Interval Estimation of Latent Variable Scores in Item Response Theory

Abstract

The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a predictive inference problem: The target of prediction is a random variable that follows the true posterior of the LV conditional on the response pattern being scored. Various Bayesian, fiducial, and frequentist prediction intervals of LV scores, which can be obtained from a simple yet generic Monte Carlo recipe, are evaluated and contrasted via simulations based on several measures of prediction quality. An empirical data example is also presented to illustrate the use of candidate methods.