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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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    4. Ogasawara, Haruhiko, 2013. "Asymptotic cumulants of ability estimators using fallible item parameters," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 144-162.
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    6. 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).
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    8. 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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    10. Howard Wainer & Benjamin Wright, 1980. "Robust estimation of ability in the Rasch model," Psychometrika, Springer;The Psychometric Society, vol. 45(3), pages 373-391, 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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