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Estimation of Generalized DINA Model with Order Restrictions

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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.

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Authors and Affiliations

  1. National Taiwan Normal University, Taipei, Taiwan

    Chen-Yu Hong

  2. National Tsing-Hua University, Hsinchu City, Taiwan

    Yu-Wei Chang

  3. Department of Mathematics, National Taiwan Normal University, No. 88, Sec. 4, Ting-Chou Rd., Taipei, 116, Taiwan

    Rung-Ching Tsai

Authors
  1. Chen-Yu Hong
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  2. Yu-Wei Chang
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  3. Rung-Ching Tsai
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Corresponding author

Correspondence to Rung-Ching Tsai.

Additional information

We are grateful to Professor Jimmy de la Torre for providing us with the original Ox codes for DINA and G-DINA models. This research was supported by the National Science Council of Taiwan [grant number NSC 99-2410-H-003-021-MY3] and the Ministry of Science and Technology of Taiwan [grant number MOST 103-2410-H-003-020].

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Hong, CY., Chang, YW. & Tsai, RC. Estimation of Generalized DINA Model with Order Restrictions. J Classif 33, 460–484 (2016). https://doi.org/10.1007/s00357-016-9215-5

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  • DOI: https://doi.org/10.1007/s00357-016-9215-5

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