基于加权距离的一种认知诊断方法
The Generalized Cognitive Diagnosis Method Based on Weighted Distance

马氏距离判别方法(MDD)是一种新的认知诊断分类方法,广义距离判别方法(GDD)和海明距离判别方法(HDD)为它的特例.使用香农熵作为马氏距离的权重矩阵,根据距离最小原则将被试的观察反应模式分类到理想反应模式,再由特殊的测验设计,将理想反应模式一一对应到知识状态上.蒙特卡洛模拟研究表明:在0-1评分模型下,选择模式匹配率和平均属性匹配率作为评价分类效果的标准,MDD的分类效果好于GDD和HDD.
Cognitive diagnostic model(CDM)is an important part of cognitive diagnosis,the main aim for CDM is to discriminate examinees into different classes.Although there existed a lot of CDMs,researchers proposed many new CDMs still.Among them,the generalized distance discrimination(GDD)and the hamming distance discrimination(HDD)have some advantages,such as,simple and easy to use,high classification accuracy,thus receive more and more attention.Mahalanobis distance discrimination(MDD)is a generalized CDM,GDD and HDD are the special cases.Mahalanobis Distance(MD)is employed for MDD to calculate the distance between an examinee's Observed Response Pattern(ORP)and all kinds of Ideal Response Pattern(IRP),and specifies the Shannon Entropy as weight. According to the principle of minimum distance and special test design,IRP can be mapped one-to-one to the state of knowledge.Under binary scoring model,the pattern match ratio and average attribute match ratio were selected as the criteria for evaluating the classification accuracy,the Monte Carlo simulation study show that the performance of MDD was better than GDD and HDD