Simulations were conducted to examine the effect of differential item functioning (DIF) on measurement consequences such as total scores, item response theory (IRT) ability estimates, and test reliability in terms of the ratio of true-score variance to observed-score variance and the standard error of estimation for the IRT ability parameter. The…

The impact of uncertainty about item parameters on test information functions is investigated. The information function of a test is one of the most important tools in item response theory (IRT). Inaccuracy in the estimation of test information can have substantial consequences on data analyses based on IRT. In this article, the major part (called…

The method of maximum-likelihood is typically applied to item response theory (IRT) models when the ability parameter is estimated while conditioning on the true item parameters. In practice, the item parameters are unknown and need to be estimated first from a calibration sample. Lewis (1985) and Zhang and Lu (2007) proposed the expected response…

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…