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

  • Koken OzakiEmail author
  • Shingo Sugawara
  • Noriko Arai
Original Paper


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.


Multiple-choice item Cognitive diagnosis model Misconception DINO model 



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

Supplementary material

41237_2019_100_MOESM1_ESM.pdf (200 kb)
Supplementary material 1 (pdf 200 KB)


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Copyright information

© The Behaviormetric Society 2019

Authors and Affiliations

  1. 1.Graduate School of Business SciencesUniversity of TsukubaTokyoJapan
  2. 2.National Institute of InformaticsTokyoJapan

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