逐步回归及通径分析在主成分分析中的应用

[目的]探讨多指标体系中对测定指标的评价、排序及简约,实现对多指标体系的降维.[方法]举例将逐步回归分析和通径分析引入主成分分析中.[结果]测定指标对主成分逐步回归分析保留了对主成分影响显著的指标,剔除了对主成分作用较小或存在共线性的指标;通径分析揭示了测定指标对主成分的直接影响和间接影响体现了指标间的相互作用.通径分析中测定指标对主成分决定系数的分解结合主成分特征值的百分贡献率可对测定指标进行评价,提取反映总体主要信息,真正实现测定指标的简约.[结论]主成分分析结合逐步回归分析和通径分析可对多指标体系中的指标进行评价,实现测定指标的真正降维.

Application of Stepwise Regression and Path Analysis in Principal Component

【Objective】The purpose of the study was to seek one practical method to assess the importance of detected attributes in multivariable systems and to reduce the data dimensions.【Method】Based on introducing stepwise regression analysis and path analysis into principal component analysis(PCA) by an example.【Result】The stepwise regressions of detected indicators against principal components were powerful in variances choice,variances with significant influence on component were remained.The path analysis revealed the direct influence and indirect influence of detected indicators on the principal component,which showed the intereaction between the indicators.Based on the determination coefficient of indicators and percentages of principal component eigenvalues,the influences of indicators on research objective can be evaluated.According to the evaluation,indicators with essential influence on the research objective can be extracted and the numbers of detected indicators in the system can be reduced.【Conclusion】PCA combined with stepwise regressions and path analysis is an useful tool in multivariable systems,which can assess the variables and choose the most important viable in a complex data to reduce the data dimensions in practice.