1. Introduction
Cities have always been among the most important objects of geography research. In this era of globalization, the competitiveness of a city in the urban system or network decides how many resources, funds and talents it can abstract and how it should develop according to its comparative advantages [
1,
2]. Urban competitiveness measurement offers a basic evaluation for a city’s development statue, potential and influence. There are two main approaches: one is comprehensive evaluation based on indicators reflecting cities’ internal attributes, and the other is judging in a city network by network analysis.
Comprehensive evaluation based on urban attribute indicators is the traditional approach to urban competitiveness measurement. Population and GDP are the most used indicators in the early studies, and are still widely used in empirical studies. As research continues, scholars have realized that what affects cities’ functioning and resource-flow control includes not only economic spatial agglomeration, but also the synthetic action of the local social, ecological, and political environment. Therefore, selecting indicators that can truly reflect urban characters and organizing an indicator system have become an important approach to the comprehensive measurement of urban competitiveness. Scholars have attempted to use different angles in indicator selection [
1,
3,
4,
5,
6]. However, there are shortcomings to this approach: the selection of indicators and the decision of relationships among indicators are inevitably subjective [
3].
On the other hand, evaluating urban competitiveness in an urban network has become a popular approach since Friedmann [
7] proposed the world city hierarchy in 1986 and Sassen’s writing on global city [
8]. From this perspective, urban competitiveness is viewed as the capacity of a city to dominate and control resources. Stronger cities have bigger outer influence in both agglomeration and radiation forms, and, therefore, can attract and expose more resource flows in the urban network [
9]. GaWC research team has done significant researches on urban competitiveness (mainly on economic success) in global scale by considering it as a networked phenomena and measuring the quantity and quality of the connections a city has with other (world) cities [
10,
11,
12]. Other scholars have measured urban competitiveness through calculating and analyzing the network, which usually consists of cities as nodes and urban flows as connections, such as population migration [
13], traffic flow [
14], and economic flow [
15]. Currently acknowledged urban flows representing inter-city connections mainly include population migration flow, logistics flow, fund flow, information flow, and technology flow [
16]. However, this approach has defects. It is mostly used in global context studies, which are supported by relatively large-scale flow data. When the study scale is smaller, the urban network becomes more elaborate, and therefore, the requirements for the inter-city flow data are refined and the data are more difficult to acquire. Taking China’s urban level as an example, because of the comprehensive traffic situation and abstraction of information flow and technology flow, it is difficult to acquire enough necessary flow data for an urban network, in which inter-city connections are measured by interactions among cities. When the necessary flow data for the whole network is difficult or even impossible to acquire, the connections a city has with other cities in a city network should be considered as the reflection of urban competitiveness rather than the cause.
Therefore, although both main approaches to urban competitiveness measurement have been developed fully in theory and practice, they still have defects. Scholars have proved there is a certain relationship between indicators presenting urban attributes and urban flows reflecting inter-city connections. According to Martin [
17], for example, observers and analysts have claimed population mobility is affected by business and job opportunities, the promise of wages and fortunes, the scope for consumption, and the array of cultural and leisure amenities. At the meantime, urban competitiveness is affected by both internal and external factors, which correspond to comprehensive evaluation and urban network analysis respectively. Therefore, taking urban competitiveness as an intermediate context, we proposed hypotheses of two sets of causality relationships: one is between the internal attributes of cities presented by indicators and the results of urban competitiveness, and the other is between urban competitiveness and urban flow intensities. Based on these hypotheses, this study attempted to find a new approach that can combine the perspectives of comprehensive evaluation and urban flow calculation for urban competitiveness measurement.
Structural equation model (SEM) was first proposed in 1970 by Jöreskog [
18]. It is theoretically based on mathematical statistics. It can describe and measure complex causality correlations between latent variables as well as between each latent variable and corresponding observed variables. Therefore, we introduced SEM into this research for a new approach to urban competitiveness measurement, combining and cross-corroborating the two abovementioned perspectives. This enabled us to verify our hypotheses by building a mathematical matrix SEM and undertaking statistical testing. We attempt to offer a new perspective and approach to urban competitiveness measurement that is theoretically feasible and statistically reliable.
We conducted our research on urban scale in China in 2010, and focus on municipal districts of cities, which to some extent follow the typical downtowns of Western cities. Cities in our research include the four municipalities directly under the central government (Beijing, Tianjin, Shanghai and Chongqing) and prefecture-level cities which were included in the state-generated statistics, namely 286 municipal districts of China in 2010. To investigate the urban competitiveness of these cities, we built an SEM to measure urban competitiveness and analyzed the results.
The rest of this paper is organized as follows.
Section 2 outlines the data used.
Section 3 presents our approach and explains the rationale of SEM as well as the model process in the order of algorithm selection, model building, model fitting and assessment, and model modification. The measurement results are described and analyzed in
Section 4.
Section 5 discusses the advantages and disadvantages of this approach compared with other measurement results, and expounds the statistical reliability of the proposed approach.
Section 6 concludes.
5. Discussion on PLS-SEM Approach
5.1. Reliability of Results
5.1.1. Result Testing Based on Rank-Size Rule
The rank-size rule is a classical theory on measuring relationships between city size and rank in an urban system, in which city size can be understood as urban competitiveness. It was first proposed by Auerbach in 1913, and developed by scholars into more patterns later [
36,
37]. The rule has been proven applicable for cities in China [
38,
39,
40], and, thus, we take it as a reference for testing the reliability of our result on quantitative distribution.
We fitted urban competitiveness scores and their ranks with the basic rank-size formula. The result is basically satisfied (as shown in
Figure 7). Multiplicative relationship between the score and rank could be found obviously, and the
R2 obtained in double-log model regression is 0.73, which demonstrates the reliability of our result on quantitative distribution.
5.1.2. Result Comparison with Other Approaches
We test the reliability of the PLS-SEM result by comparing it with traditional approaches. Chinese scholars usually take population, GDP, or area of built urban district to substitute for urban competitiveness, giving us comparable results. In addition, the Blue Book of Urban Competitiveness, which is annually released by the Chinese Academy of Social Sciences and measures all cities in China based on a comprehensive evaluation of substantial amount of urban attribute data, is supposed to be an authoritative version of urban competitiveness measurement.
We compared PLS-SEM urban competitiveness scores with scores from the
2010 Blue Book of Urban Competitiveness and single index measurements on population, GDP, and area of built urban district by correlation test, and compared the top 50 and bottom 50 cities of our results with the Blue Book to observe how much they match. As shown in the correlation matrix (
Table 6), our urban competitiveness scores are obviously correlated with the others. Moreover, considering the overall correlation, the result of PLS-SEM has slight advantages. On the other hand, according to the match test, the numbers of coincident cities in the top 50 and bottom 50 are 38 and 30, respectively, which are relatively high. Overall, we proved the reliability of the results measured by our PLS-SEM approach.
The similarities prove the reliability of our approach in reflecting the urban competitiveness situation. However, our result would be more comprehensive and considerable than reliance on just a single indicator. At the same time, as we have taken inter-city connections in the urban system as verification of urban attribute indicators, and determined the weights according to data and the SEM matrix, our result might be more concise and valid than that of the Blue Book.
5.2. Theoretical Reliability
PLS-SEM itself fits the topic and our theoretical basis well, therefore, helps to make the approach theoretically reliable for urban competitiveness measurement. The theoretical basis of our approach is causal relationship hypothesis between urban attributes and urban competitiveness, as well as urban competitiveness and inter-city connections. The statistical principle of SEM supports a causal relationship, and thus, matches well our intention and offers a good framework and foundation for testing our theoretical hypothesis. Moreover, the requirement for urban flow data was reduced by their positions in the causal relationship, thereby avoiding the limitations of smaller-scale research caused by data collection.
Meanwhile, statistical indexes used in this approach testify and ensure the theoretical reliability to a large degree. They test our expectations and hypotheses proposed in the model by verifying all sorts of indexes, path coefficients, loadings, and weights required statistically. When the theoretical hypotheses are not satisfied, the modification process helps in reconsidering the model. Thus, the indexes contained in our approach offer strong support for theoretical reliability.
5.3. Statistical Reliability
Embedded statistical skills in PLS-SEM are one of the advantages of our approach. The final model, including all of the data and relationships, can be tested statistically in the model assessment and modification. The large amount of research on PLS-SEM by statisticians provides sufficient foundations on assessment criteria and extent, which guarantee the statistical reliability of the approach. The model can be tested statistically in different aspects according to their structure and position, as shown in
Table 1.
At the same time, the influence of subjectivity has been avoided to the greatest possible extent. We have filtered each item of statistical data based on statistical analysis, such as correlation test and cluster, rather than artificial sift. Moreover, the assessment, modification, and result analysis of the approach have been performed based on objective data information instead of human opinion. Although there is still human participation in the primary selection of indicators and judgment of cluster results, the statistical data have been used and mined as much as possible.
6. Conclusions
The main purpose of this paper has been to propose a new perspective and approach to urban competitiveness measurement that is theoretically feasible and statistically reliable. Our approach could cross-corroborate the perspectives of measuring urban competitiveness by comprehensive evaluation of urban attributes and network analysis of inter-city connections, and covers their shortcomings. It avoids subjective intervention by relying on data largely in indicator selection, determining weights through SEM matrix, and adding urban flow data into traditional comprehensive evaluation verification. Meanwhile, it decreases the requirement for urban flow data by taking them as reflective rather than causes of urban competitiveness, and therefore, makes it possible to measure small-scale objectives in urban flow perspectives under the limitation of data collection. The reliability of the result has been demonstrated through comparison, and the advantages of this approach have been proven, both theoretically and statistically. We consider our approach reliable for urban competitiveness measurement.
As for the 286 municipal districts of cities which were included in the state-generated statistics in China in 2010, their urban competitiveness showed an uneven distribution. Quantitatively, cities could be clustered into five classes: Shanghai is the only city in the first class and is far ahead, while, altogether, there are only about 50 cities in the first three classes with relatively large score span. Spatially, the urban competitiveness shows an obvious regional difference: eastern China is the most prosperous region with most top three-class cities and a relatively balanced quantitative constitution, while the western part has most class-five cities. It is worth noting that, although central and north-eastern China seem to have mediocre performance, the large proportion of common cities and the lack of superior leading ones may be a forewarning of underpowered and negative development perspectives. From the spatial correlation perspective, the HH regions are coincident with the three most powerful urban agglomerations in China, while the HL regions conform quite well to the situation of Western China. Thus, the government should pay more attention to the urban competitive constitution structures of each region besides the overall development status.
We built our model and measured all 286 cities with the same set of urban attributes. Considering the differences in functions and inter-city connections between different urban hierarchies, we think much more work needs to be done through building more specific models in each hierarchy with more suitable and representative urban attributes and network linkages after having a good understanding of the hierarchy. In addition, our model could be developed further if more data were collected and added. As urban attribute statistics are usually limited for small-scale cities in China, we aim to enrich our model through big data collection in future work.