基于可达阵的一种Q矩阵标定方法  

A Method for Q-Matrix Specification based on the Reachability Matrix

作　　者：汪文义[1] 宋丽红[2] 丁树良[1] Wang Wenyi;Song Lihong;Ding Shuliang(School of Computer and Information Engineering,Jiangxi Normal University,Nanchang,330022;Elementary Educational College,Jiangxi Normal University,Nanchang,330022)

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

出　　处：《心理科学》2018年第4期968-975,共8页Journal of Psychological Science

基　　金：国家自然科学基金项目(31500909;31360237;31160203);全国教育科学规划教育部重点课题(DHA150285);江西省自然科学基金项目(20161BAB212044);江西省社会科学规划项目(17JY10);江西省教育科学2013年度一般课题(13YB032);国家社会科学基金项目(16BYY096);江西师范大学青年成长基金;江西师范大学博士启动基金的资助

摘　　要：Q矩阵标定是实施认知诊断评估的前提,已有Q矩阵修正方法并不太适合测验中已知属性向量的题目数较少的情形。根据拓展Q矩阵理论中可达阵R列与简化Q阵列存在布尔"或"关系,在一定认知假设下,率先提出可达阵R与简化Q阵的潜在反应列存在布尔"与"关系,并由此提出基于可达阵的Q矩阵标定方法。研究显示:在已知一个可达阵下,当可达阵项目的猜测或失误参数在.20以下且待标定项目的项目参数约在.30以下时,新方法所得Q矩阵元素返真率基本在.90以上,并且真实Q矩阵与估计Q矩阵下被试分类准确率差异很小;对于含5个属性的独立结构,新方法要求的随机样本的样本量较小;实证研究也印证了模拟研究的结论。新方法只需专家标定少量题目的 Q矩阵,即已经标定的Q矩阵对应属性层级结构的可达阵。Cognitive diagnostic assessment has two phases, like a statistical pattern recognition and classification methodology. The first phase is the feature generation, followed by a classification stage. Q-matrix corresponds to the feature generation phase in statistical pattern recognition. Feature generation is of paramount importance in any pattern recognition task. Therefore, Q-matrix plays a very important role in establishing a relation between latent attribute patterns and ideal response patterns. In practice, a Q-matrix is difficult to specify correctly in cognitive diagnostic assessment and misspecification of the Q-matrix can seriously affect the accuracy of both item parameter estimates and the classification of examinees. The existing methods including the δ method, the γ method, the Q-matrix refinement method, and maximum likelihood estimation method rely on estimates of examinees＇ attribute patterns and its classification accuracy. It is not suitable for the case of a test with a short test length because the short test is seldom used to obtain high classification accuracy.The purpose of this study is to propose a method for Q-matrix specification. We assume that a cognitive requirement for multiple skills within an item is conjunctive-that is, answering the item correctly requires mastery of all the skills required by that item. We consider two expected or ideal response matrices, denoted by ERMQ and ERMR. ERMQ or ERMR can be generated from a reduced Q-matrix or a reachability matrix and the universal set of attribute patterns under the conjunctive assumption. Then any column of the ERMQ can be expressed by the columns of the ERMR under the logical AND operation. This is because the augment algorithm in the generalized Q-matrix theory provides the useful fact that any column of the reduced Q-matrix can be expressed by the columns of the reachability matrix under the logical OR operation.A simulation study was conducted to investigate the performance of the new method under three factors（sample size

关 键 词：认知诊断评估 拓展Q矩阵理论 可达阵 扩张算法 Q矩阵标定方法 

分 类 号：B842.1[哲学宗教—基础心理学]