用主成分分析法作多指标综合评价应该注意的问题  

Some Problems in Comprehensive Evaluation of the Principal Component Analysis

作　　者：吴殿廷[1] 吴迪[1] 

机构地区：[1]北京师范大学地理学与遥感科学学院,北京100875

出　　处：《数学的实践与认识》2015年第20期143-150,共8页Mathematics in Practice and Theory

基　　金：北京师范大学自主科研基金资助"京津冀生态文明建设的总体战略策略"成果

摘　　要：主成分分析法是一种很好的多指标综合评价方法,但须注意其适用性,也要对评价结果恰当地使用.如果样本太少,或者各变量之间的相关性很小,则不适合使用;涉及到动态的价值型的指标评价问题必须作不变价在处理;如果仅仅是进行排序评价则只用一个主成分得分进行评价即可;若还要进行其他方面的分析,则在选取主成分个数时,只能选取特征根大于1所对应主成分;计算各样本的主成分得分一定要采取变权的方式进行;在对各主成分进行命名和特征概括时要首先考察各变量在不同主成分载荷的绝对值大小,在此基础上选择同一主成分上载荷较大的变量主成分命名和特征概括;如果要做倍比分析,则要把各样本的主成分得分映射到适当的正数区间,该区间的选择需要一定的经验,或者参照其他指标的倍比关系确定.The principal component analysis is a good multi-index comprehensive evaluation method, but it must paid attention to its applicability and the proper use of evaluation results. If there is lack of sample quantity or little correlation between variables, it＇s not suitable for use. Evaluation indicator related to the dynamic value type must be treated as constant prices. The sort evaluated can be evaluated only by a principal component score, but when there are other aspects to analyze, selecting the corresponding components which latent root is more than 1. Calculating the principal component scores of each sample must be taken by way of variable weights. Give priority to examine the loading absolute value of each variable in the different principal component and then select the larger loading variable in the same principal component to name and generalize the features. When it comes to multiple-ratio analysis, the principal component scores of each sample should be mapped to the appropriate positive range which requires experience or reference to relationship of other indicators to determine.

关 键 词：主成分分析 综合评价 特征根 综合得分 倍比分析 

分 类 号：O213[理学—概率论与数理统计]