区域可持续发展指标的相关性分析及降维模型研究——以中国省级区域为例

增大指标的覆盖面与减少指标的信息重复是可持续发展指标选取中面临的一对矛盾。在通常情况下指标数量越多，指标的覆盖面就越大，但指标的信息重复就越多。分析了近年来有关文献通常采用的指标，并结合中国省级区域可持续发展指标的可获取性，选取46个指标对其相关性进行分析。分析结果表明这些指标之间绝大多数呈现不同程度的相关关系，即指标间含有大量的重复信息。应用统计分析技术建立基于主成分分析的指标降维模型，得到 8个彼此独立的综合指标。根据综合指标得分，对中国31个省级区域（不包括港澳台）的可持续发展状况进行了排序。

A STUDY ON CORRELATION ANALYSIS AND DIMENSION REDUCTION MODELING OF REGIONAL SUSTAINABLE DEVELOPMENT LNDEX-TAKING CHINESE PROVINCIAL REGIONS AS A CASE

The purpose of this study is to measure the correlation among sustainable development indexes, and pursue a better way to reduce the dimensions of such original indexes. In the studies of sustainable development index, there is a serious contradiction between increasing the coverage of indexes and decreasing the information overlapping of indexes, for generally more indexes means more overlapping among them. Most of the leading studies in China and abroad in resent years select relatively large amount of indexes. For example, the indexes of UNSCD have 134 indexes in the beginning and 58 indexes after modified in 2000, the indexes by the government of UK included 118 indexes, the indexes by a research group of Chinese Academy of Sciences is 231 indexes. This study select 46 indexes which are often used among them, and process the correlation analysis on them. The result shows that most of them correlate each other in some ways, i.e. the overlapping information is significant.Then the dimension reduction model is developed based on statistic technique, and eight components that are regarded as independent comprehensive indexes are derived. Assume component is: z₁，z₂，…，z_n，the original indexed are:x₁，x₂ ，…，x_m，then the dimention reduction model are：
z₁=α₁₁x₁+α₁₂x₂+…+α_1mx_m
z₂=α₂₁x₁+α₂₂x₂+…+α_2mx_m
…
z_n=α_n1x₁+α_n2x₂+…+α_nmx_m
indicates the coefficient of the models. The values of are listed in Table. 4.
    According to the scoring of comprehensive indexes, the sustainable development conditions of 31 Chinese provincial regions (not including Hong Kong, Macao, and Taiwan) are sorted. The ranking of these regions is: ①Shanghai, ②Beijing, ③Tianjin, ④Jiangsu, ⑤Guangdong, ⑥Fujian, ⑦Zhejiang, ⑧Shandong, ⑨Heilongjiang, ⑩Hubei, B₁₁Hebei, B₁₂Liaoning,B₁₃Henan, B₁₄Hainan,B₁₅Jilin,B₁₆Hunan,B₁₇Anhui,B₁₈Jiangxi,B₁₉Guangxi, B₂₀-Xinjiang, B₂₁-Chongqing,B₂₂Yunnan, B₂₃Sichuan,B₂₄Tibet, B₂₅Inner Mongolia, B₂₆Shannxi,B₂₇Ningxia, B₂₈Gansu, B₂₉-Shanxi, B₃₀-Guizhou,B₃₁-Qinghai.