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On the Relationships Between Jeffreys Modal and Weighted Likelihood Estimation of Ability Under Logistic IRT Models

Published online by Cambridge University Press:  01 January 2025

David Magis  and
Gilles Raîche
David Magis*
Affiliation:
University of Liège and K.U. Leuven
Gilles Raîche
Affiliation:
Université du Québec à Montréal
*
Requests for reprints should be sent to David Magis, Department of Mathematics (B37), University of Liège, Grande Traverse 12, 4000 Liège, Belgium. E-mail: [email protected]
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Abstract

This paper focuses on two estimators of ability with logistic item response theory models: the Bayesian modal (BM) estimator and the weighted likelihood (WL) estimator. For the BM estimator, Jeffreys’ prior distribution is considered, and the corresponding estimator is referred to as the Jeffreys modal (JM) estimator. It is established that under the three-parameter logistic model, the JM estimator returns larger estimates than the WL estimator. Several implications of this result are outlined.

Keywords

logistic modelBayesian modal estimationJeffreys’ priorweighted likelihood estimation
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 1 , January 2012 , pp. 163 - 169
Copyright
Copyright © 2011 The Psychometric Society

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