基于主成分分析的居民消费水平模型

Residents’ Consumption Level Model Based on Principal Component Analysis

在冗杂的高维数据中,往往容易出现数据之间存在严重共线性的现象,导致模型参数存在不可估性,故消除多重共线性对探讨实际问题有着重要意义。本文是以居民消费水平为研究对象,通过运用方差膨胀因子对数据的多重共线性进行判断,再基于SVD分解对观测数据矩阵进行主成分回归以消除自变量之间的多重共线性,并建立原始数据之间的线性关系。国家通过居民消费水平来得到地方的发展状况,以制定更加符合发展的政策。因此,该研究具有一定的现实意义。利用SVD分解的方法进行主成分分析,简化了求解特征值及贡献率的计算问题,且通过主成分回归的方法进行共线性消除,避免了直接删除变量所导致重要变量被舍去的可能。结果表明,该模型相对误差小,故该方法所得的模型具有可靠性。In the high-dimensional data, it is easy to have collinearity among data, which leads to the immeasurable of model parameters. Therefore, eliminating multicollinearity is important to discuss practical problems. This paper takes the consumption level as the research object, uses VIF to judge the multicollinearity of the data, then carries out principal component regression(PCR) on the observation matrix based on SVD to eliminate the multicollinearity among independent variables and builds the linear relation among the original data. The state gets local development status by the consumption level of residents so as to formulate policy more in line with development. Thus the study has realistic meaning. PCA based on SVD simplifies the calculation of eigenvalue and contribution rate, and it can avoid the possibility that important variables are deleted to use PCR to eliminate the collinearity. The result shows the relative error of the model is small, so the model obtained by this method is reliable.