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Sufficient and Necessary Conditions for the Identifiability of DINA Models with Polytomous Responses

Published online by Cambridge University Press:  27 December 2024

Mengqi Lin  and
Gongjun Xu Open the ORCID record for Gongjun Xu [Opens in a new window]
Mengqi Lin
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 48109, MI, USA. Email: [email protected]
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Abstract

Cognitive diagnosis models (CDMs) provide a powerful statistical and psychometric tool for researchers and practitioners to learn fine-grained diagnostic information about respondents’ latent attributes. There has been a growing interest in the use of CDMs for polytomous response data, as more and more items with multiple response options become widely used. Similar to many latent variable models, the identifiability of CDMs is critical for accurate parameter estimation and valid statistical inference. However, the existing identifiability results are primarily focused on binary response models and have not adequately addressed the identifiability of CDMs with polytomous responses. This paper addresses this gap by presenting sufficient and necessary conditions for the identifiability of the widely used DINA model with polytomous responses, with the aim to provide a comprehensive understanding of the identifiability of CDMs with polytomous responses and to inform future research in this field.

Keywords

identifiabilitypolytomous responsesQ-matrixcognitive diagnosis modelsDINA model
Type
Theory & Methods
Information
Psychometrika , Volume 89 , Issue 2 , June 2024 , pp. 717 - 740
Copyright
Copyright © 2024 The Author(s), under exclusive licence to The Psychometric Society

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s11336-024-09961-w.

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