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Using Neural Network Analysis to Define Methods of DINA Model Estimation for Small Sample Sizes

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  • Zhan Shu
  • Robert Henson
  • John Willse

Abstract

The DINA model is a commonly used model for obtaining diagnostic information. Like many other Diagnostic Classification Models (DCMs), it can require a large sample size to obtain reliable item and examinee parameter estimation. Neural Network (NN) analysis is a classification method that uses a training dataset for calibration. As a result, if this training dataset is determined theoretically, as was the case in Gierl’s attribute hierarchical method (AHM), the NN analysis does not have any sample size requirements. However, a NN approach does not provide traditional item parameters of a DCM or allow for item responses to influence test calibration. In this paper, the NN approach will be implemented for the DINA model estimation to explore its effectiveness as a classification method beyond its use in AHM. The accuracy of the NN approach across different sample sizes, item quality and Q-matrix complexity is described in the DINA model context. Then, a Markov Chain Monte Carlo (MCMC) estimation algorithm and Joint Maximum Likelihood Estimation is used to extend the NN approach so that item parameters associated with the DINA model are obtained while allowing examinee responses to influence the test calibration. The results derived by the NN, the combination of MCMC and NN (NN MCMC) and the combination of JMLE and NN are compared with that of the well-established Hierarchical MCMC procedure and JMLE with a uniform prior on the attribute profile to illustrate their strength and weakness. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Zhan Shu & Robert Henson & John Willse, 2013. "Using Neural Network Analysis to Define Methods of DINA Model Estimation for Small Sample Sizes," Journal of Classification, Springer;The Classification Society, vol. 30(2), pages 173-194, July.
    • Handle: RePEc:spr:jclass:v:30:y:2013:i:2:p:173-194
    DOI: 10.1007/s00357-013-9134-7
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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.
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    1. 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.
    2. Weikuan Jia & Dean Zhao & Ling Ding & Yuanjie Zheng, 2019. "A Reliable Small Sample Classification Algorithm by Elman Neural Network Based on PLS and GA," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 306-321, July.

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