Standardization of first-hand data
The index system of the global urban competitiveness is enormous with numerous data. The dimension varies from index to index. First, it needs to conduct the standardized integration. All the index data have to go though the non-dimensional processing. The objective indices can be divided into singular objective indices and composite objective indices. To conduct the non-dimensional process to the original data of singular objective indices, this paper primarily adopts the standardization, indexation, and threshold value method.
Global urban competitiveness index (GUCI) of the 500 cities
In the course of the combination of comprehensive competitiveness indices, the non-linear weighted integration method is adopted. The so-called non-linear weighted integration method (or multiplicative integration method) uses the non-linear model to conduct the comprehensive assessment. In the formula, is the weight coefficient, xj≥l. As far as the non-linear model is concerned, when computing the 9 explicit indices of the urban comprehensive competitiveness, as long as one index is extremely small, the value of the comprehensive competitiveness will approach zero rapidly. In other words, this assessment model is sensitive to indices of small value, and less so to indices of relatively large value. By using the non-linear weighted integration method to measure the urban competitiveness, we can reflect the composite indices more comprehensively and scientifically.
While we synthesize the 9 explicit indices, we first employ the threshold value method to the index data in the non-dimensional processing, and then get the integrated value by applying the non-linear weighted integration method. What needs to be pointed out is that in the course of the non-dimensional processing, some indices with the value of 0 are conferred the minimum of 0.05 to avoid the phenomenon of 0 integrated product when integrating the indices. See Table 2.6 below for the weights adopted.
Table 2.6 Overview of weights of explicit indices
|
Index |
Normal exchange rate/real exchange rate |
GDP |
GDP per capita |
GDP per square kilometer |
Real economic growth rate (for 5 years) |
Em-ploy-ment rate |
Labor product-ivity |
Number of inter-national patent applica- tions |
Multinational Corporation Score |
Summa- tion |
|
Weight |
.05 |
.05 |
.1 |
.1 |
.2 |
.1 |
.1 |
.05 |
.05 |
.8 |
After determining the weights of measuring indices in the comprehensive competitiveness index integration, we can employ the non-linear weighted integration method to calculate the comprehensive competitiveness index of each city, whereupon to rank the comprehensive competitiveness of the 500 cities.
Assuming that such indices as the normal exchange rate/ real exchange rate, gross GDP, GDP per capita, GDP per square kilometer, real economic growth rate (for 5 years) , Multinational Corporation Score employment rate, labor productivity, number of international patent applications and are expressed with, , , , , , and , the comprehensive competitiveness indices can be integrated by using the above non-linear model, here , , , , , , , and are 0.05, 0.05, 0.1, 0.1, 0.2, 0.1, 0.1, 0.05, and 0.05 respectively.
The Input Index System and Subentry Competitiveness Index of the 150 Cities in the World
While integrating the input subentries of competitiveness indices by grade, we adopt the simple linear average method, namely, conferring every index the same weight. The subentry competitiveness singular indices are divided into three levels, where the third level indices can be integrated into secondary level indices after the indexation, and then the secondary level indices be integrated into first level indices. However, since some level-III indices come from the reports of other research institutes, they probably have been integrated. Table 1.3 exhibits the integrated hierarchy relationship of indices at various levels. Those indices of composite graded data at the third level are also marked out.
Regression analysis
Some variables are connected by known functional relations. For many others, however, no known functional relation exists. If variable y changes in line with variable x, but the value of variable y cannot be obtained even though the accurate value of variable x is known, the relation between variables y and x is called correlation. Regression analysis is statistical method for the study of correlations between variables.
To discuss the relations between the indices, one-variable linear regression analysis method is used on the basis of urban competitiveness assessment to determine the relations between cities and their explanation ability in accordance with their respective regression coefficients and levels of fitness of good.
I. One-variable linear regression model
The one-variable linear regression mode is as follow:
y = a + bx
where a and b are regression coefficients.Calculating a and b based on data obtained from experiments. Then the definite one-variable linear regression model and the definite regression line are obtained.
II. Correlation Coefficients
γ is a coefficient for the indication of the extent of correlation between variables y and x. It can be used to determine whether the regression model is meaningful, as follow: If γ>γa,f, the variables are highly correlated and the regression model is meaningful; Otherwise, the variables are poorly correlated and the regression model is not meaningful.
In this study, regression analysis indices are divided into two categories. The first category is 9 measuring indices, and the population index. Therefore, mutual regression explanation is made for the 10 indices. The second category includes the level-I, level-II and level-III subentry competitiveness indices, which are used for regression analysis on the overall competitiveness and GDP per capita of the cities.
Dynamic clustering analysis
The underlying idea of dynamic clustering analysis is to select a number of sample points as the clustering centers in the first place; next, the samples are made to concentrate toward the centers in accordance with specific clustering standards for an initial classification; then judgment is made on whether the classification is reasonable; if not, the clustering centers will be revised; the step is performed repeatedly until the classification is reasonable. There are a number of dynamic clustering calculation methods, among which, the most famous ones are the K-average method and the ISODATA method. In this study, the K-average method is employed. The following is a brief introduction to the method:
If there are N samples to be classified, i.e., …., , and there are K clusters, N≥K,
Step1: randomly select K initial clustering centers, , ,… , e.g., the first K samples (called the old clustering centers);
Step2: put each sample into a category of the old clustering centers in accordance with the neighboring principle;
Step3: calculate the gravity center of each category after the classification. These gravity centers are called the new clustering centers: , in which, Ni is the number of samples of category ；
Step 4: check whether , ,… , equal to , ,… respectively; if yes, the calculation is completed; if not, replace with , and return to step 2.
Based on the above theory, dynamic clustering analysis is made on the sample cities, using the 9 explicit indices of the 500 cities.
Fuzzy curve analysis method
In the research into the pivotal factors affecting comprehensive competitiveness Fuzzy Curve Analysis Method is adopted in the report. Fuzzy Curve Analysis is mainly used to reduce the dimensionality of the input variable and to discover the important factors affecting the output variable. Fuzzy Curve Analysis Method selects the important factors finally by working out contribution flexibility. The theory of Fuzzy Curve Analysis is specified as follows:
1. At the first stag, the fuzzy curve is based on the simply thought, which namely the most important input approaches to the output most contributively.
2. The fuzzy curve drawn at first stage is based on the second simply thought, namely independent input approaches to the output more contributively more than the interdependent input does.
3. The fuzzy curve drawn at second stage is based on the third simply thought, namely if (a input amount) is stochastic dependence on y (a output), therefore the estimated value of the variance owned y in formula ( -y) will approximately equal to the unbiased variance owned by , on contrary if relationship between and y is causality, we can anticipate the large difference between the estimated value on the variance owned by y and mean square deviation.
It is presumed that the data point containing the number of the data points is as many as a number ( ) and indicates （ … ,y1），（ ，… ，y2）……，（ … ,ym）, … ( an input) is correlative with y (an output), which is substituted by .Here is applied to make sure the positive value owned by all y. The fuzzy quantity defined at first stage is shown as follows:
Here, A is a group of inputs; K can be found by the foloowing 5 steps.
1）As for every input variable ( ), the data point〔（ ， ），k＝1.2，…M，i=1.2，…N〕can be marked in every formula, －y.
2）The fuzzy relation coefficient can be set for very data point in the formula ( -y).
, at time when every data point is marked in ( ), as a result it will be .
3）Make Aº=Φ, the fuzzy curve for the first stage is given; on this curve, , for all i=1.2…N.
4) The representation index about is given: , where , Ak is an aggregate of data points responding to the point K.
5) Find the smallest representation index for , then make , belong to this cluster, after that we obtain the most important input. We repeat this process to and A, thus getting , the most important index. Repeat this process and we will obtain the most important input varuables with the quantity of k.
—— From“Global Urban Competitiveness Report（2007-2008）”，Pengfei Ni with Peter Karl Kresl