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Bridging Parametric and Nonparametric Methods in Cognitive Diagnosis

Author

Listed:
  • Chenchen Ma

    (University of Michigan)

  • Jimmy Torre

    (University of Hong Kong)

  • Gongjun Xu

    (University of Michigan)

Abstract

A number of parametric and nonparametric methods for estimating cognitive diagnosis models (CDMs) have been developed and applied in a wide range of contexts. However, in the literature, a wide chasm exists between these two families of methods, and their relationship to each other is not well understood. In this paper, we propose a unified estimation framework to bridge the divide between parametric and nonparametric methods in cognitive diagnosis to better understand their relationship. We also develop iterative joint estimation algorithms and establish consistency properties within the proposed framework. Lastly, we present comprehensive simulation results to compare different methods and provide practical recommendations on the appropriate use of the proposed framework in various CDM contexts.

Suggested Citation

  • Chenchen Ma & Jimmy Torre & Gongjun Xu, 2023. "Bridging Parametric and Nonparametric Methods in Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 51-75, March.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:1:d:10.1007_s11336-022-09878-2
    DOI: 10.1007/s11336-022-09878-2
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    References listed on IDEAS

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    1. Jingchen Liu & Zhiliang Ying & Stephanie Zhang, 2015. "A Rate Function Approach to Computerized Adaptive Testing for Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 468-490, June.
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    3. 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.
    4. 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.
    5. Chia-Yi Chiu & Yan Sun & Yanhong Bian, 2018. "Cognitive Diagnosis for Small Educational Programs: The General Nonparametric Classification Method," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 355-375, June.
    6. Chia-Yi Chiu & Hans-Friedrich Köhn, 2019. "Consistency Theory for the General Nonparametric Classification Method," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 830-845, September.
    7. Steven Andrew Culpepper, 2019. "Estimating the Cognitive Diagnosis $$\varvec{Q}$$ Q Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 333-357, June.
    8. 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.
    9. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
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    11. 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.
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    Full references (including those not matched with items on IDEAS)

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