IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i23p3062-d690238.html
   My bibliography  Save this article

A Deterministic Learning Algorithm Estimating the Q-Matrix for Cognitive Diagnosis Models

Author

Listed:
  • Meng-Ta Chung

    (Department of Management Sciences, Tamkang University, New Taipei City 251301, Taiwan)

  • Shui-Lien Chen

    (Department of Management Sciences, Tamkang University, New Taipei City 251301, Taiwan)

Abstract

The goal of an exam in cognitive diagnostic assessment is to uncover whether an examinee has mastered certain attributes. Different cognitive diagnosis models (CDMs) have been developed for this purpose. The core of these CDMs is the Q-matrix, which is an item-to-attribute mapping, traditionally designed by domain experts. An expert designed Q-matrix is not without issues. For example, domain experts might neglect some attributes or have different opinions about the inclusion of some entries in the Q-matrix. It is therefore of practical importance to develop an automated method to estimate the Q-matrix. This research proposes a deterministic learning algorithm for estimating the Q-matrix. To obtain a sensible binary Q-matrix, a dichotomizing method is also devised. Results from the simulation study shows that the proposed method for estimating the Q-matrix is useful. The empirical study analyzes the ECPE data. The estimated Q-matrix is compared with the expert-designed one. All analyses in this research are carried out in R.

Suggested Citation

  • Meng-Ta Chung & Shui-Lien Chen, 2021. "A Deterministic Learning Algorithm Estimating the Q-Matrix for Cognitive Diagnosis Models," Mathematics, MDPI, vol. 9(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3062-:d:690238
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/23/3062/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/23/3062/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jonathan Templin & Laine Bradshaw, 2014. "Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 317-339, April.
    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. 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.
    4. Curtis Tatsuoka, 2002. "Data analytic methods for latent partially ordered classification models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(3), pages 337-350, July.
    5. 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.
    6. 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.
    7. Chen-Wei Liu & Björn Andersson & Anders Skrondal, 2020. "A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 322-357, June.
    8. Jimmy de la Torre & Jeffrey Douglas, 2008. "Model Evaluation and Multiple Strategies in Cognitive Diagnosis: An Analysis of Fraction Subtraction Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 595-624, December.
    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. Motonori Oka & Kensuke Okada, 2023. "Scalable Bayesian Approach for the Dina Q-Matrix Estimation Combining Stochastic Optimization and Variational Inference," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 302-331, March.
    2. Yinghan Chen & Ying Liu & Steven Andrew Culpepper & Yuguo Chen, 2021. "Inferring the Number of Attributes for the Exploratory DINA Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 30-64, March.
    3. Yinghan Chen & Shiyu Wang, 2023. "Bayesian Estimation of Attribute Hierarchy for Cognitive Diagnosis Models," Journal of Educational and Behavioral Statistics, , vol. 48(6), pages 810-841, December.
    4. Chen-Wei Liu & Björn Andersson & Anders Skrondal, 2020. "A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 322-357, June.
    5. Chun Wang & Jing Lu, 2021. "Learning Attribute Hierarchies From Data: Two Exploratory Approaches," Journal of Educational and Behavioral Statistics, , vol. 46(1), pages 58-84, February.
    6. Hans Friedrich Köhn & Chia-Yi Chiu, 2021. "A Unified Theory of the Completeness of Q-Matrices for the DINA Model," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 500-518, October.
    7. 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.
    8. Yuqi Gu & Jingchen Liu & Gongjun Xu & Zhiliang Ying, 2018. "Hypothesis Testing of the Q-matrix," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 515-537, September.
    9. 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.
    10. Juntao Wang & Yuan Li, 2023. "DINA Model with Entropy Penalization," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    11. Yinghan Chen & Steven Andrew Culpepper & Yuguo Chen & Jeffrey Douglas, 2018. "Bayesian Estimation of the DINA Q matrix," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 89-108, March.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Jimmy de la Torre & Xue-Lan Qiu & Kevin Carl Santos, 2022. "An Empirical Q-Matrix Validation Method for the Polytomous G-DINA Model," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 693-724, June.
    17. 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.
    18. Steven Andrew Culpepper, 2023. "A Note on Weaker Conditions for Identifying Restricted Latent Class Models for Binary Responses," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 158-174, March.
    19. Yinghan Chen & Steven Andrew Culpepper & Yuguo Chen, 2023. "Bayesian Inference for an Unknown Number of Attributes in Restricted Latent Class Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 613-635, June.
    20. Yinyin Chen & Steven Culpepper & Feng Liang, 2020. "A Sparse Latent Class Model for Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 85(1), pages 121-153, March.

    More about this item

    Keywords

    Q-matrix; DINA; RRUM; CDM;
    All these keywords.

    Statistics

    Access and download statistics

    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:jmathe:v:9:y:2021:i:23:p:3062-:d:690238. 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.