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A Partial Mastery, Higher-Order Latent Structural Model for Polytomous Attributes in Cognitive Diagnostic Assessments

Author

Listed:
  • Peida Zhan

    (Zhejiang Normal University)

  • Wen-Chung Wang

    (The Education University of Hong Kong)

  • Xiaomin Li

    (The Education University of Hong Kong)

Abstract

The latent attribute space in cognitive diagnosis models (CDMs) is often assumed to be unstructured or saturated. In recent years, the number of latent attributes in real tests has often been found to be large, and polytomous latent attributes have been advocated. Therefore, it is preferable to adopt substantive theories to connect seemingly unrelated latent attributes, to replace the unstructured or saturated latent structural models (LSMs) with structured or parsimonious ones, with simplified parameter estimation. In the present study, we developed a partial mastery, higher-order LSM for polytomous attributes, which was built upon the framework of adjacent-category logit models to account for a higher-order latent structure of multiple polytomous attributes. The proposed model can be incorporated into many existing CDMs. We conducted simulations to evaluate the psychometric properties of the proposed model and obtained good parameter recovery. We then provided an empirical example to demonstrate the applications and the advantages of the proposed model.

Suggested Citation

  • Peida Zhan & Wen-Chung Wang & Xiaomin Li, 2020. "A Partial Mastery, Higher-Order Latent Structural Model for Polytomous Attributes in Cognitive Diagnostic Assessments," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 328-351, July.
    • Handle: RePEc:spr:jclass:v:37:y:2020:i:2:d:10.1007_s00357-019-09323-7
    DOI: 10.1007/s00357-019-09323-7
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    References listed on IDEAS

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    1. Chia-Yi Chiu & Jeffrey Douglas & Xiaodong Li, 2009. "Cluster Analysis for Cognitive Diagnosis: Theory and Applications," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 633-665, December.
    2. Gongjun Xu & Zhuoran Shang, 2018. "Identifying Latent Structures in Restricted Latent Class Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1284-1295, July.
    3. 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.
    4. 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.
    5. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
    6. Yunxiao Chen & Jingchen Liu & Gongjun Xu & Zhiliang Ying, 2015. "Statistical Analysis of Q -Matrix Based Diagnostic Classification Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 850-866, June.
    7. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    8. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    9. Chen, Yunxiao & Liu, Jingchen & Xu, Gongjun & Ying, Zhiliang, 2015. "Statistical analysis of Q-matrix based diagnostic classification models," LSE Research Online Documents on Economics 103183, London School of Economics and Political Science, LSE Library.
    10. Elizabeth Ayers & Sophia Rabe-Hesketh & Rebecca Nugent, 2013. "Incorporating Student Covariates in Cognitive Diagnosis Models," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 195-224, July.
    11. 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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