可达阵功能的不可替代性

The Irreplaceability of a Reachability Matrix

可达阵有2个重要性质:(i)Q矩阵中的列均可由可达阵的列线性表示;(ii)在0-1评分、属性之间作用不可相互补偿条件下,若可达阵(或者其列的置换)是测验Q矩阵的子矩阵,则任何2个不同的属性掌握模式(知识状态)对应的理想反应模式仍然不同.在Q矩阵当中,是否有其他的K阶子矩阵,具有其中1个或者2个性质?这对于认知诊断测验蓝图设计和计算机自适应诊断测验(CD-CAT)的选题策略的制定非常重要.但是,十分遗憾,可以证明这2个性质都不可以由其他Q矩阵代替.在一定条件下必要Q矩阵才能够表示知识结构,才能够提高认知诊断测验的构念效度.

A reachability matrix R has two important properties： one is that any column in Q matrix can be expressed by a linear combination of the columns of R with the combination coefficients being 1 or 0,the other is that under the conditions of 0-1 scoring rubric and the noncompensatory among the attributes,if R（ or a permutation of its columns） is a sub-matrix of the test Q matrix,then the ideal response patterns corresponding to any two different knowledge states are different. It is proved that these properties of R are irreplaceability,i. e.,any other Q matrix does not have one of these properties. A counterexample is provided to explain that the concept of necessary Q matrix instead of the concept of sufficient Q matrix can promote the construct validity.