基于多维名义反应模型的分类数据测验下新题的LASSO模式识别  

A LASSO-Based Pattern Recognition Method for Replenished Items Fitted by Multidimensional Nominal Response Model

作　　者：赵恒 孙佳楠[1] 邵明雨 ZHAO Heng;SUN Jia-nan;SHAO Ming-yu(College of Science,Beijing Forestry University,Beijing 100083,China)

机构地区：[1]北京林业大学理学院,北京100083

出　　处：《数理统计与管理》2024年第4期635-655,共21页Journal of Applied Statistics and Management

基　　金：国家自然科学基金青年科学基金项目(11701029);国家社科基金青年科学基金项目(20CSH075);湖南省教育科学“十四五”规划重点资助课题(XJK22AJC002)。

摘　　要：多维项目反应理论(MIRT)作为数理统计潜变量建模研究的一个分支,在国际测验研究领域具有重要地位。多维名义反应模型(MNRM)是MIRT中一种拟合多级评分题目的模型,用于开发具有分类数据的诊断型测验以实现对多维潜变量的测量。MNRM构建的纸笔或计算机化自适应测验是测验研究的热点之一;更新基于该模型的题库时函待解决新题的多维度自动识别问题,以确保参数估计、数据挖掘及诊断反馈的精度和安全性。本研究提出的基于LASSO的MNRM的测验新题模式识别方法简称LPRM-NR,能够对相应的纸笔测验及MCAT有效地解决新题的模式识别。本研究通过统计模拟考察LPRM-NR方法的模式识别效果,发现该方法在两类测验情境中,对能力参数不同维数及不同关联度的多种组合的最优识别准确率在77.18%至99.61%之间,模式识别效果良好且兼具易实施、低成本的优点。对纸笔测验情境进行的一项实证研究也表明提出方法的较好效果。LPRM-NR方法对基于MNRM的多维纸笔测验和新兴的MCAT,均具有很好的题库新增题目的模式识别效果,为分类测验的题目更新奠定了基础。Multidimensional item response theory(MIRT),a branch of mathematical and statistical latent variable modeling research,has an important position in the international testing research field.Multidimensional nominal response model(MNRM)is a typical polytomous-response model in MIRT for developing diagnostic tests with categorical data for valuable data mining of measurement targets in the form of multidimensional latent variables.Paper-and-pencil tests or computerized adaptive testing constructed based on the MNRM is one of the hotspots in testing research,which requires regular item replenishment of item pool;so the automatic item dimensional identification of replenished items should be addressed and solved to ensure the precise parameter estimation,good accuracy and security of the corresponding data mining and diagnostic information feedback.The proposed LPRM-NR,as a LASSO based pattern recognition method for the MNRM,can effectively recognized the item-trait patterns of multidimensional items for the item replenishment problem of the paper-and-pencil test or the MCAT.Simulation study investigated pattern recognition accuracy of the LPRM-NR,and showed its optimal correct specification rate reached 77.18%to 99.61%for various scenarios with respect to different dimensionalities and ability correlation conditions for the paper-pencil test and the MCAT.An empirical study under a paper-and-pencil test situation also showed good performance of the proposed method.Thus,the proposed method can accurately and effectively detect the item-trait patterns of replenished items,and has advantage of easy implementation with low cost.The LPRM-NR has good performance in pattern recognition accuracy and efficiency for replenished items from the MNRM-based multidimensional paper-and-pencil test and the MCAT,individually.The proposed method has laid a foundation for updating item pools.

关 键 词：LASSO 多维名义反应模型 题库新题的模式识别 多维纸笔测验 多维计算机化自适应测验 

分 类 号：O212[理学—概率论与数理统计] O212.4[理学—数学]