Speaker

Dr. Alexander Robitzsch
IPN – Leibniz Institute for Science and Mathematics Education, Kiel, Germany

Title

Estimation of Standard Error, Linking Error, and Total Error for Linking Methods in the 2PL Model

Abstract

The two-parameter logistic (2PL) item response theory model is a statistical framework for analyzing multivariate binary data. In this article, two groups are placed on a common metric under the 2PL model using various linking methods. The mean–mean, mean–geometric–mean, and Haebara linking methods are examined in the presence of differential item functioning (DIF). Whereas the standard error reflects uncertainty arising from the sampling of respondents, the linking error captures variability in group comparisons due to item selection.

In this study, M-estimation theory is employed to derive linking errors for the considered methods. However, estimated linking errors are affected by sampling error in the estimated item parameters, leading to artificially inflated linking error estimates in finite samples. To address this issue, a bias-corrected linking error estimate is proposed.

The effectiveness of the bias-corrected estimate is demonstrated through a simulation study. Results show that valid statistical inference requires a joint assessment of the standard error and the linking error within the proposed total error framework. Using the bias-corrected linking error instead of the conventional estimate yields more accurate coverage rates for the total error.