多级评分认知诊断测验蓝图的设计——根树型结构

Design of Polytomous Cognitively Diagnostic Test Blueprint ——For the Rooted Tree Type

在某种给定的评分方式下,假设属性之间没有补偿作用,讨论多级评分认知诊断测验蓝图设计问题.根据图论,将J.P.Leighton等定义的线型、发散型、无结构型属性层级结构归结为根树型,构造出相应的完备测验Q阵,即是使知识状态与期望反应模式一一对应,且列数最少的测验Q阵.完备Q矩阵均受到测验Q阵的秩的制约.

Giving a polytomous scoring rule, suppose that there is no compensation among the attributes, for the rooted tree type （RTT） which concludes the linear type ,the divergent type and the unstructured type named by Leighton and her colleagues, the design of polytomous cognitively diagnostic test blueprint is discussed in this paper. The concepts of basic perfect Q matrix and perfect Q matrix are given. A perfect Q matrix is the Q matrix which contains the fewest columns and is the bijective mapping between the set of knowledge states and the set of the expected response patterns. The perfect Q matrix corresponding to the RTT and for polytomous scoring is proposed and proved. The number of the items in the perfect Q matrices is equal to the number of the leaves in the rooted tree and is restricted by the rank of the Q matrix. It is obvious that there is a difference between the related results for dichotomous and polytomous, respectively.