IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v14y2022i10p5773-d812396.html
   My bibliography  Save this article

A Nonparametric Weighted Cognitive Diagnosis Model and Its Application on Remedial Instruction in a Small-Class Situation

Author

Listed:
  • Cheng-Hsuan Li

    (Graduate Institute of Educational Information and Measurement, National Taichung University of Education, Taichung City 40306, Taiwan)

  • Yi-Jin Ju

    (Graduate Institute of Educational Information and Measurement, National Taichung University of Education, Taichung City 40306, Taiwan)

  • Pei-Jyun Hsieh

    (Graduate Institute of Educational Information and Measurement, National Taichung University of Education, Taichung City 40306, Taiwan)

Abstract

CDMs can provide a discrete classification of mastery skills to diagnose relevant conceptions immediately for Education Sustainable Development. Due to the problem of parametric CDMs with only a few training sample sizes in small classroom teaching situations and the lack of a nonparametric model for classifying error patterns, two nonparametric weighted cognitive diagnosis models, NWSD and NWBD, for classifying mastery skills and knowledge bugs were proposed, respectively. In both, the variances of items with respect to the ideal responses were considered for computing the weighted Hamming distance, and the inverse distances between the observed and ideal responses were used as weights to obtain the probabilities of the mastering attributes of a student. Conversely, NWBD can classify students’ “bugs”, so teachers can provide suitable examples for precision assistance before teaching non-mastery skills. According to the experimental results on simulated and real datasets, the proposed methods outperform some standard methods in a small-class situation. The results also demonstrate that a remedial course with NWSD and NWBD is better than one with traditional group remedial teaching.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:10:p:5773-:d:812396
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/14/10/5773/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/14/10/5773/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Laine Bradshaw & Jonathan Templin, 2014. "Combining Item Response Theory and Diagnostic Classification Models: A Psychometric Model for Scaling Ability and Diagnosing Misconceptions," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 403-425, July.
    2. 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.
    3. Susan Embretson (Whitely), 1984. "A general latent trait model for response processes," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 175-186, June.
    4. Tobias Hoppe & Alexander Renkl & Tina Seidel & Stephanie Rettig & Werner Rieß, 2020. "Exploring How Teachers Diagnose Student Conceptions about the Cycle of Matter," Sustainability, MDPI, vol. 12(10), pages 1-15, May.
    5. 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.
    6. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    7. Gisela Cebrián & Ramon Palau & Jordi Mogas, 2020. "The Smart Classroom as a Means to the Development of ESD Methodologies," Sustainability, MDPI, vol. 12(7), pages 1-18, April.
    8. Jimmy Torre, 2011. "Erratum to: The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 510-510, July.
    9. Shiyu Wang & Jeff Douglas, 2015. "Consistency of Nonparametric Classification in Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 85-100, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    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. 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.
    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. Kazuhiro Yamaguchi & Jonathan Templin, 2022. "Direct Estimation of Diagnostic Classification Model Attribute Mastery Profiles via a Collapsed Gibbs Sampling Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1390-1421, December.
    6. Kazuhiro Yamaguchi & Kensuke Okada, 2020. "Variational Bayes Inference for the DINA Model," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 569-597, October.
    7. Kazuhiro Yamaguchi & Kensuke Okada, 2020. "Variational Bayes Inference Algorithm for the Saturated Diagnostic Classification Model," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 973-995, December.
    8. 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.
    9. 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.
    10. Chun Wang, 2021. "Using Penalized EM Algorithm to Infer Learning Trajectories in Latent Transition CDM," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 167-189, March.
    11. Chia-Yi Chiu & Hans-Friedrich Köhn & Yi Zheng & Robert Henson, 2016. "Joint Maximum Likelihood Estimation for Diagnostic Classification Models," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1069-1092, December.
    12. Peida Zhan & Hong Jiao & Kaiwen Man & Lijun Wang, 2019. "Using JAGS for Bayesian Cognitive Diagnosis Modeling: A Tutorial," Journal of Educational and Behavioral Statistics, , vol. 44(4), pages 473-503, August.
    13. Shiyu Wang & Jeff Douglas, 2015. "Consistency of Nonparametric Classification in Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 85-100, March.
    14. Yuqi Gu & Gongjun Xu, 2019. "The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 468-483, June.
    15. 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.
    16. Kazuhiro Yamaguchi & Jonathan Templin, 2022. "A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 24-54, March.
    17. Matthew S. Johnson & Sandip Sinharay, 2020. "The Reliability of the Posterior Probability of Skill Attainment in Diagnostic Classification Models," Journal of Educational and Behavioral Statistics, , vol. 45(1), pages 5-31, February.
    18. 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.
    19. Chenchen Ma & Jing Ouyang & Gongjun Xu, 2023. "Learning Latent and Hierarchical Structures in Cognitive Diagnosis Models," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 175-207, March.
    20. James Joseph Balamuta & Steven Andrew Culpepper, 2022. "Exploratory Restricted Latent Class Models with Monotonicity Requirements under PÒLYA–GAMMA Data Augmentation," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 903-945, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jsusta:v:14:y:2022:i:10:p:5773-:d:812396. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.