一种多级评分的认知诊断模型：P-DINA模型的开发

当前绝大多数认知诊断计量模型仅适用于0-1评分数据资料, 大大限制了认知诊断在实际中的应用, 也限制了认知诊断的进一步推广和发展。本文对具有较好发展前景的DINA模型进行拓展, 开发出适合多种评分(含0-1二级评分和多级评分)数据资料的P-DINA模型, 同时采用MCMC算法实现模型参数的估计, 并对该模型性能进行研究。结果表明：(1)本文开发的P-DINA模型无论是在无结构型属性层级关系下还是在结构型属性层级关系下, 参数估计的精度均较高, 参数估计的稳健性较强, 说明开发的P-DINA模型基本合理、可行。(2)P-DINA模型可采用MCMC算法实现参数估计, 且参数估计的精度较高。(3)整体来看, 无结构型属性层级关系和结构型属性层级关系下, P-DINA模型在项目参数的估计精度上两者基本相当; 但在被试属性判准率(MMR和PMR)上无结构型属性层级关系表现的稍差一些。(4)无结构型属性阶层关系下：模型诊断的属性个数越多, 参数 估计的精度越差、属性诊断的正确率(MMR和PMR)越低, 但参数 的估计精度越好; 若想保证属性模式判准率在80%以上, 建议诊断的属性个数不宜超过7个。总之, 本研究为拓展认知诊断在教育学和心理学中的应用提供了一种新方法、新模型。

A Polytomous Cognitive Diagnosis Model: P- DINA Model

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.