[1]丁树良,汪文义,罗 芬,等.可达阵功能的不可替代性[J].江西师范大学学报(自然科学版),2016,40(03):290-294.
 DING Shuliang,WANG Wenyi,LUO Fen,et al.The Irreplaceability of a Reachability Matrix[J].,2016,40(03):290-294.
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可达阵功能的不可替代性()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
40
期数:
2016年03期
页码:
290-294
栏目:
出版日期:
2016-07-01

文章信息/Info

Title:
The Irreplaceability of a Reachability Matrix
作者:
丁树良汪文义罗 芬熊建华
江西师范大学计算机信息工程学院,江西 南昌 330022
Author(s):
DING ShuliangWANG WenyiLUO FenXIONG Jianhua
College of Computer Information Engineering,Jiangxi Normal University,Nanchang Jiangxi 330022,China
关键词:
可达矩阵 不可替代性 充分Q矩阵 必要Q矩阵
Keywords:
reachability matrix irreplaceability sufficient Q matrix necessary Q matrix
分类号:
B 841
文献标志码:
A
摘要:
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.
Abstract:
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.

参考文献/References:

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相似文献/References:

[1]丁树良,罗芬,汪文义,等.0-1和多值可达矩阵的性质及应用[J].江西师范大学学报(自然科学版),2015,(01):64.
 DING Shuliang,LUO Fen,WANG Wenyi,et al.The Properties of 0-1 and Polytomous Reach Ability Matrices and Their Applications[J].,2015,(03):64.

备注/Memo

备注/Memo:
收稿日期:2016-03-29基金项目:国家自然科学基金(31500909,31360237,31300876,31160203,31100756,30860084,11401271),教育部人文社会科学研究青年基金(13YJC880060)和江西省教育科学2013年度一般课题(13YB032)资助项目.作者简介:丁树良(1949-),男,江西樟树人,教授,主要从事计算辅助教学及教育和心理测量方面的研究.
更新日期/Last Update: 1900-01-01