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Extended Asymptotic Identifiability of Nonparametric Item Response Models

Published online by Cambridge University Press:  01 January 2025

Yinqiu He Open the ORCID record for Yinqiu He [Opens in a new window]
Yinqiu He*
Affiliation:
University of Wisconsin-Madison
*
Correspondence should be made to Yinqiu He, Department of Statistics, University of Wisconsin-Madison, 1200 University Ave., Madison, WI 53706, USA. Email: [email protected]
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Abstract

Nonparametric item response models provide a flexible framework in psychological and educational measurements. Douglas (Psychometrika 66(4):531–540, 2001) established asymptotic identifiability for a class of models with nonparametric response functions for long assessments. Nevertheless, the model class examined in Douglas (2001) excludes several popular parametric item response models. This limitation can hinder the applications in which nonparametric and parametric models are compared, such as evaluating model goodness-of-fit. To address this issue, We consider an extended nonparametric model class that encompasses most parametric models and establish asymptotic identifiability. The results bridge the parametric and nonparametric item response models and provide a solid theoretical foundation for the applications of nonparametric item response models for assessments with many items.

Keywords

nonparametric item response theoryidentifiabilityasymptotic theory
Type
Theory & Methods
Information
Psychometrika , Volume 89 , Issue 3 , September 2024 , pp. 958 - 973
Copyright
Copyright © 2024 The Author(s), under exclusive licence to The Psychometric Society

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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

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