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Anchor Point Selection - Scale Alignment Based on an Inequality Criterion

Carolin Strobl (), Julia Kopf (), Lucas Kohler (), Timo von Oertzen () and Achim Zeileis ()

Working Papers from Faculty of Economics and Statistics, University of Innsbruck

Abstract: For detecting differential item functioning (DIF) between two or more groups of test takers in the Rasch model, their item parameters need to be placed on the same scale. Typically this is done by means of choosing a set of so-called anchor items based on statistical tests or heuristics. Here we suggest an alternative strategy: By means of an inequality criterion from economics, the Gini Index, the item parameters are shifted to an optimal position where the item parameter estimates of the groups best overlap. Several toy examples, extensive simulation studies and two empirical application examples are presented to illustrate the properties of the Gini Index as an anchor point selection criterion and compare its properties to those of the criterion used in the alignment approach of Asparouhov and Muthen. In particular, we show that - in addition to the globally optimal position for the anchor point - the criterion plot contains valuable additional information and may help discover unaccounted DIF-inducing multidimensionality. We further provide mathematical results that enable an efficient sparse grid optimization and make it feasible to extend the approach, e.g. to multiple group scenarios.

Keywords: Differential item functioning (DIF); item bias; anchor items; item clusters (search for similar items in EconPapers)
JEL-codes: C30 C52 C87 (search for similar items in EconPapers)
Date: 2018-03
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Forthcoming in Applied Psychological Measurement

Downloads: (external link) Revised preprint version, 2020-09 (application/pdf) First working paper version, 2018-03 (application/pdf)

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