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Mixed Compensation Multidimensional Item Response Theory

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Intelligent Tutoring Systems (ITS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12149))

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Abstract

Computerized Assisted Testing (CAT) has supported the development of numerous adaptive testing approaches. Such approach as Item Response Theory (IRT) estimates a student’s competency level by modeling a test as a function of the individual’s knowledge ability, and the parameters of the question (i.e. item). Multidimensional Item Response Theory (MIRT) extends IRT so that each item depends on multiple competency areas (i.e., knowledge dimensions). MIRT models consider two opposing types of relationship between knowledge dimensions: compensatory and noncompensatory. In a compensatory model, having a higher competency with one knowledge dimension compensates for having a lower competence in another dimension. Conversely, in a noncompensatory model all the knowledge dimensions are independent and do not compensate for each other. However, using only one type of relationship at a time restricts the use of MIRT in practice. In this work, we generalize MIRT to a mixed-compensation multidimensional item response theory (MCMIRT) model that incorporates both types of relationships. We also relax the MIRT assumption that each item must include every knowledge dimension. Thus, the MCMIRT can better represent real-world curricula. We show that our approach outperforms random item selection with synthetic data.

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Notes

  1. 1.

    See Chap. 4 of [14] for a thorough introduction.

  2. 2.

    If a dimension is not covered by i, the value is 0 by default.

References

  1. Anderson, J.R.: Act: a simple theory of complex cognition. Am. Psychol. 51(4), 355 (1996)

    Article  MathSciNet  Google Scholar 

  2. Ashburner, M., et al.: Gene ontology: tool for the unification of biology. Nat. Genet. 25(1), 25 (2000)

    Article  Google Scholar 

  3. Bloom, B.S., Engelhart, M.D., Furst, E.J., Hill, W.H., Krathwohl, D.R.: Taxonomy of Educational Objectives: Handbook 1: Cognitive Domain. Longman Publishing Group (1984)

    Google Scholar 

  4. Bollacker, K., Evans, C., Paritosh, P., Sturge, T., Taylor, J.: Freebase: a collaboratively created graph database for structuring human knowledge. In: Proceedings of the 2008 ACM SIGMOD International Conference on Management of Data, pp. 1247–1250. ACM (2008)

    Google Scholar 

  5. Conejo, R., Guzmán, E., Pérez-de-la Cruz, J.L., Millán, E.: Introducing adaptive assistance in adaptive testing. In: AIED, pp. 777–779 (2005)

    Google Scholar 

  6. Doignon, J.P., Falmagne, J.C.: Knowledge Spaces and Learning Spaces, November 2015

    Google Scholar 

  7. Galvez, J., Guzman, E., Conejo, R., Millan, E.: Student knowledge diagnosis using item response theory and constraint-based modeling. In: AIED, pp. 291–298 (2009)

    Google Scholar 

  8. Goodfellow, I., Bengio, Y., Courville, A., Bengio, Y.: Deep Learning, vol. 1. MIT Press, Cambridge (2016)

    MATH  Google Scholar 

  9. Hernando, M., Guzmán, E., Conejo, R.: Measuring procedural knowledge in problem solving environments with item response theory. In: Lane, H.C., Yacef, K., Mostow, J., Pavlik, P. (eds.) AIED 2013. LNCS (LNAI), vol. 7926, pp. 653–656. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39112-5_81

    Chapter  Google Scholar 

  10. Van der Linden, W.J., Pashley, P.J.: Item selection and ability estimation in adaptive testing. In: van der Linden, W., Glas, C. (eds.) Elements of Adaptive Testing, pp. 3–30. Springer, Heidelberg (2009). https://doi.org/10.1007/978-0-387-85461-8_1

    Chapter  Google Scholar 

  11. Lord, F.: Application of Item Response Theory to Practical Testing Problems (1980)

    Google Scholar 

  12. Lord, F.M.: Applications of Item Response Theory to Practical Testing Problems. Routledge (2012)

    Google Scholar 

  13. Miller, G.A.: WordNet: a lexical database for English. Commun. ACM 38(11), 39–41 (1995)

    Article  Google Scholar 

  14. Reckase, M.D.: Multidimensional Item Response Theory. Statistics for Social and Behavioral Sciences. Springer, New York (2009). https://doi.org/10.1007/978-0-387-89976-3

    Book  MATH  Google Scholar 

  15. Ypma, T.J.: Historical development of the Newton-Raphson method. SIAM Rev. 37(4), 531–551 (1995)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of EECS, Oregon State University, Corvallis, OR, USA

    Béatrice Moissinac

  2. Xio Research, New York, NY, USA

    Aditya Vempaty

Authors
  1. Béatrice Moissinac
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  2. Aditya Vempaty
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Correspondence to Aditya Vempaty .

Editor information

Editors and Affiliations

  1. Athabasca University, Athabasca, AB, Canada

    Vivekanandan Kumar

  2. University of West Attica, Egaleo, Greece

    Christos Troussas

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Moissinac, B., Vempaty, A. (2020). Mixed Compensation Multidimensional Item Response Theory. In: Kumar, V., Troussas, C. (eds) Intelligent Tutoring Systems. ITS 2020. Lecture Notes in Computer Science(), vol 12149. Springer, Cham. https://doi.org/10.1007/978-3-030-49663-0_17

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  • DOI: https://doi.org/10.1007/978-3-030-49663-0_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-49662-3

  • Online ISBN: 978-3-030-49663-0

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