Abstract: Almost all of cognitive diagnosis models are only adaptive for dichotomous data, which can not satisfy the demands in real work and limit the application and development of cognitive diagnosis. In this paper the dichotomous DINA model was extended to polytomous model, called P-DINA model, and MCMC algorithm was employed to estimate its parameters.
Monte Carlo method was used here to explore the feasibility of MCMC algorithm and to probe the estimated precision and the properties of P-DINA model. Three experiments were conducted. The former two experiments were performed under unstructured and structured attribute hierarchy with six cognitive attributes, 60 test items and 500 examinees. The target of these two experiments was to explore the feasibility of MCMC algorithm and the estimated precision of P-DINA model. The third experiment intended to study the properties of P-DINA model under unstructured attribute hierarchy with the number of cognitive attributes varying from 4 to 8.
Simulation results showed that: (1) Under P-DINA model, the estimated method of MCMC algorithm held fairly robustness, and the precision of item and person parameters was preferably great. Furthermore, the estimated precision of item parameters was similar between both attribute hierarchies, while the estimated precision of person parameters (MMR and PRM) under structured attribute hierarchy was better than those under unstructured attribute hierarchy. It indicated that the P-DINA model was reasonable and feasible; (2) Under unstructured attribute hierarchy: the estimated precision of slipping parameter, s, and the attribute match ration (MMR & PMR) decreased with the increase of the number of attributes, while the estimate precision of guessing parameter, g, was on the contrary. In real application, if PMR was asked to be higher than 80%, then the number of cognitive attributes was suggested not greater than seven.

Key words: cognitive diagnosis model, DINA model, polytomous DINA model, MCMC algorithm