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Rasch Trees: A New Method for Detecting Differential Item Functioning in the Rasch Model


  • Carolin Strobl


  • Julia Kopf


  • Achim Zeileis



A variety of statistical methods have been suggested for detecting differential item functioning (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 the detection of 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 pre-specified, but result from combinations of observed covariates. These groups are directly interpretable and can thus help generate hypotheses about the psychological sources of DIF. The statistical background and construction of the new method are introduced by means of an instructive example, and extensive simulation studies are presented to support and illustrate the statistical properties of the method, which is then applied to empirical data from a general knowledge quiz. A software implementation of the method is freely available in the R system for statistical computing. Copyright The Psychometric Society 2015

Suggested Citation

  • 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.
  • Handle: RePEc:spr:psycho:v:80:y:2015:i:2:p:289-316
    DOI: 10.1007/s11336-013-9388-3

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    References listed on IDEAS

    1. Strobl, Carolin & Boulesteix, Anne-Laure & Augustin, Thomas, 2007. "Unbiased split selection for classification trees based on the Gini Index," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 483-501, September.
    2. 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.
    3. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
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    5. 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).
    6. 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.
    7. Rizopoulos, Dimitris, 2006. "ltm: An R Package for Latent Variable Modeling and Item Response Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 17(i05).
    8. 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.
    9. 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.
    10. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    11. Robert Mislevy & Norman Verhelst, 1990. "Modeling item responses when different subjects employ different solution strategies," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 195-215, June.
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    Cited by:

    1. Gerhard Tutz & Moritz Berger, 2016. "Item-focussed Trees for the Identification of Items in Differential Item Functioning," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 727-750, September.
    2. Jones, Payton J. & Mair, Patrick & Simon, Thorsten & Zeileis, Achim, 2019. "Network Model Trees," OSF Preprints ha4cw, Center for Open Science.
    3. Ting Wang & Carolin Strobl & Achim Zeileis & Edgar C. Merkle, 2018. "Score-Based Tests of Differential Item Functioning via Pairwise Maximum Likelihood Estimation," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 132-155, March.


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