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Estimation of Generalized DINA Model with Order Restrictions

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  • Chen-Yu Hong

    (National Taiwan Normal University)

  • Yu-Wei Chang

    (National Tsing-Hua University)

  • Rung-Ching Tsai

    (National Taiwan Normal University)

Abstract

Cognitive diagnostic models provide valuable information on whether a student has mastered each of the attributes a test intends to evaluate. Despite its generality, the generalized DINA model allows for the possibility of lower correct rates for students who master more attributes than those who know less. This paper considers the use of order-constrained parameter space of the G-DINA model to avoid such a counter-intuitive phenomenon and proposes two algorithms, the upward and downward methods, for parameter estimation. Through simulation studies, we compare the accuracy in parameter estimation and in classification of attribute patterns obtained from the proposed two algorithms and the current approach when the restricted parameter space is true. Our results show that the upward method performs the best among the three, and therefore it is recommended for estimation, regardless of the distribution of respondents’ attribute patterns, types of test items, and the sample size of the data.

Suggested Citation

  • Chen-Yu Hong & Yu-Wei Chang & Rung-Ching Tsai, 2016. "Estimation of Generalized DINA Model with Order Restrictions," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 460-484, October.
    • Handle: RePEc:spr:jclass:v:33:y:2016:i:3:d:10.1007_s00357-016-9215-5
    DOI: 10.1007/s00357-016-9215-5
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    References listed on IDEAS

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    1. 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.
    2. El Barmi, Hammou & Johnson, Matthew, 2006. "A unified approach to testing for and against a set of linear inequality constraints in the product multinomial setting," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1894-1912, September.
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    Cited by:

    1. 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.

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