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Extended Asymptotic Identifiability of Nonparametric Item Response Models

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  • Yinqiu He

    (University of Wisconsin-Madison)

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.

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  • Yinqiu He, 2024. "Extended Asymptotic Identifiability of Nonparametric Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 958-973, September.
    • Handle: RePEc:spr:psycho:v:89:y:2024:i:3:d:10.1007_s11336-024-09972-7
    DOI: 10.1007/s11336-024-09972-7
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    References listed on IDEAS

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    1. J. Ramsay & S. Winsberg, 1991. "Maximum marginal likelihood estimation for semiparametric item analysis," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 365-379, September.
    2. Jeffrey Douglas, 2001. "Asymptotic identifiability of nonparametric item response models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 531-540, December.
    3. Jeff Douglas, 1997. "Joint consistency of nonparametric item characteristic curve and ability estimation," Psychometrika, Springer;The Psychometric Society, vol. 62(1), pages 7-28, March.
    4. J. Ramsay, 1991. "Kernel smoothing approaches to nonparametric item characteristic curve estimation," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 611-630, December.
    5. Michael Peress, 2012. "Identification of a Semiparametric Item Response Model," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 223-243, April.
    6. Johnson, Matthew S., 2007. "Modeling dichotomous item responses with free-knot splines," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4178-4192, May.
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