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A new method for detecting differential item functioning in the Rasch model

Author

Listed:
  • Carolin Strobl
  • Julia Kopf
  • Achim Zeileis

Abstract

Differential item functioning (DIF) can lead to an unfair advantage or disadvantage for certain subgroups in educational and psychological testing. Therefore, a variety of statistical methods has been suggested for detecting DIF in the Rasch model. Most of these methods are designed for the comparison of pre-specified focal and reference groups, such as males and females. Latent class approaches, on the other hand, allow to detect previously unknown groups exhibiting DIF. However, this approach provides no straightforward interpretation of the groups with respect to person characteristics. Here we propose a new method for DIF detection based on model-based recursive partitioning that can be considered as a compromise between those two extremes. With this approach it is possible to detect groups of subjects exhibiting DIF, which are not prespecified, but result from combinations of observed ovariates. These groups are directly interpretable and can thus help understand the psychological sources of DIF. The statistical background and construction of the new method is first introduced by means of an instructive example, and then applied to data from a general knowledge quiz and a teaching evaluation.

Suggested Citation

  • Carolin Strobl & Julia Kopf & Achim Zeileis, 2011. "A new method for detecting differential item functioning in the Rasch model," Working Papers 2011-01, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2011-01
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    References listed on IDEAS

    as
    1. Mair, Patrick & Hatzinger, Reinhold, 2007. "Extended Rasch Modeling: The eRm Package for the Application of IRT Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i09).
    2. William Stout, 2002. "Psychometrics: From practice to theory and back," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 485-518, December.
    3. Achim Zeileis & Kurt Hornik, 2007. "Generalized M‐fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508, November.
    4. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    5. Michaela Gelin & Bruce Carleton & M. Smith & Bruno. Zumbo, 2004. "The Dimensionality and Gender Differential Item Functioning of the Mini Asthma Quality of Life Questionnaire (MiniAQLQ)," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 68(1), pages 91-105, August.
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    Cited by:

    1. Ting Wang & Edgar C. Merkle & Achim Zeileis, 2013. "Score-Based Tests of Measurement Invariance: Use in Practice," Working Papers 2013-33, Faculty of Economics and Statistics, Universität Innsbruck.
    2. Edgar C. Merkle & Achim Zeileis, 2011. "Generalized Measurement Invariance Tests with Application to Factor Analysis," Working Papers 2011-09, Faculty of Economics and Statistics, Universität Innsbruck.
    3. Edgar Merkle & Jinyan Fan & Achim Zeileis, 2014. "Testing for Measurement Invariance with Respect to an Ordinal Variable," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 569-584, October.
    4. Frick, Hannah & Strobl, Carolin & Leisch, Friedrich & Zeileis, Achim, 2012. "Flexible Rasch Mixture Models with Package psychomix," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i07).
    5. Edgar Merkle & Achim Zeileis, 2013. "Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 59-82, January.

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    More about this item

    Keywords

    item response theory; IRT; Rasch model; di erential item functioning; DIF; structural change; multidimensionality.;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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