Variance Analysis of Regional Per Capita Income Based on Principal Component Analysis and Cluster Analysis

Transcription

1 0 rd International Conference on Social Science (ICSS 0) ISBN: Variance Analysis of Regional Per Capita Income Based on Principal Component Analysis and Cluster Analysis Yun HU,*, Ruo-Yu WANG, Ping-Ping DUAN and Xing-Yu CHEN,,, College of Science, Beijing Forestry University, Beijing 000, China. *Corresponding author Keywords: Per capita income, Principal component analysis, Cluster analysis, Discriminant analysis Abstract. This paper is to study the relationships among the annual per capita income, areas and professions. The data of different professions about areas was processed through the establishment of model. And the principal component analysis, cluster analysis and discriminant analysis were used. In this paper, we know that geographical environment have an effect on the per capita income and the Macroscopic Control Policy of government can improve the level of average income. Introduction With the constant deepening of China s Reform and Opening, average wages of residents have changed a lot, and the disparities have gradually displayed. The gap in average wages may lead to social instability. And it will also impede the development of national economy and the achievement of harmonious society. From a different perspective, these differences are reflected in the regions, urban and rural areas, gender, industry, ownership and so on. In this paper, we analyze industry categories in the primary industry, the secondary industry and the tertiary industry. And we use principal component analysis, cluster analysis and discriminant analysis and study the differences of urban employment average wage level in provinces and autonomous regions in China. Data and Analysis Data sources and Variable Indicators According to the data of China Statistical Yearbook (0), this paper selects indicators about different industries in the average salary of employees. The primary industry is agriculture, forestry, animal husbandry and fishery industry. The secondary industry includes mining industry, manufacturing industry, electric power, the fuel gas, the water production, the supply industry and construction industry. The tertiary industry embodies wholesale and retail industry, transportation, warehousing, post and communication, hotel and catering industry, information service industry, financial industry, real estate industry, business service industry, scientific research and technical service industry, environmental administration industry, Residential Service Industry, educational industry, hygiene industry, entertainment industry and social ensure industry.

2 Principal Component Analysis Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The indicators were reduced by principal component analysis with the aid of the software of SPSS.0. Through the software analysis, we can obtain the total variance explanation (Table ), the component matrix of principal components (Table ). Table. Total variance explanation. Initial eigenvalues Extraction sums of squared loading Total Contribution [%] Cumulative [%] Total Contribution [%] Cumulative [%] From Table, we can see that the eigenvalues of the first principal component was., and it reflected.0% of the whole data information. The two principal components were finally selected because their cumulative information reached.%, which can undoubtedly fully meet the demand. Further, the component matrix of the principal components extracted was shown in Table. According to Table, we could obtain the expression of principal components:

3 F 0.0X 0.0X 0.0X + 0.0X 0.0X 0.0X + 0.0X + 0.0X + 0.0X F = 0.X + 0.X + 0.0X - 0.0X - 0.X X 0.00X + 0.0X - 0.0X + 0.0X 0.0X + 0.0X + 0.0X - 0.0X 0.0X + 0.0X + 0.0X - 0.0X 0.0X + 0.0X - 0.X + 0.0X 0.0X + 0.0X () - 0.X + 0.0X - 0.0X - 0.0X X () F represents the first principal component and their uniform coefficients are positive numbers, so it reflected the size of each industry s average salary level in provinces and autonomous regions. If the average wage in each industry was higher, the value of F would be greater, so the first principal component is referred to the size factor. And F that we call it the second principal component, mainly reflected the information of So we called the second principal component as the foundational factor. Table. The component matrix. The contribution rate of the two principal components could be regarded as the weights, therefore, the comprehensive principal component model of annual per-capita income can be obtained by the formula (): F = 0.F + 0.0F () According to the comprehensive principal component model of annual per capita income, the comprehensive property value F can be figured out, and then, comprehensive evaluation can be obtained after ranking these F values in order. The result shown in Table. From Table, it shows that income levels have great differences in different areas. With the development of social and economic, per capita income in all regions of the country has been greatly improved. But the income gap among different regions in different industries is gradually expanding. Mostly, top-ranking regions belong to economic and cultural centers or coastal areas and whose per capita income level are much higher than the average level of the country. And those regions ranking in the back are mostly landlocked or in the remote northwestern of China.

4 Table. Comprehensive evaluation of annual per-capita income. Cluster Analysis Cluster analysis belongs to mathematical statistic method which is suitable for analyzing samples with murky ownership. The main idea of cluster analysis is to definite the distance between samples, the two closed samples are combined and the distance between the new category and other categories are recalculated then classified by the minimum distance, repeating the progress and reducing one category each time until all samples become one category, In this study, cluster analysis was adopted and determined by Euclidean distance, each sample is connected with another by average linkage, mapping in sequence. For a given data clustering software application SPSS, we take the principal component ranks in table as the new samples of provinces and autonomous regions, we can calculate distance between samples using Euclidean distance method. The distance between the shortest distance defined category and then we could get Figure. According to Figure, areas were divided into three categories. Figure. Tree-type of cluster analysis. Category Ⅰ consists of Beijing and Shanghai, which were called highly developed areas. Category Ⅱ includes four areas, i.e., Tianjin, Zhejiang, Guangdong and Jiangsu, which were 0

5 called developed areas; and category Ⅲ consists of twenty five areas, including Hunan, Guangxi, Jiangxi, Yunnan, Anhui, Hubei, Jilin, Gansu, Henan, Hebei, Shanxi, Liaoning, Hainan, Fujian, Chongqing, Neimenggu, Qinghai, Ningxia, Shandong, Sichuan, Guizhou, Shanxi, Xinjiang, Heilongjiang, Xizang, which were called general areas. Discriminant Analysis Linear discriminant analysis (LDA) is a generalization of Fisher's linear discriminant, a method used in statistics, pattern recognition and machine learning to find a linear combination of features that characterizes or separates two or more classes of objects or events. Fisher's discriminant analysis explicitly attempts to model the difference between the classes of data. The result of discriminant analysis (Table ) showed that the Fisher equations were as follows: D -0.X - 0.X + 0.X + 0.X + 0.X + 0.X - 0.X - 0.0X - 0.0X + 0.X D + 0.0X X = - 0.0X X + 0.X - 0.X - 0.X +.0X 0 -.X -.00X +.X - 0.0X +.0X +.X - 0.X + 0.X + 0.X - 0.0X - 0.X - 0.0X - 0.X + 0.X + 0.0X + 0.X + 0.0X +.0X () - 0.0X - 0.0X After standardizing the original data of Beijing, Tianjin, Tibet, the value and can be figured out, and then, we can obtain the Two-dimensional discriminant results: (.0,-0.), (-.,.), (-0.,-.00). According to Territorial Map, it was not difficult to verify the correctness of the discriminant results. In fact, in the first and secondary industries, the per capita income of Beijing and Tianjin were similar, but in the tertiary industry, the per-capita income of Tianjin was much less than Beijing, therefore, Beijing was classified as Category Ⅰ and Tianjin belonged to category Ⅱ. Then comparing Tibet and Tianjin, the per capita income of Tibet was a little bit more than Tianjin, but the two indicators had little influence on the discriminant results, and the per-capita income of Tianjin was far greater than Tibet in other industries which led to these two places are different categories. Table. Standardized Canonical Discriminant Function Coefficients. () Functio n X X X X X X X X X X0 X X X X X X X X X Conclusions Through principal component analysis, cluster analysis and discriminant analysis, provinces and autonomous regions can be divided into four classes in accordance with wage level. The first category is the coastal and developed cities, such as Shanghai, Beijing, Tianjin, Zhejiang, Guangdong, Jiangsu. The second concentrated in the eastern and southern regions such as: Chongqing, Fujian Sichuan and so on. And the third class is the areas affected by the state's

6 financial support, although located in remote, such as: Tibet, Xinjiang, Guizhou, Ningxia and other places. The last class concentrated in the Midwest and northern remote areas such as Heilongjiang, Jilin, Gansu, etc. The regions divided by the per capita income maintain a higher consistency to the districts by East, South, West and North. As far as policy is concerned, many provinces and cities located in the southeast coast are supported by national preferential policies for which they are the pilots of Reform and Opening. Therefore, economic development is faster than the central and western areas and the per capita income are at a high level. Geographically, transportation of the coastal areas is convenient, which this creates favorable conditions for economic development outside. So it illustrates that geographical environment will affect economic development, and it is also a factor to influence the per capita income. As for Tibet and Xinjiang, both of them have high per capita income although located in the remote western region. And which is due largely to the government's financial support. And it also shows that the government's regulation policy or development strategy contribute to the economy of the region. References [] Information on [] C Liu, X Zheng, N Ding. Principal Component Analysis of Cooked Rice Texture Qualities [J]. Journal of Northeast Agricultural University, 00, ():0-. [] Guo H W, Su B X, Zhang J L, et al. Extracting the core indicators of pulverized coal for blast furnace injection based on principal component analysis[j]. International Journal of Minerals Metallurgy & Materials, 0, 0():-. [] Yuan Wu, Yang Lei. Annual Per-capita Income Differences Analysis of the Mainland Areas Based on the Factor Analysis[J]. Journal of Chongqing Jiaotong University (Social Sciences Edition) 0, ():-0 (in Chinese). [] Jin Shang, You Yang, Xiao-hong Li. Cluster and Discriminant Analysis of Regional Economic Development in Our Country[J]. Journal of China West Normal University (Natural Sciences) 00, ():- (in Chinese). [] J C Wang. Solving the Puzzlement in the Notion of Cluster Talking about the Problem of Regional Cluster Development in Our Country[J]. Economic Survey, 00. [] L B Zhou, Z Q Jiang. Principal Component Analysis and Cluster Analysis of Trace Elements in Nitraria Leaf From Qinghai Region[J]. Medicinal Plant, 00(). [] D J Han, Jing-fang L U. Research on Competitiveness of County Economy Based on Factor Analysis and Cluster Analysis Taking Counties in Guizhou as Samples[J]. Asian Journal of Agricultural Research, 0, 0():-. [] Everitt B, Hothorn T. Cluster analysis /[M]. Wiley, 0. [0]Sachs J D. Institutions Don't Rule: Direct Effects of Geography on Per Capita Income[J]. Nber Working Papers, 00, (Suppl ):A-A.