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Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies

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  • Jonathan Templin
  • Laine Bradshaw

Abstract

Although latent attributes that follow a hierarchical structure are anticipated in many areas of educational and psychological assessment, current psychometric models are limited in their capacity to objectively evaluate the presence of such attribute hierarchies. This paper introduces the Hierarchical Diagnostic Classification Model (HDCM), which adapts the Log-linear Cognitive Diagnosis Model to cases where attribute hierarchies are present. The utility of the HDCM is demonstrated through simulation and by an empirical example. Simulation study results show the HDCM is efficiently estimated and can accurately test for the presence of an attribute hierarchy statistically, a feature not possible when using more commonly used DCMs. Empirically, the HDCM is used to test for the presence of a suspected attribute hierarchy in a test of English grammar, confirming the data is more adequately represented by hierarchical attribute structure when compared to a crossed, or nonhierarchical structure. Copyright The Psychometric Society 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:2:p:317-339
    DOI: 10.1007/s11336-013-9362-0
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    References listed on IDEAS

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    1. Jonathan Templin & Laine Bradshaw, 2013. "Measuring the Reliability of Diagnostic Classification Model Examinee Estimates," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 251-275, July.
    2. Maydeu-Olivares, Albert & Joe, Harry, 2005. "Limited- and Full-Information Estimation and Goodness-of-Fit Testing in 2n Contingency Tables: A Unified Framework," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1009-1020, September.
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    4. E. Maris, 1999. "Estimating multiple classification latent class models," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 187-212, June.
    5. Jimmy Torre, 2011. "Erratum to: The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 510-510, July.
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    Cited by:

    1. Juntao Wang & Yuan Li, 2023. "DINA Model with Entropy Penalization," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    2. 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.
    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. 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.
    5. 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.
    6. George, Ann Cathrice & Robitzsch, Alexander & Kiefer, Thomas & Groß, Jürgen & Ünlü, Ali, 2016. "The R Package CDM for Cognitive Diagnosis Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i02).
    7. Chun Wang, 2024. "A Diagnostic Facet Status Model (DFSM) for Extracting Instructionally Useful Information from Diagnostic Assessment," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 747-773, September.
    8. 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.
    9. 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.
    10. 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.
    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. Jonathan Templin & Laine Bradshaw, 2014. "The Use and Misuse of Psychometric Models," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 347-354, April.
    13. 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.
    14. 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.
    15. 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.
    16. Steven Andrew Culpepper & Yinghan Chen, 2019. "Development and Application of an Exploratory Reduced Reparameterized Unified Model," Journal of Educational and Behavioral Statistics, , vol. 44(1), pages 3-24, February.
    17. 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.
    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. Mona Tabatabaee-Yazdi, 2020. "Hierarchical Diagnostic Classification Modeling of Reading Comprehension," SAGE Open, , vol. 10(2), pages 21582440209, June.
    20. Chia-Yi Chiu & Hans-Friedrich Köhn, 2016. "Consistency of Cluster Analysis for Cognitive Diagnosis: The Reduced Reparameterized Unified Model and the General Diagnostic Model," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 585-610, September.
    21. 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.
    22. 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.
    23. 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.

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