Join us on Zoom for a Joint Quantitative Psychology Brownbag with Alexander Robitzsch (IPN – Leibniz Institute for Science and Mathematics Education, Kiel, Germany)
This event is online only. Please join us using this meeting link.
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.
Corresponding Article: Robitzsch, A. (2024). Estimation of standard error, linking error, and total error for robust and nonrobust linking methods in the two-parameter logistic model. Stats, 7, 592–612. DOI.
Joint Quantitative Psychology Brownbags are organized by psychology programs at universities around the nation, including: The Ohio State University, University of Notre Dame, University of Maryland, College Park, University of North Carolina at Chapel Hill, University of Virginia, Vanderbilt University and University of South Carolina. Participating programs also include those from York University, McGill University, University of Missouri and University of British Columbia.