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Identifiability of Diagnostic Classification Models

Published online by Cambridge University Press:  01 January 2025

Gongjun Xu  and
Stephanie Zhang
Gongjun Xu*
Affiliation:
University of Minnesota
Stephanie Zhang
Affiliation:
Google Inc.
*
Correspondence should be made to Gongjun Xu, School of Statistics, University of Minnesota, 313 Ford Hall, 224 Church St SE, Minneapolis, MN 55455 USA. Email: [email protected]
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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.

Keywords

diagnostic classification modelsthe DINA modelmodel identifiabilityQ-matrix
Type
Original Paper
Information
Psychometrika , Volume 81 , Issue 3 , September 2016 , pp. 625 - 649
Copyright
Copyright © 2015 The Psychometric Society

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