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Cognitive Diagnosis for Small Educational Programs: The General Nonparametric Classification Method

Author

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  • Chia-Yi Chiu

    (Rutgers, The State University of New Jersey)

  • Yan Sun

    (Rutgers, The State University of New Jersey)

  • Yanhong Bian

    (Rutgers, The State University of New Jersey)

Abstract

The focus of cognitive diagnosis (CD) is on evaluating an examinee’s strengths and weaknesses in terms of cognitive skills learned and skills that need study. Current methods for fitting CD models (CDMs) work well for large-scale assessments, where the data of hundreds or thousands of examinees are available. However, the development of CD-based assessment tools that can be used in small-scale test settings, say, for monitoring the instruction and learning process at the classroom level has not kept up with the rapid pace at which research and development proceeded for large-scale assessments. The main reason is that the sample sizes of the small-scale test settings are simply too small to guarantee the reliable estimation of item parameters and examinees’ proficiency class membership. In this article, a general nonparametric classification (GNPC) method that allows for assigning examinees to the correct proficiency classes with a high rate when sample sizes are at the classroom level is proposed as an extension of the nonparametric classification (NPC) method (Chiu and Douglas in J Classif 30:225–250, 2013). The proposed method remedies the shortcomings of the NPC method and can accommodate any CDM. The theoretical justification and the empirical studies are presented based on the saturated general CDMs, supporting the legitimacy of using the GNPC method with any CDM. The results from the simulation studies and real data analysis show that the GNPC method outperforms the general CDMs when samples are small.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:2:d:10.1007_s11336-017-9595-4
    DOI: 10.1007/s11336-017-9595-4
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    References listed on IDEAS

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    1. Hans-Friedrich Köhn & Chia-Yi Chiu, 2017. "A Procedure for Assessing the Completeness of the Q-Matrices of Cognitively Diagnostic Tests," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 112-132, March.
    2. Kikumi K. Tatsuoka, 1985. "A Probabilistic Model for Diagnosing Misconceptions By The Pattern Classification Approach," Journal of Educational and Behavioral Statistics, , vol. 10(1), pages 55-73, March.
    3. Chia-Yi Chiu & Jeff Douglas, 2013. "A Nonparametric Approach to Cognitive Diagnosis by Proximity to Ideal Response Patterns," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 225-250, July.
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    9. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
    10. 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.
    11. Shiyu Wang & Jeff Douglas, 2015. "Consistency of Nonparametric Classification in Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 85-100, March.
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    Cited by:

    1. Yu Wang & Chia-Yi Chiu & Hans Friedrich Köhn, 2023. "Nonparametric Classification Method for Multiple-Choice Items in Cognitive Diagnosis," Journal of Educational and Behavioral Statistics, , vol. 48(2), pages 189-219, April.
    2. 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.
    3. Cheng-Hsuan Li & Yi-Jin Ju & Pei-Jyun Hsieh, 2022. "A Nonparametric Weighted Cognitive Diagnosis Model and Its Application on Remedial Instruction in a Small-Class Situation," Sustainability, MDPI, vol. 14(10), pages 1-17, May.
    4. 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.
    5. David Arthur & Hua-Hua Chang, 2024. "DINA-BAG: A Bagging Algorithm for DINA Model Parameter Estimation in Small Samples," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 342-367, June.
    6. Chia-Yi Chiu & Yuan-Pei Chang, 2021. "Advances in CD-CAT: The General Nonparametric Item Selection Method," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 1039-1057, December.
    7. 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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