基于Q矩阵和广义距离的认知诊断方法

A Cognitive Diagnosis Method Based on Q-Matrix and Generalized Distance

规则空间方法(RSM)和属性层级方法(AHM)是两种重要的认知诊断方法,近年来受到了广泛关注。本文在属性层级方法和丁树良等人(2009,2010)改进的Q矩阵理论的基础上,通过定义观察反应模式与理想反应模式之间的广义距离,给出了一种识别被试知识状态的认知诊断方法,即广义距离判别法。通过DINA模型生成被试的作答反应矩阵进行模拟研究,以模式判准率和属性判准率作为衡量被试知识状态分类准确率指标,将广义距离判别法、RSM和AHM的分类A方法分别与DINA模型进行比较。结果表明,本文提出的广义距离判别法具有更好的分类效果。

In recent years,cognitive diagnosis research has become a popular issue in psychological and educational measurement.Researchers are always challenging the problem how to develop a Cognitive Diagnosis Model（CDM） that has promising performance for respondent classification.Although many researchers gave some theoretical framework or structures to classify the existing CDMs,systematic comparisons of those CDMs from the aspect of classification accuracy has not been given,except for that between RSM and AHM（e.g.,Zhu,Deng,Zhou, Ding,2008）.This article introduces a new approach called Generalized Distance Discrimination（GDD）,based on the compliment of Q-matrix theory（Tatsuoka,1991） by Leighton et al.（2004） and Ding et al.（2009,2010）.Specifically,GDD develops a type of generalized distance which measures the similarity between an Observed Response Pattern（ORP） and an Expected Response Pattern（ERP）,and this method uses the IRT-based item response probability of an examinee as the weight of Hamming Distance between his ORP and an ERP.Furthermore,Monte Carlo simulation study is used to compare classification accuracy for respondents of GDD with that of RSM and AHM.The two methods are chosen to do the comparison with GDD due to their representative status in CDMs and being widely used and discussed by many researchers.In the simulation study,the pattern match ratio and average attribute match ratio are used as criterions to evaluate the classification accuracy of different approaches.Under four attribute hierarchical structures used in AHM of Leighton et al.（2004）,four kinds of Q-matrix with 6 attributes were simulated individually.Then,Under each type of Q-matrix,we use four kinds of combination of slip and guess parameters in DINA model（i.e.,s=g=2%,5%,10%,15%） to simulate ORPs of examinees with a sample size of 1000.As a matter of fact,because the simulation data here are generated from DINA model,the goodness of fit of the model will be good,i.e.,DINA model will have high classification accuracy to the simulated examinees.Then,we use DINA model as a comparison baseline to check the performance among GDD,RSM and AHM under 16 different conditions.The result shows that GDD and DINA model perform almost equally,and they both perform better than RSM and AHM significantly.In conclusion,this study proves that the Generalized Distance Discrimination performs better than AHM and RSM from the aspect of classification accuracy,and GDD as a new CDM is recommended to be used into practice in future.