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Item-focussed Trees for the Identification of Items in Differential Item Functioning


  • Gerhard Tutz

    () (Ludwig-Maximilians-Universit├Ąt)

  • Moritz Berger



Abstract A novel method for the identification of differential item functioning (DIF) by means of recursive partitioning techniques is proposed. We assume an extension of the Rasch model that allows for DIF being induced by an arbitrary number of covariates for each item. Recursive partitioning on the item level results in one tree for each item and leads to simultaneous selection of items and variables that induce DIF. For each item, it is possible to detect groups of subjects with different item difficulties, defined by combinations of characteristics that are not pre-specified. The way a DIF item is determined by covariates is visualized in a small tree and therefore easily accessible. An algorithm is proposed that is based on permutation tests. Various simulation studies, including the comparison with traditional approaches to identify items with DIF, show the applicability and the competitive performance of the method. Two applications illustrate the usefulness and the advantages of the new method.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:psycho:v:81:y:2016:i:3:d:10.1007_s11336-015-9488-3
    DOI: 10.1007/s11336-015-9488-3

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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. 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.
    3. David Magis & Francis Tuerlinckx & Paul De Boeck, 2015. "Detection of Differential Item Functioning Using the Lasso Approach," Journal of Educational and Behavioral Statistics, , vol. 40(2), pages 111-135, April.
    4. Gerhard Tutz & Gunther Schauberger, 2015. "A Penalty Approach to Differential Item Functioning in Rasch Models," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 21-43, March.
    5. Hothorn, Torsten & Lausen, Berthold, 2003. "On the exact distribution of maximally selected rank statistics," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 121-137, June.
    6. Shih, Yu-Shan & Tsai, Hsin-Wen, 2004. "Variable selection bias in regression trees with constant fits," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 595-607, April.
    7. Nambury Raju, 1988. "The area between two item characteristic curves," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 495-502, December.
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