基于KL信息矩阵的动态加权选题策略

Dynamic Posterior-Weighted Selection Strategy Based on the KL Information Matrix

在Henson和Douglas提出的KL信息矩阵(用D矩阵表示)基础上,借鉴后验加权的思想,将原始KL信息矩阵修正为后验加权KL矩阵,并基于认知诊断中项目区分度的计算方式,提出2种新的CD-CAT选题策略:DPWKL1和DPWKL2方法,在不同测验长度、不同诊断模型以及不同属性相关程度下,与传统PWKL方法进行了比较研究.模拟研究表明,不论实验条件如何变化,DPWKL1和DPWKL2方法的属性判准率及模式判准率均要优于PWKL方法.

Based on the KL information matrix（denoted as D matrix）proposed by Henson and Douglas（2005）,the posterior probabilities of the examinees＇knowledge state were integrated into the D matrix,and then the double posterior-weighted D matrix could be built.Meanwhile this study introduced two highefficiency KL-based item selection algorithms named posterior-weighted cognitive diagnostic index（DPWKL1）and posterior-weighted attribute-level CDI（DPWKL2）by modifying the two item discrimination indexes,the cognitive diagnostic index（CDI）and the cognitive diagnostic attribute-level discrimination index（ACDI）.To compare the two new methods with the PWKL method,this paper investigates the impact of three factors on both attribute correct classification rate（ACCR）and pattern correct classification rate（PCCR）：（1）different cognitive diagnostic models（including two models：the DINA model and the fusion model）;（2）different correlation among the attributes（including two levels：0and 0.5）;（3）different test length（including three size：5,10,and 15items）.In this paper,simulation study was conducted to investigate the efficiency of the DPWKL1 and DPWKL2methods.The results indicated that：Compare with the PWKL method,the two new methods had higher ACCR and PCCR values across all experimental conditions.