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On the Finiteness of the Weighted Likelihood Estimator of Ability

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  • David Magis

    (University of Liège)

  • Norman Verhelst

    (Eurometrics)

Abstract

The purpose of this note is to focus on the finiteness of the weighted likelihood estimator (WLE) of ability in the context of dichotomous and polytomous item response theory (IRT) models. It is established that the WLE always returns finite ability estimates. This general result is valid for dichotomous (one-, two-, three- and four-parameter logistic) IRT models, the class of polytomous difference models and divide-by-total models, independently of the number of items, the item parameters and the response patterns. Further implications of this result are outlined.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:3:d:10.1007_s11336-016-9518-9
    DOI: 10.1007/s11336-016-9518-9
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    References listed on IDEAS

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    7. 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.
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