Investigating the Impact of Uncertainty About Item Parameters on Ability Estimation

Jinming Zhang, Minge Xie, Xiaolan Song, Ting Lu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)97-118
Number of pages22
Issue number1
StatePublished - Jan 2011


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

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics


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