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Consistency of Nonparametric Classification in Cognitive Diagnosis

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  • Shiyu Wang
  • Jeff Douglas

Abstract

Latent class models for cognitive diagnosis have been developed to classify examinees into one of the 2 K attribute profiles arising from a K-dimensional vector of binary skill indicators. These models recognize that response patterns tend to deviate from the ideal responses that would arise if skills and items generated item responses through a purely deterministic conjunctive process. An alternative to employing these latent class models is to minimize the distance between observed item response patterns and ideal response patterns, in a nonparametric fashion that utilizes no stochastic terms for these deviations. Theorems are presented that show the consistency of this approach, when the true model is one of several common latent class models for cognitive diagnosis. Consistency of classification is independent of sample size, because no model parameters need to be estimated. Simultaneous consistency for a large group of subjects can also be shown given some conditions on how sample size and test length grow with one another. Copyright The Psychometric Society 2015

Suggested Citation

  • Shiyu Wang & Jeff Douglas, 2015. "Consistency of Nonparametric Classification in Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 85-100, March.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:85-100
    DOI: 10.1007/s11336-013-9372-y
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    References listed on IDEAS

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    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.
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    4. Jimmy de la Torre, 2011. "The Generalized DINA Model Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 179-199, April.
    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 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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    Citations

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    Cited by:

    1. Shiyu Wang & Yan Yang & Steven Andrew Culpepper & Jeffrey A. Douglas, 2018. "Tracking Skill Acquisition With Cognitive Diagnosis Models: A Higher-Order, Hidden Markov Model With Covariates," Journal of Educational and Behavioral Statistics, , vol. 43(1), pages 57-87, February.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

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