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Investigating the Impact of Uncertainty About Item Parameters on Ability Estimation

Published online by Cambridge University Press:  01 January 2025

Jinming Zhang ,
Minge Xie ,
Xiaolan Song  and
Ting Lu
Jinming Zhang*
Affiliation:
University of Illinois at Urbana-Champaign
Minge Xie
Affiliation:
Rutgers University
Xiaolan Song
Affiliation:
JP Morgan Chase
Ting Lu
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Jinming Zhang, Department of Educational Psychology, University of Illinois at Urbana-Champaign, 236A Education Building, 1310 S Sixth Street, Champaign, IL 61820, USA. E-mail: jmzhang@illinois.edu
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Abstract

Asymptotic expansions of the maximum likelihood estimator (MLE) and weighted likelihood estimator (WLE) of an examinee’s ability are derived while item parameter estimators are treated as covariates measured with error. The asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators. A numerical example is presented to illustrate how to apply the formulae to evaluate the impact of uncertainty about item parameters on ability estimation and the appropriateness of estimating ability using the regular MLE or WLE method.

Keywords

biasitem response theory (IRT)measurement errormaximum likelihood estimator (MLE)weighted likelihood estimator (WLE)
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 1 , January 2011 , pp. 97 - 118
Copyright
Copyright © 2010 The Psychometric Society

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Footnotes

The research was partially supported by Grants NSF-SES0851521, NSF-DMS0915139 and NSAH98230-08-1-0104.

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