HO-GDINA模型的EM算法参数估计

发布时间：2018-02-17 08:58

  本文关键词： 认知诊断模型 HO-GDINA模型 EM算法 估计精度　出处：《心理学探新》2017年05期 　论文类型：期刊论文

【摘要】：Generalized DINA Model(G-DINA)为认知诊断模型提供了一个一般性的理论框架,而高阶诊断模型不仅能描述被试的总体水平,还能描述被试对属性的掌握情况(微观的认知状态)以及被试掌握属性与能力的关系,提供更丰富的信息。如果能把这两者结合起来,可能对实际诊断工作的操作有较大帮助。文章首先对考虑高阶结构的整合性模型——HO-GDINA模型的形式进行讨论,探讨其参数估计EM算法的实现,并用模拟过程对模型的估计精度进行研究,结果验证了HO-GDINA的EM算法的正确性,并且说明该算法对该模型有较高估计精确度。然后用饱和模型在约束条件下的特殊形式HO-DINA模型对"分数减法"这一经典数据进行EM算法参数估计和具体分析,展示了HO-GDINA在实际情况中的具体使用,并与de la Torre之前用MCMC估计算法得到的研究结果做比较,基本一致,进一步表明HO-GDINA模型的参数估计EM算法在实际情境中的特殊形式下仍然适用。
[Abstract]:Generalized DINA Model-G-DINA provides a general theoretical framework for cognitive diagnostic models, and higher-order diagnostic models can not only describe the overall level of subjects. It can also describe the subjects' mastery of attributes (micro-cognitive state) and the relationship between the attributes and the ability of the subjects, and provide more information. If the two can be combined, This paper discusses the form of HO-GDINA model considering higher order structure, and discusses the realization of EM algorithm for parameter estimation. The estimation accuracy of the model is studied by the simulation process, and the results show that the EM algorithm of HO-GDINA is correct. It is shown that the algorithm has a high estimation accuracy for the model. Then the EM algorithm parameter estimation and concrete analysis of the classical data of "fractional subtraction" are carried out by using the special form HO-DINA model of saturated model under constraint conditions. The application of HO-GDINA in practice is demonstrated and compared with the results obtained by MCMC estimation algorithm before de la Torre. It is further shown that the EM algorithm for parameter estimation of HO-GDINA model is still applicable in the special form of the actual situation.
【作者单位】： 北京第五中学分校;中国基础教育质量监测协同创新中心;中国教育大数据研究院;
【基金】：国家自然科学基金面上项目(31371047)
【分类号】：B842.1
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本文编号：1517697