Cognitive Diagnosis Testlet Model for Multiple-Choice Items

The testlet design is very popular in educational and psychological assessments. This article proposes a new cognitive diagnosis model, the multiple-choice cognitive diagnostic testlet (MC-CDT) model for tests using testlets consisting of MC items. The MC-CDT model uses the original examinees' responses to MC items instead of dichotomously scored data (i.e., correct or incorrect) to retain information of different distractors and thus enhance the MC items' diagnostic power. The Markov chain Monte Carlo algorithm was adopted to calibrate the model using the WinBUGS software. Then, a thorough simulation study was conducted to evaluate the estimation accuracy for both item and examinee parameters in the MC-CDT model under various conditions. The results showed that the proposed MC-CDT model outperformed the traditional MC cognitive diagnostic model. Specifically, the MC-CDT model fits the testlet data better than the traditional model, while also fitting the data without testlets well. The findings of this empirical study show that the MC-CDT model fits real data better than the traditional model and that it can also provide testlet information.