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

Published online by Cambridge University Press:  01 January 2025

David Magis
David Magis*
Affiliation:
University of Liège and Ku Leuven
*
Correspondence should be made to David Magis, Department of Education (B32), University of Liège, Boulevard du Rectorat 5, 4000 Liège, Belgium. Email: david.magis@ulg.ac.be
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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.

Keywords

item response theoryability estimationasymptotic standard errormaximum likelihoodweighted likelihoodBayesian estimationRobust estimation
Type
Original paper
Information
Psychometrika , Volume 81 , Issue 1 , March 2016 , pp. 184 - 200
Copyright
Copyright © 2015 The Psychometric Society

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