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.