IDEAS home Printed from https://ideas.repec.org/p/inn/wpaper/2018-03.html
   My bibliography  Save this paper

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

    Download full text from publisher

    File URL: https://www2.uibk.ac.at/downloads/c4041030/wpaper/2018-03.pdf
    File Function: Revised preprint version, 2020-09
    Download Restriction: no

    File URL: https://www2.uibk.ac.at/downloads/c4041030/wpaper/2018-03-orig.pdf
    File Function: First working paper version, 2018-03
    Download Restriction: no
    ---><---

    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lisbeth Nielsen, 2017. "Measuring the Subjective Well-Being of Diverse Populations in the U.S," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 12(2), pages 237-240, June.
    2. Setareh Ranjbar & Stefan Sperlich, 2020. "A Note on Empirical Studies of Life-Satisfaction: Unhappy with Semiparametrics?," Journal of Happiness Studies, Springer, vol. 21(6), pages 2193-2212, August.
    3. Carolin Strobl & Julia Kopf & Achim Zeileis, 2015. "Rasch Trees: A New Method for Detecting Differential Item Functioning in the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 289-316, June.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inn:wpaper:2018-03. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Janette Walde (email available below). General contact details of provider: https://edirc.repec.org/data/fuibkat.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.