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Extending the Basic Local Independence Model to Polytomous Data

Author

Listed:
  • Luca Stefanutti

    (University of Padua)

  • Debora Chiusole

    (University of Padua)

  • Pasquale Anselmi

    (University of Padua)

  • Andrea Spoto

    (Department of General Psychology)

Abstract

A probabilistic framework for the polytomous extension of knowledge space theory (KST) is proposed. It consists in a probabilistic model, called polytomous local independence model, that is developed as a generalization of the basic local independence model. The algorithms for computing “maximum likelihood” (ML) and “minimum discrepancy” (MD) estimates of the model parameters have been derived and tested in a simulation study. Results show that the algorithms differ in their capability of recovering the true parameter values. The ML algorithm correctly recovers the true values, regardless of the manipulated variables. This is not totally true for the MD algorithm. Finally, the model has been applied to a real polytomous data set collected in the area of psychological assessment. Results show that it can be successfully applied in practice, paving the way to a number of applications of KST outside the area of knowledge and learning assessment.

Suggested Citation

  • Luca Stefanutti & Debora Chiusole & Pasquale Anselmi & Andrea Spoto, 2020. "Extending the Basic Local Independence Model to Polytomous Data," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 684-715, September.
    • Handle: RePEc:spr:psycho:v:85:y:2020:i:3:d:10.1007_s11336-020-09722-5
    DOI: 10.1007/s11336-020-09722-5
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    References listed on IDEAS

    as
    1. Pasquale Anselmi & Egidio Robusto & Luca Stefanutti & Debora Chiusole, 2016. "An Upgrading Procedure for Adaptive Assessment of Knowledge," Psychometrika, Springer;The Psychometric Society, vol. 81(2), pages 461-482, June.
    2. Pasquale Anselmi & Egidio Robusto & Luca Stefanutti, 2012. "Uncovering the Best Skill Multimap by Constraining the Error Probabilities of the Gain-Loss Model," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 763-781, October.
    3. Debora Chiusole & Luca Stefanutti & Pasquale Anselmi & Egidio Robusto, 2013. "Assessing Parameter Invariance in the BLIM: Bipartition Models," Psychometrika, Springer;The Psychometric Society, vol. 78(4), pages 710-724, October.
    4. Jinsong Chen & Hui Zhou, 2017. "Test designs and modeling under the general nominal diagnosis model framework," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-14, June.
    5. Jimmy de la Torre & Jeffrey Douglas, 2008. "Model Evaluation and Multiple Strategies in Cognitive Diagnosis: An Analysis of Fraction Subtraction Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 595-624, December.
    6. Jürgen Heller & Luca Stefanutti & Pasquale Anselmi & Egidio Robusto, 2016. "Erratum to: On the Link between Cognitive Diagnostic Models and Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 250-251, March.
    7. 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.
    8. Jürgen Heller & Luca Stefanutti & Pasquale Anselmi & Egidio Robusto, 2016. "Erratum to: On the Link between Cognitive Diagnostic Models and Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 250-251, March.
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    Cited by:

    1. Chia-Yi Chiu & Hans Friedrich Köhn & Wenchao Ma, 2023. "Commentary on “Extending the Basic Local Independence Model to Polytomous Data” by Stefanutti, de Chiusole, Anselmi, and Spoto," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 656-671, June.

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