基于主成分方法的集群数据因子模型的统计推断  

Statistical Inference of Clustered Data Factor Model Based on Principal Component Method

作　　者：陈博文 李亚磊 李兴平[1] CHEN Bo-wen;LI Ya-lei;LI Xing-ping(School of Mathematics,Yunnan Normal University,Kunming 650500,China)

机构地区：[1]云南师范大学数学学院,云南昆明650500

出　　处：《数学的实践与认识》2024年第2期250-256,共7页Mathematics in Practice and Theory

摘　　要：集群数据在神经科学与社会调查数据中广泛存在,备受统计学者关注.经典的因子分析方法常被用来刻画非集群数据下协变量之间的关联.集群数据中众多观测个体或变量之间的关联性却并未在因子模型框架下充分考虑.对集群数据建立因子分析模型,并通过主成分分析方法进行统计推断.随机模拟表明了模型和方法的有效性.实例分析对比了集群数据有内部关系与不考虑内部关系的情况,结果表明,考虑集群数据内部关系的效果更优.Clustered data is widely used in neuroscience and social investigation and has attracted much attention from statisticians.Classical factor analysis methods are often used to characterize the association between covariables in non-clustered data.However,the correlation between many observed individuals or variables in clustered data is not fully considered under the framework of factor model.In this paper,factor analysis model is established for clustered data,and statistical inference is made by principal component analysis method.The effectiveness of the method is demonstrated by random simulation.The case analysis compares the clustered data with internal relation and without internal relation.The result shows that considering internal relation of clustered data is better.

关 键 词：集群数据 因子分析模型 主成分分析法 对比研究 

分 类 号：O212.1[理学—概率论与数理统计]