Cognitive diagnosis models for estimation of misconceptions analyzing multiple-choice data


Incorrect options for multiple-choice questions are often intentionally included so that they may be selected by an examinee who possesses a misconception. Determining whether an examinee possess a misconception is useful for educational purposes. In the present paper, two statistical models that can estimate examinees’ possession of misconceptions by analyzing multiple-choice data, which are unscored data were developed. By converting multiple-choice data to binary data, which are scored data (\(1=\) correct, \(0=\) incorrect), the Bug-DINO model can estimate examinees’ possession of misconceptions. However, converting multiple-choice data to binary data causes a loss in information, because which incorrect option an examinee chooses is important information for an examinee’s knowledge state. The three models (two developed models and the Bug-DINO model) are compared in a simulation study, and the developed models are applied to the Reading Skill Test data.

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This research was funded by Grant-in-Aid for Scientific Research(C) 18K03057.

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Correspondence to Koken Ozaki.

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Communicated by Russell George Almond.

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Ozaki, K., Sugawara, S. & Arai, N. Cognitive diagnosis models for estimation of misconceptions analyzing multiple-choice data. Behaviormetrika 47, 19–41 (2020).

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  • Multiple-choice item
  • Cognitive diagnosis model
  • Misconception
  • DINO model