The Impact of Three Factors on the Recovery of Item Parameters for the Three-Parameter Logistic Model

This article provides a detailed description of three factors (specification of the ability distribution, numerical integration, and frame of reference for the item parameter estimates) that might affect the item parameter estimation of the three-parameter logistic model, and compares five item calibration methods, which are combinations of the three factors, using a simulation study. The five item calibration methods are Normal-Midpoint-Prior (NMPr), Normal-Hermite-Prior (NHPr), Normal-Midpoint-Posterior (NMPo), Normal-Hermite-Posterior (NHPo), and Empirical-Midpoint-Prior (EMPr). In addition, four item response theory computer programs (BILOG-MG, PARSCALE, flexMIRT, and ICL) are compared in terms of their default specifications and available options of the three factors. The EMPr method recovered item parameters accurately regardless of the shape of the population ability distribution and the number of quadrature points. The NMPr, NHPr, NMPo, and NHPo methods returned item parameter estimates with low bias when abilities followed a standard normal distribution, but tended to either underestimate or overestimate the item parameters when the population ability distribution was skewed. Also, unlike the EMPr method, the performance of these four methods depended on the number of quadrature points.