IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v88y2023i2d10.1007_s11336-022-09873-7.html
   My bibliography  Save this article

Commentary on “Extending the Basic Local Independence Model to Polytomous Data” by Stefanutti, de Chiusole, Anselmi, and Spoto

Author

Listed:
  • Chia-Yi Chiu

    (University of Minnesota)

  • Hans Friedrich Köhn

    (University of Illinois at Urbana-Champaign)

  • Wenchao Ma

    (University of Alabama)

Abstract

The Polytomous Local Independence Model (PoLIM) by Stefanutti, de Chiusole, Anselmi, and Spoto, is an extension of the Basic Local Independence Model (BLIM) to accommodate polytomous items. BLIM, a model for analyzing responses to binary items, is based on Knowledge Space Theory, a framework developed by cognitive scientists and mathematical psychologists for modeling human knowledge acquisition and representation. The purpose of this commentary is to show that PoLIM is simply a paraphrase of a DINA model in cognitive diagnosis for polytomous items. Specifically, BLIM is shown to be equivalent to the DINA model when the BLIM-items are conceived as binary single-attribute items, each with a distinct attribute; thus, PoLIM is equivalent to the DINA for polytomous single-attribute items, each with a distinct attribute.

Suggested Citation

  • Chia-Yi Chiu & Hans Friedrich Köhn & Wenchao Ma, 2023. "Commentary on “Extending the Basic Local Independence Model to Polytomous Data” by Stefanutti, de Chiusole, Anselmi, and Spoto," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 656-671, June.
  • Handle: RePEc:spr:psycho:v:88:y:2023:i:2:d:10.1007_s11336-022-09873-7
    DOI: 10.1007/s11336-022-09873-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-022-09873-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11336-022-09873-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Luca Stefanutti & Debora Chiusole & Pasquale Anselmi & Andrea Spoto, 2020. "Extending the Basic Local Independence Model to Polytomous Data," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 684-715, September.
    3. Hans-Friedrich Köhn & Chia-Yi Chiu, 2019. "Attribute Hierarchy Models in Cognitive Diagnosis: Identifiability of the Latent Attribute Space and Conditions for Completeness of the Q-Matrix," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 541-565, October.
    4. 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.
    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Yuqi Gu, 2023. "Generic Identifiability of the DINA Model and Blessing of Latent Dependence," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 117-131, March.
    6. Zhenke Wu & Livia Casciola‐Rosen & Antony Rosen & Scott L. Zeger, 2021. "A Bayesian approach to restricted latent class models for scientifically structured clustering of multivariate binary outcomes," Biometrics, The International Biometric Society, vol. 77(4), pages 1431-1444, December.
    7. 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.
    8. Hans-Friedrich Köhn & Chia-Yi Chiu, 2016. "A Proof of the Duality of the DINA Model and the DINO Model," Journal of Classification, Springer;The Classification Society, vol. 33(2), pages 171-184, July.
    9. Hans-Friedrich Köhn & Chia-Yi Chiu, 2018. "How to Build a Complete Q-Matrix for a Cognitively Diagnostic Test," Journal of Classification, Springer;The Classification Society, vol. 35(2), pages 273-299, July.
    10. Guanhua Fang & Jingchen Liu & Zhiliang Ying, 2019. "On the Identifiability of Diagnostic Classification Models," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 19-40, March.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    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. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Youn Seon Lim & Fritz Drasgow, 2019. "Conditional Independence and Dimensionality of Cognitive Diagnostic Models: a Test for Model Fit," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 295-305, July.

    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:spr:psycho:v:88:y:2023:i:2:d:10.1007_s11336-022-09873-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.