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Efficient Standard Error Formulas of Ability Estimators with Dichotomous Item Response Models

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  • David Magis

Abstract

This paper focuses on the computation of asymptotic standard errors (ASE) of ability estimators with dichotomous item response models. A general framework is considered, and ability estimators are defined from a very restricted set of assumptions and formulas. This approach encompasses most standard methods such as maximum likelihood, weighted likelihood, maximum a posteriori, and robust estimators. A general formula for the ASE is derived from the theory of M-estimation. Well-known results are found back as particular cases for the maximum and robust estimators, while new ASE proposals for the weighted likelihood and maximum a posteriori estimators are presented. These new formulas are compared to traditional ones by means of a simulation study under Rasch modeling. Copyright The Psychometric Society 2016

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  • David Magis, 2016. "Efficient Standard Error Formulas of Ability Estimators with Dichotomous Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 184-200, March.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:1:p:184-200
    DOI: 10.1007/s11336-015-9443-3
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    References listed on IDEAS

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    1. Frederic Lord, 1983. "Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability," Psychometrika, Springer;The Psychometric Society, vol. 48(2), pages 233-245, June.
    2. Ogasawara, Haruhiko, 2013. "Asymptotic properties of the Bayes and pseudo Bayes estimators of ability in item response theory," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 359-377.
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    6. Christof Schuster & Ke-Hai Yuan, 2011. "Robust Estimation of Latent Ability in Item Response Models," Journal of Educational and Behavioral Statistics, , vol. 36(6), pages 720-735, December.
    7. Ogasawara, Haruhiko, 2013. "Asymptotic cumulants of ability estimators using fallible item parameters," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 144-162.
    8. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
    9. Magis, David & Raîche, Gilles, 2012. "Random Generation of Response Patterns under Computerized Adaptive Testing with the R Package catR," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i08).
    10. Zeileis, Achim, 2006. "Object-oriented Computation of Sandwich Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(i09).
    11. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
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    Cited by:

    1. David Magis & Norman Verhelst, 2017. "On the Finiteness of the Weighted Likelihood Estimator of Ability," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 637-647, September.

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