一种高效的CD-CAT在线标定新方法:基于熵的信息增益与EM视角  

A high-efficiency and new online calibration method in CD-CAT based on information gain of entropy and EM algorithm

作　　者：谭青蓉 汪大勋 罗芬 蔡艳[1] 涂冬波[1] TAN Qingrong;WANG Daxun;LUO Fen;CAI Yan;TU Dongbo(School of Psychology,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学心理学院,南昌330022

出　　处：《心理学报》2021年第11期1286-1298,I0002,I0003,共15页Acta Psychologica Sinica

基　　金：国家自然科学基金项目(31760288,31960186,31660278)。

摘　　要：项目增补(Item Replenishing)对认知诊断计算机自适应测验(CD-CAT)题库的维护有着至关重要的作用,而在线标定是一种重要的项目增补方式。基于数据挖掘中特征选择(Feature Selection)的思路,提出一种高效的基于熵的信息增益的在线标定方法(记为IGEOCM),该方法利用被试在新旧题上的作答联合估计新题的Q矩阵和项目参数。研究采用Monte Carlo模拟实验验证所开发新方法的效果,并同时与已有的在线标定方法SIE、SIE-R-BIC和RMSEA-N进行比较。结果表明:新开发的IGEOCM在各实验条件下均具有较好的项目标定精度和项目估计效率,且整体上优于已有的SIE等方法;同时,IGEOCM标定新题所需的时间低于SIE等方法。总之,研究为CD-CAT题库中项目的增补提供了一种更为高效、准确的方法。Cognitive diagnostic computerized adaptive testing(CD-CAT)includes the advantages of both cognitive diagnosis(CD)and computerized adaptive testing(CAT),which can offer detailed diagnosis feedback for each examinee by applying fewer test items and time.It has been a promising field.An item bank is a prerequisite for the implementation of CD-CAT.However,its maintenance is a very challenging task.One of the effective ways to maintain the item bank is online calibration.Till now,there are only a few online calibration methods in the CD-CAT context that can calibrate Q-matrix and item parameters simultaneously.Moreover,the computational efficiency of these methods needs to be further improved.Therefore,it is crucial to find more online calibration methods that jointly calibrate the Q-matrix and item parameters.Inspired by the SIE(Single-Item Estimation)method proposed by Chen et al.(2015)and information gain feature selection criteria in feature selection,an information gain of entropy-based online calibration method(IGEOCM)was proposed in this study.The proposed method can jointly calibrate Q-matrix and item parameters in a sequential manner.The calibration process of the new items was described as follows:First,for the new item j,the q-vector can be calibrated by maximizing the information gain of entropy-based on the basis of the attribute patterns of examinees and the examinees’responses to item j.Second,the item parameters of the new item j are estimated by the EM algorithm based on the posterior distribution of examinees’attribute pattern,the examinees’responses to item j,and the q-vector estimated in the first step.The first and second step are repeated for all other new items to obtain their estimated Q-matrix and item parameters item by item.Two simulation studies were conducted to examine whether the IGEOCM could accurately and efficiently calibrate the Q-matrix and item parameters of the new items under different calibration sample sizes(40,80,120,160,and 200),different attribute pattern distributions

关 键 词：认知诊断计算机自适应测验 项目增补 在线标定 Q 矩阵 熵的信息增益 

分 类 号：B841[哲学宗教—基础心理学]