Estimation of Standard Error, Linking Error, and Total Error for Robust and Nonrobust Linking Methods in the Two-Parameter Logistic Model

Alexander Robitzsch ()
Additional contact information
Alexander Robitzsch: IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, Germany

Stats, 2024, vol. 7, issue 3, 1-21

Abstract: The two-parameter logistic (2PL) item response theory model is a statistical model for analyzing multivariate binary data. In this article, two groups are brought onto a common metric using the 2PL model using linking methods. The linking methods of mean–mean linking, mean–geometric–mean linking, and Haebara linking are investigated in nonrobust and robust specifications in the presence of differential item functioning (DIF). M-estimation theory is applied to derive linking errors for the studied linking methods. However, estimated linking errors are prone to sampling error in estimated item parameters, thus resulting in artificially increased the linking error estimates in finite samples. For this reason, a bias-corrected linking error estimate is proposed. The usefulness of the modified linking error estimate is demonstrated in a simulation study. It is shown that a simultaneous assessment of the standard error and linking error in a total error must be conducted to obtain valid statistical inference. In the computation of the total error, using the bias-corrected linking error estimate instead of the usually employed linking error provides more accurate coverage rates.

Keywords: item response model; linking; 2PL model; M-estimation; linking error; standard error; total error; robust linking; nonrobust linking (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2571-905X/7/3/36/pdf (application/pdf)
https://www.mdpi.com/2571-905X/7/3/36/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jstats:v:7:y:2024:i:3:p:36-612:d:1419601

Access Statistics for this article

Stats is currently edited by Mrs. Minnie Li

More articles in Stats from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().