Linking Error in the 2PL Model

Abstract

The two-parameter logistic (2PL) item response model is likely the most frequently applied item response model for analyzing dichotomous data. Linking errors quantify the variability in means or standard deviations due to the choice of items. Previous research presented analytical work for linking errors in the one-parameter logistic model. In this article, we present linking errors for the 2PL model using the general theory of M-estimation. Linking errors are derived in the case of log-mean-mean linking for linking two groups. The performance of the newly proposed formulas is evaluated in a simulation study. Furthermore, the linking error estimation in the 2PL model is also treated in more complex settings, such as chain linking, trend estimation, fixed item parameter calibration, and concurrent calibration.

Keywords

• item response model
• 2PL model
• linking error
• M-estimation