In view of the existing literature panel data factor analysis model in practical application of the deficiency, this paper established the model of factor analysis based on TOPSIS method, which is applied to the analysis of the panel data factor in practice. Compared with the generalized dynamic factor analysis model, the model does not need to satisfy the 4 assumptions of the generalized dynamic factor analysis model at the same time. The model is calculated with regard to every year’s cross section data factor composite scores the highest and lowest, respectively, for the best and worst vector. By TOPSIS theory, the optimal factor scheme approach degree of each research object is obtained. Take the development of China’s service industry as an example; use the optimal factor scheme proximity of model degree to depict the eastern, central, and western development of service industry. The study found that the development of service industry in eastern provinces and in central and western regions differs greatly. In total, China’s service industry has a great development space.
For the generalized dynamic factor analysis model put forward by Forni, set a variable system
The
It illustrates the
The spectral density matrix of
The first eigenvalue
From the perspective of a model itself, although the generalized dynamic factor analysis model put forward by Forni relatively traditional factor analysis model shows many advantages, it can be a very good factor analysis that was carried out on the panel data. However, in practical applications, factor analysis was carried out on the panel data; the generalized dynamic factor analysis model’s four assumptions are sometimes difficult to get and satisfy at the same time.
On this basis, the article will be supported by the traditional theory of factor analysis and establish factor analysis model based on TOPSIS improvement, relatively generalized dynamic factor analysis; this model avoids the variable system of generalized dynamic factor analysis model which must satisfy four assumptions at the same time. At the same time, this study is not based on annual factor cumulative variance contribution rate weighted sum, and this can avoid the error caused by the annual data caliber inconsistencies. We use the highest and lowest comprehensive score of annual cross sectional data of each research object as the best and worst vector respectively, by TOPSIS method to get the proximity between the comprehensive score vector and the optimal factor vector so as to describe the development status of service industry of each research object.
Specific steps are as follows.
There are
Maximum index uniform transformation and minimum index normalization transformation are as follows:
The maximum and minimum values of each column constitute the best and the worst vector, expression with
The distances between the
The proximity between the
This method attempts with less number of common factors to get linear function and the sum of specific factors to express each variable of the original observations, in order to achieve a reasonable explanation of the correlation between the original variables and the dimension of the simplified variable. Specific steps are as follows.
We assume there are
It is the original data standardization.
Calculating coefficient of correlation matrix
Seeking
Extract the previous
Calculate each common factor score which is
Calculate comprehensive evaluation index value, which is a comprehensive factor score:
Establish index system,
Factor analysis of cross section data for
In the above formula,
Make the final evaluation with TOPSIS method on the factor comprehensive score
(A) With every year of the cross section data score factor analysis
(B) Because the factor composite score
(C) Find the maximum value
(D) Make
(E) Set
The value of
This article is based on the service industry development since China’s accession to WTO Case empirical research [
This article is based on the establishment of index system services (China 14 Index) which are divided into sets and each province annually national statistics services subsectors of employment (Unit: 10,000) as an index of data values, that is,
There were a total of 14 services subsector indicators to study and evaluate 25 Chinese provinces in 2004–2013 years of service industry development.
By Section
Factor comprehensive scoring functions of cross section data of factor analysis of 2013 are as follows:
Factor comprehensive scoring function of cross section data of factor analysis of 2004 are as follows:
Factor loading quantity of cross section data based on factor analysis (part of the data table).







 


0.468  0.315  0.691  0.394  0.437  0.352  0.673  0.431 

0.876  0.569  0.498  −0.031  0.826  0.506  0.427  −0.051 

0.479  0.521  0.236  0.250  0.498  0.507  0.266  0.271 

0.213  0.796  0.276  0.293  0.260  0.806  0.239  0.339 

−0.078  0.113  0.358  0.824  −0.069  0.172  0.401  0.805 

0.268  0.812  0.433  0.420  0.312  0.796  0.633  0.420 

0.832  0.293  0.591  −0.088  0.807  0.341  0.579  −0.067 

0.165  −0.077  0.817  0.344  0.231  −0.062  0.798  0.387 

0.391  0.295  0.729  0.089  0.401  0.267  0.738  0.076 

0.763  −0.073  −0.076  0.006  0.751  −0.065  −0.071  0.009 

0.136  0.771  0.469  0.270  0.201  0.768  0.473  0.239 

−0.118  0.666  0.541  0.649  −0.109  0.657  0.573  0.681 

−0.113  0.250  −0.026  0.804  −0.107  0.271  −0.021  0.807 

0.319  −0.115  0.591  0.167  0.376  −0.152  0.573  0.189 
By 2004–2013 years of crosssectional data factor composite score function and using mathematical software MATLAB, the relevant data into the factor score function can be calculated in 25 provinces of 2004–2013 years on the factor composite score:
By this section 2.3 parts of TOPSIS theory of factor analysis model are set up, and, with the aid of mathematical software MATLAB, calculated results are shown in Table
Factor analysis based on TOPSIS theory: the development of service industry in 2004–2013, China.
Region 



Ranking  area 

Hebei  2.342  0.0753  0.0312  6  Eastern 
Liaoning  2.2122  0.2042  0.0845  5  
Jiangsu  0.8023  1.6200  0.6688  2  
Zhejiang  1.0876  1.4298  0.568  3  
Fujian  2.3482  0.0741  0.0305  7  
Shandong  1.9918  0.4274  0.1767  4  
Guangdong  0.0000  2.4158  1.0000  1  
Hainan  2.3941  0.0263  0.0109  15  
Mean  1.6473  0.7841  0.3213  


Henan  2.3751  0.0574  0.0236  9  Central 
Hubei  2.3714  0.0458  0.0189  11  
Hunan  2.3601  0.0561  0.0233  10  
Shanxi  2.4016  0.0151  0.0062  18  
Jilin  2.3803  0.0361  0.0149  14  
Heilongjiang  2.4071  0.0102  0.0042  19  
Anhui  2.3787  0.0376  0.0156  13  
Jiangxi  2.3761  0.0433  0.0179  12  
Mean  2.3813  0.0377  0.0156  


Sichuan  2.3577  0.0679  0.028  8  Western 
Guizhou  2.4128  0.0047  0.0019  22  
Yunnan  2.4108  0.0063  0.0026  21  
Shan’xi  2.3993  0.018  0.0074  17  
Gansu  2.4142  0.0024  0.0010  23  
Qinghai  2.4158  0.0001  0.0001  25  
Ningxia  2.4143  0.0016  0.0007  24  
Neimenggu  2.407  0.0094  0.0039  20  
Guangxi  2.391  0.0259  0.0107  16  
Mean  2.4025  0.0151  0.0063 
The number of times of
The number of times of
The number of times of
Firstly, it was found from the data in Table
Secondly, Table
On the one hand, from the frequency distribution diagram, that is, Figures
On the other hand, as Figures
Table
Factor analysis model of TOPSIS established in this paper, research and analysis of the development of the services sector in 25 provinces of China, concluded that, in addition to China’s coastal areas, that is, Guangdong, Jiangsu and Zhejiang province, most of the provinces and the proximity of optimal schemes is bigger, especially in the western region, which shows that most of China’s service industry development degree is far lower than coastal areas. For service industry development is relatively backward area, China can promote their resource advantages of the existence of the region, such as the western region of Guizhou province has a very good climate environment, beautiful mountains, and rich mineral resources; Yunnan region has rich and colorful ethnic minorities and the beautiful Lijiang; Xinjiang region has a beautiful Uygur dance, rich fruit, and so on. Through the support of the government and vigorously promoting their existing resources advantages, we need to attract foreign enterprises and intellectuals to promote service industry development in the region.
The model is calculated for each sample and the distance between the worst and the best vector by TOPSIS method; then calculate the samples and the proximity of optimal solution, as the final results of the evaluation. On the processing of data, the model does not need the deflator to time series data of sample, which overcomes the Dynamic Factor Model which needs to meet four preconditions. The model will also be used to research the biological, medical, and other fields.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China (Grants nos. 71461027, 71471158, and 71001072); Science and Technology Plan Project of Guizhou Province (no. LH