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On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory

Author

Listed:
  • Stefano Noventa

    (Universität Tübingen)

  • Andrea Spoto

    (University of Padova)

  • Jürgen Heller

    (Universität Tübingen)

  • Augustin Kelava

    (Universität Tübingen)

Abstract

Knowledge space theory (KST) structures are introduced within item response theory (IRT) as a possible way to model local dependence between items. The aim of this paper is threefold: firstly, to generalize the usual characterization of local independence without introducing new parameters; secondly, to merge the information provided by the IRT and KST perspectives; and thirdly, to contribute to the literature that bridges continuous and discrete theories of assessment. In detail, connections are established between the KST simple learning model (SLM) and the IRT General Graded Response Model, and between the KST Basic Local Independence Model and IRT models in general. As a consequence, local independence is generalized to account for the existence of prerequisite relations between the items, IRT models become a subset of KST models, IRT likelihood functions can be generalized to broader families, and the issues of local dependence and dimensionality are partially disentangled. Models are discussed for both dichotomous and polytomous items and conclusions are drawn on their interpretation. Considerations on possible consequences in terms of model identifiability and estimation procedures are also provided.

Suggested Citation

  • Stefano Noventa & Andrea Spoto & Jürgen Heller & Augustin Kelava, 2019. "On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 395-421, June.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:2:d:10.1007_s11336-018-9645-6
    DOI: 10.1007/s11336-018-9645-6
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    1. Fumiko Samejima, 1973. "A comment on Birnbaum's three-parameter logistic model in the latent trait theory," Psychometrika, Springer;The Psychometric Society, vol. 38(2), pages 221-233, June.
    2. Robert Jannarone, 1986. "Conjunctive item response theory kernels," Psychometrika, Springer;The Psychometric Society, vol. 51(3), pages 357-373, September.
    3. Mark Wilson & Raymond Adams, 1995. "Rasch models for item bundles," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 181-198, June.
    4. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    5. Edward Ip, 2002. "Locally dependent latent trait model and the dutch identity revisited," Psychometrika, Springer;The Psychometric Society, vol. 67(3), pages 367-386, September.
    6. R. Darrell Bock, 1972. "Estimating item parameters and latent ability when responses are scored in two or more nominal categories," Psychometrika, Springer;The Psychometric Society, vol. 37(1), pages 29-51, March.
    7. Bas Hemker & L. Andries van der Ark & Klaas Sijtsma, 2001. "On measurement properties of continuation ratio models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 487-506, December.
    8. Fumiko Samejima, 1995. "Acceleration model in the heterogeneous case of the general graded response model," Psychometrika, Springer;The Psychometric Society, vol. 60(4), pages 549-572, December.
    9. Hartmann Scheiblechner, 1995. "Isotonic ordinal probabilistic models (ISOP)," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 281-304, June.
    10. Johan Braeken & Francis Tuerlinckx & Paul Boeck, 2007. "Copula Functions for Residual Dependency," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 393-411, September.
    11. David Thissen & Lynne Steinberg, 1986. "A taxonomy of item response models," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 567-577, December.
    12. Paul Holland, 1981. "When are item response models consistent with observed data?," Psychometrika, Springer;The Psychometric Society, vol. 46(1), pages 79-92, March.
    13. Eric Bradlow & Howard Wainer & Xiaohui Wang, 1999. "A Bayesian random effects model for testlets," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 153-168, June.
    14. Paul Rosenbaum, 1984. "Testing the conditional independence and monotonicity assumptions of item response theory," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 425-435, September.
    15. Hans Irtel, 1995. "An extension of the concept of specific objectivity," Psychometrika, Springer;The Psychometric Society, vol. 60(1), pages 115-118, March.
    16. Wen-Hung Chen & David Thissen, 1997. "Local Dependence Indexes for Item Pairs Using Item Response Theory," Journal of Educational and Behavioral Statistics, , vol. 22(3), pages 265-289, September.
    17. Wim J. Linden & Michelle D. Barrett, 2016. "Linking Item Response Model Parameters," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 650-673, September.
    18. Stefano Noventa & Luca Stefanutti & Giulio Vidotto, 2014. "An Analysis of Item Response Theory and Rasch Models Based on the Most Probable Distribution Method," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 377-402, July.
    19. Jürgen Heller & Luca Stefanutti & Pasquale Anselmi & Egidio Robusto, 2015. "On the Link between Cognitive Diagnostic Models and Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 995-1019, December.
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