Refinement of a Bias- Correction Procedure for the Weighted Likelihood Estimator of Ability

In practical applications of item response theory (IRT), item parameters are usually estimated first from a calibration sample. After treating these estimates as fixed and known, ability parameters are then estimated. However, the statistical inferences based on the estimated abilities can be misleading if the uncertainty of the item parameter estimates is ignored. Instead, estimated item parameters can be regarded as covariates measured with error. Along the line of this measurement-error-model approach, asymptotic expansions of the maximum likelihood estimator (MLE) and weighted likelihood estimator (WLE) of ability were derived by Zhang, Xie, Song, and Lu (2007). In this paper, we propose an estimator of an ability parameter based on the asymptotic formula of the WLE. A simulation study shows that the new estimator effectively reduces the bias of the MLE or WLE of ability caused by the uncertainty of the item parameter estimates not taken into account.