Linking Error Estimation in Stocking–Lord Linking

Stocking–Lord (SL) linking is a widely used linking method based on item response theory (IRT). This article examines the variability in SL linking parameter estimates within the two-parameter logistic (2PL) model. The uncertainty in SL linking arises from the sampling variability (standard error) and item selection (linking error), which can induce variability due to random differential item functioning (DIF). Three linking error estimation approaches are compared in this paper: the conventional jackknife linking error method, a newly developed approximate jackknife linking error method, and a Taylor approximation-based estimate. Simulation studies showed that the approximate jackknife method closely aligns with the traditional jackknife linking error method and outperforms the linking error estimation approach based on Taylor approximation. The adequacy of coverage rates for SL linking parameter estimates was also assessed using estimates of the total error. Results from a simulation study demonstrate that the bias-corrected total error provides superior coverage rates compared to both the conventional total error and the standard error, which does not account for item-related uncertainty due to random DIF.