基于余弦相似度列置换的Q矩阵修正方法  

The Column Permutation for Q-Matrix Validation Method Based on Cosine Similarity

作　　者：汪文义[1] 许依纯 宋丽红[2] WANG Wenyi;XU Yichun;SONG Lihong(School of Computer and Information Engineering,Jiangxi Normal University,Nanchang Jiangxi 330022,China;School of Education,Jiangxi Normal University,Nanchang Jiangxi 330022,China)

机构地区：[1]江西师范大学计算机信息工程学院,江西南昌330022 [2]江西师范大学教育学院,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2024年第2期116-130,共15页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(62267004,62067005,61967009);江西省普通高校教育教学改革研究课题(JXJG-22-2-44)资助项目.

摘　　要：国内外研究者已开发出多种有效的Q矩阵修正方法,但当Q矩阵错误率较高时,仍存在修正效果不佳的问题.该文将基于塔克一致性系数和余弦相似度的列置换方法融入4种Q矩阵修正方法(GDI、Hull、MLR-B和stepwise)中,并借助Q矩阵向量和元素正确率等指标来评价新方法的修正效果.蒙特卡罗(Monte Carlo)模拟研究结果表明:在各种条件组合下,4种Q矩阵修正方法经过列置换后的修正效果得到明显提升,特别是当Q矩阵错误率较高时效果更加显著.Researchers have developed a variety of effective Q-matrix validation methods,but almost all of them have the problem that their performance is not very well when the proportion of misspecified elements in the Q-matrix is high.The column permutation method based on cosine similarity or Tucker′s congruence coefficient is proposed for Q-matrix validation.The Monte Carlo simulation study is conducted under different conditions and four Q-matrix validation methods(GDI,Hull,MLR-B and stepwise).The mean percentage of correct vector or entries of Q-matrix is calculated as evaluation criteria of recovery rates.The simulation results show that under various conditions combination,the column permutation for Q-matrix validation method can accurately identify misspecified Q-entries,especially when the high proportion of misspecified entries is involved in the Q-matrix.

关 键 词：Q矩阵修正 余弦相似度 列置换 正确率 

分 类 号：B841[哲学宗教—基础心理学] O212[哲学宗教—心理学]