Article2015

Identifiability of Diagnostic Classification Models

116 citations0/0 files storedPsychometrika

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Intelligent Tutoring Systems and Adaptive Learning

Abstract

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.

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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 2010Diagnostic measurement: Theory, methods, and applications.2008DINA Model and Parameter Estimation: A Didactic 2006Measurement of psychological disorders using cognitive diagnosis models.2004Higher-Order Latent Trait Models for Cognitive Diagnosis

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2017Identifiability of restricted latent class models with binary responses 2017Cognitive diagnosis modelling incorporating item response times 2017Bayesian Estimation of the DINA Q matrix 2018The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model 2020Partial identifiability of restricted latent class models

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