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

Mengqi Lin and Gongjun Xu ()
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Mengqi Lin: University of Michigan
Gongjun Xu: University of Michigan

Psychometrika, 2024, vol. 89, issue 2, No 14, 717-740

Abstract: 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: identifiability; polytomous responses; $${\textbf{Q}}$$ Q -matrix; cognitive diagnosis models; DINA model (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11336-024-09961-w

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