求解简化Q矩阵的扩张算法  

Augment algorithm for reduced Q-matrix

作　　者：杨淑群[1,2] 蔡声镇[3] 丁树良[4] 林海菁[4] 丁秋林[1] 

机构地区：[1]南京航空航天大学信息科学与技术学院 [2]福建师范大学软件学院,福建福州350007 [3]福建师范大学软件学院 [4]江西师范大学计算机信息工程学院

出　　处：《兰州大学学报（自然科学版）》2008年第3期87-91,96,共6页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金(60263005，60673014);福建省自然科学基金(2007J0178)资助．

摘　　要：认知诊断研究中常使用属性与项目的关联矩阵(Q矩阵),其中规则空间模型与属性层次方法涉及简化Q矩阵并给出求解简化Q矩阵的方法.从属性层次结构出发,给出了属性层次结构的可达矩阵与有效项目之间的关系及理论证明.基于向前回归的思想提出了求解简化Q矩阵的扩张算法,在考虑属性层次结构的有效项目数的基础上,与Tatsuoka方法进行了实验比较,并对属性个数为10的情况采用一元线性回归方法为两种方法建立了数学模型,模型中有效项目数为自变量,算法的运行时间为随机变量.经检验,回归效果显著.Attribute and item incidence matrix（i.e. Q-matrix） are usually used in cognitive diagnosis. Reduced Q-matrix from Q-matrix was considered in rule space model and attribute hierarchy method, and the method of acquiring Q-matrix was given. The relation between the reachability matrix and valid items in attribute hierarchy was studied with the graph theory. An augment algorithm for reduced Q-matrix was proposed based on the idea of forward regression, and was proved theoretically. Considering the number of valid items, the augment algorithm was compared with Tatsuoka＇s method upon running time. The number of valid items was regarded as the independent variable and running time as the random variable. Mathematical models with 10 attributes were built for the two algorithms by unitary linear regression analysis, and the testing indicates the regression effect is significant.

关 键 词：简化Q矩阵 扩张算法 有效项目数 线性回归 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] B841.2[自动化与计算机技术—计算机科学与技术]