应用多维项目反应理论模型探索分数减法测验的维度识别

Dimension Identification of A Fraction Subtraction Test Based on Multidimensional Item Response Theory Model

多维项目反应理论(MIRT)模型是国际教育统计与心理测量学研究的热点模型.在简要介绍一种常见的MIRT模型和数理统计学热门的变量筛选方法的基础上,针对教育统计研究者常用的分数减法测验数据进行测验题目的维度识别.通过分别使用传统的因子分析法、LASSO方法和弹性网方法分析测验数据,获得了测验题目的维度识别结果,并对它们的识别准确率进行比较.研究表明使用变量筛选方法尤其是LASSO方法能够较好地识别该测验的题目维度间隶属关系,为多维测验的维度识别提供可靠的信息.

Multidimensional item response theory （MIRT） has become a hot research issue in the field of psychological and educational assessment. By briefly introducing the popular M2PL model, the methods of LASSO and elastic net, this paper analyzed the real data of the fraction subtraction test introduced within the CDM package in R software. Specifically, this research applied factor analysis, LASSO and elastic net methods to identify dimensions of the real test items. The results showed that variable selection methods especially the LASSO can provide sufficient and reliable information to the dimension identification of the fraction subtraction test.