Adaptive Item Selection Under Matroid Constraints

Authors

  • Daniel Bengs German Institute for International Educational Research Technische Universität Darmstadt
  • Ulf Brefeld Leuphana Universität Lüneburg, Institute of Electronic Business Processes
  • Ulf Kröhne German Institute for International Educational Research

DOI:

https://doi.org/10.7333/jcat.v6i2.64

Abstract

The shadow testing approach (STA; van der Linden & Reese, 1998) is considered the state of the art in constrained item selection for computerized adaptive tests. The present paper shows that certain types of constraints (e.g., bounds on categorical item attributes) induce a matroid on the item bank. This observation is used to devise item selection algorithms that are based on matroid optimization and lead to optimal tests, as the STA does. In particular, a single matroid constraint can be treated optimally by an efficient greedy algorithm that selects the most informative item preserving the integrity of the constraints. A simulation study shows that for applicable constraints, the optimal algorithms realize a decrease in standard error (SE) corresponding to a reduction in test length of up to 10% compared to the maximum priority index (Cheng & Chang, 2009) and up to 30% compared to Kingsbury and Zara's (1991) constrained computerized adaptive testing.

Author Biographies

  • Daniel Bengs, German Institute for International Educational Research Technische Universität Darmstadt
    PhD Student, Centre for Technology-Based Assessment / Information Center for Education
  • Ulf Brefeld, Leuphana Universität Lüneburg, Institute of Electronic Business Processes
    Professor in Business Information Systems, esp. Machine Learning 
  • Ulf Kröhne, German Institute for International Educational Research
    Senior Researcher, Centre for Technology-Based Assessment / Department of Educational Quality and Evaluation

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Published

2018-08-07