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

  • Theory & Methods
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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.

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Acknowledgements

This work is partially supported by NSF grants SES-1846747 and SES-2150601. We are grateful to the editor, an associate editor, and anonymous referees for their helpful comments and suggestions.

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  1. Department of Statistics, University of Michigan, 456 West Hall, 1085 South University, Ann Arbor, 48109, MI, USA

    Mengqi Lin & Gongjun Xu

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  1. Mengqi Lin
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  2. Gongjun Xu
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Correspondence to Gongjun Xu.

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Lin, M., Xu, G. Sufficient and Necessary Conditions for the Identifiability of DINA Models with Polytomous Responses. Psychometrika (2024). https://doi.org/10.1007/s11336-024-09961-w

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