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Peida Zhan1, Hong Jiao2, Manqian Liao2

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This study introduces a new Bayesian approach to model within-item characteristic dependency (WICD) in the DINA model, improving parameter estimation accuracy and efficiency for cognitive diagnosis.

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Cognitive Diagnosis

Background:

  • Current deterministic inputs noisy "and" gate (DINA) models often overlook within-item characteristic dependency (WICD).
  • WICD refers to dependencies among different item characteristic parameters within a single item.
  • Ignoring WICD can lead to suboptimal parameter estimation in cognitive diagnosis models.

Purpose of the Study:

  • To develop and evaluate a modified Bayesian DINA model that explicitly accounts for WICD.
  • To assess the impact of modeling WICD on the accuracy, precision, and efficiency of parameter estimation.
  • To demonstrate the robustness of the proposed approach in the presence of item blocks.

Main Methods:

  • Proposed a modified Bayesian DINA model incorporating a bivariate normal distribution for correlated item parameters.
  • Employed simulation studies to evaluate model performance under various conditions.
  • Applied the model to fraction subtraction data to illustrate practical application.

Main Results:

  • The modified Bayesian DINA model successfully recovered model parameters.
  • Explicitly modeling WICD significantly improved the accuracy, precision, and efficiency of parameter estimation.
  • The proposed approach maintained good performance and robustness even with potential item blocks.

Conclusions:

  • Explicitly modeling within-item characteristic dependency (WICD) enhances the estimation of parameters in the DINA model.
  • The proposed Bayesian approach offers a more accurate and efficient method for cognitive diagnosis.
  • This methodology provides a valuable tool for analyzing complex item structures in educational and psychological assessments.