基于属性界定的认知诊断Q矩阵估计方法研究

发布时间：2018-05-12 01:02

本文选题：认知诊断评估 + Q矩阵估计　；参考：《华中师范大学》2017年硕士论文

【摘要】：认知诊断以微观认知视角对学生的学习过程做出科学的准确评估,已经在心理学和教育数据挖掘领域中发挥了巨大潜力。然而目前应用认知诊断理论编制的测验有限,其主要困难是反映项目和属性间关系的Q矩阵无法合理界定。构建正确的Q矩阵是认知诊断实践中的关键环节,是认知诊断测验理论不同于传统测量理论的本质所在。Q矩阵的界定一般是由领域专家和心理测量学家基于诊断目的,通过讨论共同完成。但是这种方式存在着界定成本高、主观性较强以及专家意见不一致等问题。因此,认知诊断亟需研究更加客观地估计Q矩阵的方法,近年来这方面成为国内外学者关注的焦点,相继研究出一系列的估计方法。本论文在研究了一些经典Q矩阵估计方法的基础上,主要针对经典Barnes爬山法搜索能力差和易陷入局部极值的缺陷,提出利用全局优化搜索的遗传算法改进经典爬山法,实现Q矩阵的估计,并提出借助DeCarlo贝叶斯法估计精度较高的优势对估计结果进一步优化。论文在模拟数据和真实数据集合上分别进行了实验验证,通过分析Q矩阵边际判准率MMR、差异距离DD和模型拟合指数等评价指标来研究新方法与其他方法估计性能的差异。模拟数据采用Xiang(2013)的方法生成,使用Monte Carlo模拟系统研究了测验学生人数、属性数目和项目总数等因素对各方法估计性能的影响。真实数据来源于经典的Tatsuoka分数减法和SAT测验,经过实验对比验证了算法的实用性。大量实验研究表明:在同等条件下,本文遗传算法的估计性能优于Barnes爬山法和非线性惩罚估计法,而贝叶斯法进一步优化后的Q矩阵更加接近于真实Q矩阵,明显提升了估计精度。
[Abstract]:Cognitive diagnosis has played a great potential in the field of psychology and educational data mining to make a scientific and accurate assessment of students' learning process from the perspective of micro-cognition. However, there are limited tests compiled by cognitive diagnostic theory, the main difficulty of which is that the Q matrix, which reflects the relationship between items and attributes, cannot be reasonably defined. Constructing a correct Q matrix is a key link in the practice of cognitive diagnosis. It is the essence of cognitive diagnostic test theory that is different from traditional measurement theory. The definition of Q matrix is generally based on the diagnostic purpose by domain experts and psychometrists. To complete together through discussion. But there are some problems in this way, such as high definition cost, strong subjectivity and different opinions of experts. Therefore, cognitive diagnosis needs to study the methods of estimating Q matrix more objectively. In recent years, researchers at home and abroad have paid close attention to this aspect, and a series of estimation methods have been developed one after another. In this paper, based on the study of some classical Q matrix estimation methods, the classical Barnes mountain climbing algorithm is proposed to improve the classical mountain climbing method by using the genetic algorithm with global optimization, which is poor in searching ability and easy to fall into local extremum. The estimation of Q matrix is realized, and the DeCarlo Bayesian method is proposed to further optimize the estimation results. In this paper, experiments are carried out on the set of simulation data and real data, and the performance difference between the new method and other methods is studied by analyzing the evaluation indexes such as the marginal accuracy rate of Q matrix MMRs, difference distance DD and model fitting index. The Monte Carlo simulation system was used to study the effects of the number of students, the number of attributes and the total number of items on the estimation performance of each method. The real data come from the classical Tatsuoka score subtraction and SAT test. A large number of experiments show that under the same conditions, the estimation performance of genetic algorithm in this paper is better than that of Barnes mountain climbing method and nonlinear penalty estimation method, and the Q matrix after further optimization by Bayesian method is closer to the real Q matrix. The estimation accuracy is obviously improved.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：B842.1;TP311.13

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