Area Measures for Differential Item and Test Functioning on the Logit Scale: Relationships to Linking Errors in the 2PL Model
- 1Educational Measurement and Data Science, IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, Germany
- 2Centre for International Student Assessment, Zentrum für Internationale Bildungsvergleichsstudien (ZIB), Olshausenstraße 62, 24118 Kiel, Germany
Abstract
Area measures for differential item functioning and differential test functioning are conventionally defined as functions of the difference in item response functions. This probability scale may be less convenient for interpretation than an assessment carried out on the logit scale of the latent variable θ. This article proposes modified area measures on the logit scale and derives approximate closed-form expressions for the two-parameter logistic model. The noncompensatory measures are decomposed into uniform and nonuniform components, yielding interpretable summaries of differential functioning in item difficulties and item discriminations, respectively. A central finding approximately links the expected values of the proposed test-level measures to the linking errors of mean-geometric mean linking: the uniform component bounds the linking error for the group mean—with equality in the absence of differential functioning in item discriminations—while the nonuniform component equals the linking error for the group standard deviation. Analogous approximate relationships hold at the item level through newly introduced item-specific linking errors. The proposed measures thus offer intuitive summaries that directly quantify the impact of differential item functioning on group comparisons in the logit scale of θ.
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BibTeX
@article{robitzsch2026area,
title = {{Area Measures for Differential Item and Test Functioning on the Logit Scale: Relationships to Linking Errors in the 2PL Model}},
author = {Alexander Robitzsch},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193612},
url = {https://www.mdpi.com/2227-7390/14/19/3612},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Area Measures for Differential Item and Test Functioning on the Logit Scale: Relationships to Linking Errors in the 2PL Model
AU - Alexander Robitzsch
PY - 2026
DA - 2026/10/05
JO - Mathematics
DO - 10.3390/math14193612
UR - https://www.mdpi.com/2227-7390/14/19/3612
AB - Area measures for differential item functioning and differential test functioning are conventionally defined as functions of the difference in item response functions. This probability scale may be less convenient for interpretation than an assessment carried out on the logit scale of the latent variable θ. This article proposes modified area measures on the logit scale and derives approximate closed-form expressions for the two-parameter logistic model. The noncompensatory measures are decomposed into uniform and nonuniform components, yielding interpretable summaries of differential functioning in item difficulties and item discriminations, respectively. A central finding approximately links the expected values of the proposed test-level measures to the linking errors of mean-geometric mean linking: the uniform component bounds the linking error for the group mean—with equality in the absence of differential functioning in item discriminations—while the nonuniform component equals the linking error for the group standard deviation. Analogous approximate relationships hold at the item level through newly introduced item-specific linking errors. The proposed measures thus offer intuitive summaries that directly quantify the impact of differential item functioning on group comparisons in the logit scale of θ.
SN - 2227-7390
ER -