BASED ON ITEM RESPONSE THEORY 2011The Generalized DINA Model Framework 2006Measurement of psychological disorders using cognitive diagnosis models.2008Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables 2007A general diagnostic model applied to language testing data 2005A GENERAL DIAGNOSTIC MODEL APPLIED TO LANGUAGE TESTING DATA

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