第八章因子分析新.ppt

第八章 因子分析 因子分析的目的与类型 探索性因子分析的模型 因子模型的求解 因子旋转 因子得分 因子分析的SPSS实现 实例分析 确认性因子分析 Origins of Factor Analysis Origins of Factor Analysis Wanted to estimate intelligence of 24 children in a village school. Realized way of measuring intelligence was imperfect and that the correlation between any two variables (say, one’s score on a mathematics exam and on a classics exam) would be underestimated. Noticed that the observed correlations between the variables he was interested in were all positive and followed a pattern. Spearman wanted to develop a model that would reflect the pattern he saw. What did Spearman notice? two-factor theory of intelligence Could model each test score as having two types of components: one common to all the scores and one specific to the particular test f: available to the same individual to the same degree for all intellectual acts ?: varies in strength from one act to another If one knows how a person performs on one task that is highly saturated with “f, one can safely predict a similar level of performance for a another highly “f saturated task. the most important information to have about a persons intellectual ability is an estimate of their “f Schematically Goals of Factor Analysis model correlation patterns in useful way 通过对多个变量的相关系数矩阵的研究，找出同时影响或支配多个变量的共性因素。 allow for contextual interpretation of the new variables evaluate the original data in light of the new variables 实例1 考查人体的五项生理指标：收缩压、舒张压、心跳间隔、呼吸间隔和舌下温度。 从生理学知识可知，这五项指标是受植物神经支配的，植物神经又分为交感神经和负交感神经，因此这五项指标至少受到两个公共因子的影响，也可用因子模型去处理。 五项指标均可观测，而两个公共因子是不可直接观测的：通过指标与公共因子的关系诊病。 实例2 林登根据他收集的来自139名运动员的比赛数据，对第二次世界大战以来奥林匹克十项全能比赛的得分作了因子分析研究。这十个全能项目为： 100米跑x1、跳远x2、铅球x3、跳高x4、400米跑x5、110米跨栏x6、铁饼x7、撑杆跳x8、标枪x9、1500米跑x10 对10个变量标准化后的因子分析表明，十项得分基本上可归结于他们的短跑速度、爆发性臂力、爆发性腿力和耐力这四个方面，每一方面都称为一个公共因子。 因子分析的类型 探索性因子分析exploratory Factor Analysis 根据变量间相关关系探索因子结构 实例2 确认性因子分析Confirmatory Factor Analysis 检验对因子结构的先验认识是否合理，评估因子模型的拟合程度 实例1 二、探索性因子分析模型 正交因子模型 重要假设 因子载荷阵的统计意义 1. 正交因子模型 一般因子模型：反映了各变量与公共因子的关系 因子模型 十项全能例 2.