Incorporating Measurement Errors in Fixed Person Parameter Calibration

Abstract

In this study, we propose a new fixed person parameter calibration (FPC) strategy that incorporates measurement error in examinee ability estimates. Specifically, the proposed FPC method is an application of the mixed-effect structural equation model of Junker et al. (2012) to the small-sample item calibration context and relies on a Bayesian iterative sampling procedure for parameter estimation. We evaluated the proposed FPC method using simulated data sets that varied in terms of sample size, item composition, and examinee ability distribution. The parameter recovery performance of the proposed method was compared to those from alternative small-sample calibration methods two other FPC methods and the state-of-the-art fixed item parameter calibration (FIC) method. The results from the simulation study showed that the proposed method consistently outperformed the compared FPC and FIC methods. The encouraging performance of the proposed method demonstrates the impact of properly accounting for measurement error and provides a justification for its use as a competent small-sample item calibration method.