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Psychometrika

, Volume 76, Issue 1, pp 97–118 | Cite as

Investigating the Impact of Uncertainty About Item Parameters on Ability Estimation

  • Jinming ZhangEmail author
  • Minge Xie
  • Xiaolan Song
  • Ting Lu
Article

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

bias item response theory (IRT) measurement error maximum likelihood estimator (MLE) weighted likelihood estimator (WLE) 

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Copyright information

© The Psychometric Society 2010

Authors and Affiliations

  • Jinming Zhang
    • 1
    Email author
  • Minge Xie
    • 2
  • Xiaolan Song
    • 3
  • Ting Lu
    • 1
  1. 1.Department of Educational PsychologyUniversity of Illinois at Urbana-ChampaignChampaignUSA
  2. 2.Rutgers UniversityPiscatawayUSA
  3. 3.JP Morgan ChaseNew YorkUSA

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