基于属性掌握概率的认知诊断计算机化自适应测验选题策略

Item Selection Strategies Based on Attribute Mastery Probabilities in CD-CAT

在认知诊断计算机化自适应测验(CD-CAT)中,被试对每个属性的掌握概率更直接地反映了被试能力的当前估计值。因此,基于被试的属性掌握概率来构建选题策略,选择最能改变被试属性掌握概率的题目作为下一个测验项目,这应该是一个值得尝试的方案。本文借鉴已有相关研究的数据生成模式进行探索,模拟实验结果表明:假设属性间相互独立,在定长(长度为16)、变长(长度为16或后验属性掌握模式概率达到0.8)以及短测验(长度分别为4、6、8、10)的情况下,基于属性掌握概率的选题策略PPWKL和PHKL有较好的分类准确率,在题目曝光率,题库使用均匀性等方面也有较好的表现;与研究较多的PWKL、HKL等策略相比,也略有优势;当属性间存在不同程度的相关时,在定长、变长以及较短的测验条件下,基于PHKL和MI的测验对知识状态估计精度较好,基于PPWKL和PHKL的测验综合表现占优。

Cognitive diagnostic computerized adaptive testing（CD-CAT） is a popular mode of online testing of cognitive diagnostic assessment（CDA）. The key to a CD-CAT system is the item selection strategies. Someof the popular strategies are developed based on Kullback-Leibler information（KL）, Shannon entropy（SHE） toselect items in CD-CAT. Typically, during CD-CAT, thesefamiliar methods would use a cutoff point to transform the attribute mastery probabilities＇ provisional value to binary values, but at the initial stage, the cutoff point method may lead to a larger deviation. A method that can take advantage of the probabilistic information with regard to attributes may offer a better alternative. This paper proposed two item selection strategies based on the provisional value of the attribute mastery probabilities, as follows：（1） the first strategy, which is called as PPWKL（Posterior Probability WeightedKullback-Leibler）, is based on the KL information, and it can lead to maximum difference of the sum of attribute mastery probabilities, and it is weighted bythe pattern＇s posterior probability as well asthe difference of the attribute mastery probabilities between the ？？ and any possible latent state;（2） the PPWKL considers the fact that not all the patterns are equally likely, but overlooks the fact that the distances between different patterns and the current estimate are not all of equal importance. Therefore, the PPWKL can be weighed by the inverse of the distance between the ？？ and any possible latent state, which is called as PHKL（Posterior Hybrid KullbackLeibler）. Then, three simulation studies were carried out, one was the fixed length of CD-CAT, and the secondwas the variant length CD-CAT, and the last wasshort length CD-CAT.Variant item selection strategiesweretaken intoconsideration in these studies, including KL, SHE, PWKL, HKL, MI, PPWKL and PHWKL. The results were compared in terms of pattern or attribute classification correct rate, itemaverage exposure ratio, item maximum exposure ratio, item minimum exposure ratio, average test length, unused item number, number of items with exposure ratioover 20%, test overlap ratio.The simulation results indicate that：（1） the comprehensive performance of PPWKL and PHKLare better than other mentioned strategies in fixed and variant length CD-CAT; as to PHKL and MI, each has different strengths in short length CD-CAT;（2） PHKL and PPWKL can retain a good measurement accuracy, and also improve the utilization ratio of item pool.