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A Class of Cognitive Diagnosis Models for Polytomous Data

Author

Listed:
  • Xuliang Gao

    (12642Jiangxi Normal University
    12686Guizhou Normal University)

  • Wenchao Ma

    (The 8063University of Alabama)

  • Daxun Wang
  • Yan Cai
  • Dongbo Tu

    (12642Jiangxi Normal University)

Abstract

This article proposes a class of cognitive diagnosis models (CDMs) for polytomously scored items with different link functions. Many existing polytomous CDMs can be considered as special cases of the proposed class of polytomous CDMs. Simulation studies were carried out to investigate the feasibility of the proposed CDMs and the performance of several information criteria (Akaike’s information criterion [AIC], consistent Akaike’s information criterion [CAIC], and Bayesian information criterion [BIC]) in model selection. The results showed that the parameters of the proposed CDMs could be recovered adequately under varied conditions. In addition, CAIC and BIC had better performance in selecting the most appropriate model than AIC. Finally, a set of real data was analyzed to illustrate the application of the proposed CDMs.

Suggested Citation

  • Xuliang Gao & Wenchao Ma & Daxun Wang & Yan Cai & Dongbo Tu, 2021. "A Class of Cognitive Diagnosis Models for Polytomous Data," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 297-322, June.
    • Handle: RePEc:sae:jedbes:v:46:y:2021:i:3:p:297-322
    DOI: 10.3102/1076998620951986
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    References listed on IDEAS

    as
    1. Jimmy Torre & Jeffrey Douglas, 2004. "Higher-order latent trait models for cognitive diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 333-353, September.
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    3. Steven Andrew Culpepper, 2019. "An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 921-940, December.
    4. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    5. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    6. Guanhua Fang & Jingchen Liu & Zhiliang Ying, 2019. "On the Identifiability of Diagnostic Classification Models," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 19-40, March.
    7. Jimmy Torre, 2011. "Erratum to: The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 510-510, July.
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    Cited by:

    1. Pablo Nájera & Francisco J. Abad & Chia-Yi Chiu & Miguel A. Sorrel, 2023. "The Restricted DINA Model: A Comprehensive Cognitive Diagnostic Model for Classroom-Level Assessments," Journal of Educational and Behavioral Statistics, , vol. 48(6), pages 719-749, December.

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