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Extended Asymptotic Identifiability of Nonparametric Item Response Models

Published online by Cambridge University Press:  01 January 2025

Yinqiu HeOpen 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: yinqiu.he@wisc.edu
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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

Information

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.

References

Chen, Y., Li, X., Liu, J., & Ying, Z. (2021). Item response theory—a statistical framework for educational and psychological measurement. arXiv preprint arXiv:2108.08604.Google Scholar
Douglas, J. (1997). Joint consistency of nonparametric item characteristic curve and ability estimation. Psychometrika, 62, 7–28.CrossRefGoogle Scholar
Douglas, J. A. (2001). Asymptotic identifiability of nonparametric item response models. Psychometrika, 66(4), 531–540.CrossRefGoogle Scholar
Douglas, J., Cohen, A. (2001). Nonparametric item response function estimation for assessing parametric model fit. Applied Psychological Measurement, 25(3), 234–243.CrossRefGoogle Scholar
Falk, C. F., Cai, L. (2016). Maximum marginal likelihood estimation of a monotonic polynomial generalized partial credit model with applications to multiple group analysis. Psychometrika, 81, 434–460.CrossRefGoogle ScholarPubMed
Johnson, M. S. (2007). Modeling dichotomous item responses with free-knot splines. Computational Statistics & Data Analysis, 51(9), 4178–4192.CrossRefGoogle Scholar
Lee, Y.-S., Wollack, J. A., Douglas, J. (2009). On the use of nonparametric item characteristic curve estimation techniques for checking parametric model fit. Educational and Psychological Measurement, 69(2), 181–197.CrossRefGoogle Scholar
Mikhailov, V. G. (1994). On a refinement of the central limit theorem for sums of independent random indicators. Theory of Probability & Its Applications, 38(3), 479–489.CrossRefGoogle Scholar
Peress, M. (2012). Identification of a semiparametric item response model. Psychometrika, 77, 223–243.CrossRefGoogle Scholar
Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56(4), 611–630.Google Scholar
Ramsay, J. O., Abrahamowicz, M. (1989). Binomial regression with monotone splines: A psychometric application. Journal of the American Statistical Association, 84(408), 906–915.CrossRefGoogle Scholar
Ramsay, J. O., Winsberg, S. (1991). Maximum marginal likelihood estimation for semiparametric item analysis. Psychometrika, 56(3), 365–379.CrossRefGoogle Scholar
Sijtsma, K. & Molenaar, I. W. (2002). Introduction to nonparametric item response theory. SAGE Publications, Inc.CrossRefGoogle Scholar
Sijtsma, K. (1998). Methodology review: Nonparametric IRT approaches to the analysis of dichotomous item scores. Applied Psychological Measurement, 22(1), 3–31.CrossRefGoogle Scholar
Van der Linden, W. J. (2018). Handbook of item response theory, CRC Press.Google Scholar
Winsberg, S., Thissen, D., Wainer, H. (1984). Fitting item characteristic curves with spline functions. ETS Research Report Series, 1984(2), i14.CrossRefGoogle Scholar