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Anchor Point Selection - Scale Alignment Based on an Inequality Criterion

Author

Listed:
  • Carolin Strobl
  • Julia Kopf
  • Lucas Kohler
  • Timo von Oertzen
  • Achim Zeileis

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.

Suggested Citation

  • Carolin Strobl & Julia Kopf & Lucas Kohler & Timo von Oertzen & Achim Zeileis, 2018. "Anchor Point Selection - Scale Alignment Based on an Inequality Criterion," Working Papers 2018-03, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2018-03
    as

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    File URL: https://www2.uibk.ac.at/downloads/c4041030/wpaper/2018-03.pdf
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    File URL: https://www2.uibk.ac.at/downloads/c4041030/wpaper/2018-03-orig.pdf
    File Function: First working paper version, 2018-03
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    References listed on IDEAS

    as
    1. Jeanne A. Teresi & Katja Ocepek-Welikson & John A. Toner & Marjorie Kleinman & Mildred Ramirez & Joseph P. Eimicke & Barry J. Gurland & Albert Siu, 2017. "Methodological Issues in Measuring Subjective Well-Being and Quality-of-Life: Applications to Assessment of Affect in Older, Chronically and Cognitively Impaired, Ethnically Diverse Groups Using the F," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 12(2), pages 251-288, June.
    2. Paul Westers & Henk Kelderman, 1992. "Examining differential item functioning due to item difficulty and alternative attractiveness," Psychometrika, Springer;The Psychometric Society, vol. 57(1), pages 107-118, March.
    3. Theo Eggen & Norman Verhelst, 2006. "Loss of Information in Estimating Item Parameters in Incomplete Designs," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 303-322, June.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Differential item functioning (DIF); item bias; anchor items; item clusters;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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