关键词: 认知诊断模型, HO-DINA模型, 多级评分HO-DINA模型, MCMC算法

Abstract: Almost all of cognitive diagnosis models are only adaptive for dichotomous items, which can not satisfy the demands in real work and become the bars of the application and development of cognitive diagnosis. This paper extended the dichotomous HO-DINA model to polytomous and used MCMC algorithm to estimate its parameters of polytomous HO-DINA model. To explore the feasibility of MCMC algorithm and the estimated precision, and to probe the properties of polytomous HO-DINA model, Monte Carlo method is used here. There are two experiments: (1) Fixed the number of cognitive attributes(6), of test items(60) and of examinees (500). The target of this experiment is to explore the feasibility of MCMC algorithm and the estimated precision. (2) This experiment intent to study the properties of polytomous HO-DINA model. In this experiment, the number of cognitive attributes varied with possible values of 4, 5, 6, 7, 8. Simulation results showed: (1)Under polytomous HO-DINA model ,the estimation method of MCMC algorithm holds fairly robustness, and it’s precision of item and ability parameters are preferably great. Which indicates the MCMC algorithm method is feasible; (2) The estimate precision of parameters, , and , and the attribute match ration (MMR & PRM) are decreasing with the increasing of the number of attributes, but the estimate precision of and parameters are on the contrary. (3)In real work, if PRM is asked to be higher than 80%, then the number of cognitive attributes is suggested not greater than seven.

Key words: Cognitive Diagnosis Model, High Order DINA Model, Polytomous HO-DINA model, MCMC Algorithm