基于属性掌握概率的认知诊断模型

The Attribute Mastery Probability Cognitive Diagnostic Model

认知诊断模型研究主要包括模型建构、模型性能评估及结果报告几个方面.用多维连续向量表示被试的属性掌握概率,并假设属性应用满足局部独立的条件下建构属性掌握概率认知诊断模型,然后运用马尔科夫链蒙特卡洛方法估计模型参数,模拟研究表明该算法的准确性和稳定性较好.最后,运用该模型分析分数减法数据的结果表明被试属性水平和项目参数的诊断结果与规则空间方法分析的结果一致,从而表明该模型是可信和有效的.

The research of cognitive diagnosis models mainly contains the following three subjects：the construction of diagnosis models,the assessment of the performance of cognitive models and the report of the diagnose results.The present study views students＇knowledge level as multi-dimensional continuous vectors and supposes the application of attributes are independent with each other.Then the attribute mastery probability model is put forward on the basis of the above suppositions.Markov chain Monte Carlo algorithms for parameter estimation are given for estimating model parameters.The results of simulation study demonstrated that the parameters could be accurately and stably estimated.Further,an analysis of fraction subtraction response data is provided.The results of students＇ attribute mastery levels obtained by using the proposed model are in consistence with those produced by the rule space method which indicates the reliability and validity of the attribute mastery probability model.