IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v81y2016i4d10.1007_s11336-016-9534-9.html
   My bibliography  Save this article

Joint Maximum Likelihood Estimation for Diagnostic Classification Models

Author

Listed:
  • Chia-Yi Chiu

    (Rutgers, The State University of New Jersey)

  • Hans-Friedrich Köhn

    (University of Illinois at Urbana-Champaign)

  • Yi Zheng

    (Arizona State University)

  • Robert Henson

    (University of North Carolina)

Abstract

Joint maximum likelihood estimation (JMLE) is developed for diagnostic classification models (DCMs). JMLE has been barely used in Psychometrics because JMLE parameter estimators typically lack statistical consistency. The JMLE procedure presented here resolves the consistency issue by incorporating an external, statistically consistent estimator of examinees’ proficiency class membership into the joint likelihood function, which subsequently allows for the construction of item parameter estimators that also have the consistency property. Consistency of the JMLE parameter estimators is established within the framework of general DCMs: The JMLE parameter estimators are derived for the Loglinear Cognitive Diagnosis Model (LCDM). Two consistency theorems are proven for the LCDM. Using the framework of general DCMs makes the results and proofs also applicable to DCMs that can be expressed as submodels of the LCDM. Simulation studies are reported for evaluating the performance of JMLE when used with tests of varying length and different numbers of attributes. As a practical application, JMLE is also used with “real world” educational data collected with a language proficiency test.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:4:d:10.1007_s11336-016-9534-9
    DOI: 10.1007/s11336-016-9534-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-016-9534-9
    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/s11336-016-9534-9?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. 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. George B. Macready & C. Mitchell Dayton, 1977. "The Use of Probabilistic Models in the Assessment of Mastery," Journal of Educational and Behavioral Statistics, , vol. 2(2), pages 99-120, June.
    3. Brian Junker, 1991. "Essential independence and likelihood-based ability estimation for polytomous items," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 255-278, June.
    4. 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.
    5. 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.
    6. 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.
    7. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    8. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Haoran Zhang & Yunxiao Chen & Xiaoou Li, 2020. "A Note on Exploratory Item Factor Analysis by Singular Value Decomposition," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 358-372, June.
    3. Zhang, Haoran & Chen, Yunxiao & Li, Xiaoou, 2020. "A note on exploratory item factor analysis by singular value decomposition," LSE Research Online Documents on Economics 104166, London School of Economics and Political Science, LSE Library.
    4. Yunxiao Chen & Xiaoou Li & Siliang Zhang, 2019. "Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 124-146, March.

    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, 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. 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. 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.
    4. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.
    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. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:81:y:2016:i:4:d:10.1007_s11336-016-9534-9. 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.