Q矩阵理论的扩展

Extension to Tatsuoka's Q Matrix Theory

对Q矩阵理论及其改进、拓展进行了简略的回顾。给出基本矩阵的概念,针对两个属性之间存在多条路径的这种层级结构,提出将基本矩阵作为测验蓝图的子矩阵以提高认知诊断准确率;在某种期望反应得分模式下,讨论多级评分的认知诊断测验蓝图的设计问题,给出了知识状态和期望反应模式一一对应的充分条件。

Tatsuoka＇ s Q matrix theory and its modification and extension were reviewed briefly. In order to describe the situation that there is a pair of attributes and at least there are two roads connected with them, the concept of basic matrix, which included the reach- ability matrix,is proposed. The test Q matrix is a mapping from the set of knowledge states to the set of the expected response patterns. For a kind of polytomous scoring,we proposed a principle of the design of the test blueprint. The principle is that the rank of the test Q matrix equals to the number of the attributes, the mapping, determined by the test Q matrix,is one -to -one and onto under the scoring mode. It should be noted that this condition is a sufficient only.