稳健性因子分析在城镇居民家庭现金消费支出中的应用

利用面向对象的稳健性因子分析R软件包Robustfa,对2011年全国除港、澳、湾以外的31个省、市、自治区的城镇居民家庭现金消费支出的8个指标进行了因子分析.通过使残差矩阵的元素平方和达到最小,发现了一个组合一主因子法与稳健性Mve估计量.通过由稳健性Mve估计量计算的马氏距离大于临界值,我们发现共有10个异常点.用经典估计量和稳健性Mve估计量计算的样本相关阵、旋转后的因子载荷矩阵、因子对原始变量的贡献、贡献率、累积贡献率、样本相关阵的特征值的碎石图、前两个因子得分的散点图、因子得分、按因子得分排序等结果均有较大的不同.最后通过组合主因子法与稳健性Mve估计量将8个指标归结为两个因子:基础消费因子和消费倾向因子,根据每个省份的两个因子得分情况对该省份的家庭现金消费支出情况作出综合评价,并根据稳健性因子分析的结果给出了相应建议.

Robust Factor Analysis and Its Applications in Urban Households Cash Consumption Expenditure

We apply the object-oriented robust factor analysis R package robustfa to the8 indexes of cash consumption expenditure of urban households from the 2011 national 31 provinces,municipalities,and autonomous regions.To minimize the sum of squares of the elements of the residual error matrix,we find a combination- the principal factor analysis method and the robust Mve estimator.By the Mahalanobis distances which are computed by the robust Mve estimator,greater than the critical value,we find a total of 10 abnormal points.This paper discovers that the results of the sample correlation matrix,the rotated factor loading matrix,the contribution of the factors to the original variables,the contribution rate,the cumulative contribution rate,the screeplot of the eigenvalues of the sample correlation matrix,the scatter plot of the first two factor scores,factor scores,and the sorted scores according to factor scores etc.computed by the classical estimator and the robust Mve estimator are quite different.Finally we condense the 8 indexes to 2 factors by combining the principal factor analysis method and the robust Mve estimator:the basic consumption factor and the consumption tendency factor.According to two factor scores of the provinces,we make comprehensive evaluations of the provinces' household cash consumption expenditures,and give the corresponding suggestions according to the results of robust factor analysis.