An application of canonical correlation analysis in regional science : the interrelationships between transport and development in China's Zhujiang Delta

ABSTRACT. Canonical correlation analysis (CCA) has the ability to deal with two sets of multivariate variables simultaneously and to produce both structural and spatial meanings. In view of the valuable insights to be gained, in this paper I examine the potential applications of CCA in regional science by describing its algorithm in a regional or spatial context. Next, I apply CCA to explore the mutually interdependent relationship between transport and development in China's Zhujiang Delta. The results highlight the utility of CCA in revealing the structural and spatial patterns of two dominant and four subdominant transport-development relationships in this growing region of China.

1. INTRODUCTION

Regional science often deals with a multitude of variables or events relating to different domains of the physical and human environment in discrete regional entities. Various multivariate statistical techniques such as multiple regression analysis, principal component analysis, and factor analysis are commonly used. However, canonical correlation analysis (CCA), one of the most direct ways of analyzing relationships between sets of variables, has often been "coolly received" (Gittins, 1985). The major reason given by Clark (1975) is that the algorithms and results of canonical correlation analysis are even more difficult to understand and interpret than principal component and factor analyses which deal with the internal structure of one set of variables only. By the 1990s, Hair et al. still remarked that "until recent years, canonical analysis was a relatively unknown statistical technique" (1995, p. 327).

Ever since the mid-1980s the application of CCA has become increasingly common in ecology and biogeography (Gittins, 1985). Nonetheless, the utility and potentials of CCA in analyzing urban and regional problems have remained largely untapped. In a search for the application of this technique in journals included in the Social Sciences Citation Index from 1980 to 1995, 11 articles are listed. Of these, six are on psychology and education (Holland, Levi, and Watson, 1980; Lambert, Wildt, and Durand, 1988; Drumheller and Owen, 1994; Jelinek and Morf, 1995; Lutz and Eckert, 1994; Thompson, 1995), two on econometrics (Bewley, Orden, Yang, and Fisher, 1994; Gonzalo, 1994) and only one on urban studies (Black and Schweitzer, 1985). Nonetheless, CCA is a very powerful methodological tool in urban and regional analysis. It has the ability to deal with two sets of multivariate variables simultaneously and to produce both structural and spatial meanings. In view of the valuable insights to be gained, this paper applies CCA in examining the interdependent relationship between multiple transport and development variables in China's Zhujiang Delta. It is hoped that such efforts will serve to highlight the opportunities afforded by this statistical model as a means of identifying the intertwined relationships between arrays of variables underlying one common regional structure.

2. THE RESEARCH QUESTION

In the late twentieth century, the reform and Open Policy of the People's Republic of China (PRC) represented one of the most important landmarks in the transition of the global economy. Under the Open Policy, the Zhujiang Delta, which is the economic core of Guangdong province, was designated as the "experimental ground" in the transition of the socialist economy to a more market-oriented economy. Figure I shows the geographical location of the Zhujiang Delta. The region takes up 47,455 square kilometers and comprises the Shenzhen Special Economic Zone (SEZ), Zhuhai SEZ, Guangzhou Open City (OC) and the Zhujiang Open Economic Zone (OEZ). In 1995 there were 32 administrative units, of which 14 were urban municipalities either at the prefectural or local levels[1] and 18 were rural counties at the local level.[2]

Between 1990 and 1995 the aggregate Gross Domestic Product (GDP) of the region has grown at an amazing average annual growth rate of 15.3 percent. (Guangdong tongji nianjian, various years). Transport infrastructure development has also taken place rapidly. If one looks at the construction of new transport facilities, over 680 kilometers of railways, 917.4 kilometers of expressways, 8.6 kilometers of long bridges (over 500 m), 10 deep-water berths (over 10,000 ton) and 2 international airports were under construction during this five-year period (Loo, 1997a). Such rapid transport development poses important theoretical and practical questions to geographers and regional scientists as to the role of transport in the drastic transformation of the regional economy.

Theoretically, transport improvements may be seen to have spread, redistributive, or backwash effects on the spatial pattern of development (Loo, 1997a). First, transport infrastructure development is seen to have a spread effect on development by reducing the barriers of distance and allowing community, personal, and business relationships to realign and to capitalize on the comparative advantages of different locations of a region. As a result, geographical specialization and interdependency develop and all localities in the region benefit (Hundleston and Pangotra, 1990; Filani, 1993). A different school of thought interprets the new economic development generated "by" the new transport facilities as supported only by economic decline in the other subareas disadvantaged by traffic diversion (Forkenbrock and Foster, 1990; Foster, Forkenbrock, and Pogue, 1991). Finally, transport infrastructure development may cause a polarization of regional development because an improved transport line between a less-developed and a more-developed area may cause a drain of economic and human resources from the former to the latter (Keeble, Owen, and Thompson, 1982; Eagle and Stephanedes, 1987).

Despite the fact that development requires sufficient transport seems to be axiomatic, there is no consensus on the role of transport in economic development.[3] Historically, the catalytic role of transport in development has been emphasized (e.g., Rostow, 1964; Fishlow, 1965). A transport improvement lowers transport costs, widens markets, allows economies of scale in production, creates agglomeration economies, and encourages exports. In addition, transport development generates demand for multiple basic industries, such as the coal and iron and steel industries (backward linkages). On a broader scale, transport facilitates innovation as a source of external economies. Hence, economic growth is a direct result of improved transport and there is a causal linkage between the two (Liew and Liew, 1985; Mills and Carlino, 1989; Pachner, 1995). For others, transport is a permissive rather than a lead factor of development. This view was forcefully presented by Fogel (1964) in his calculation of the net social savings of railroad construction in America. His study started much theoretical debate and is associated with a wider contemporary literature that views transport development as a necessary but not sufficient condition for development (Bruinsma, Nijkamp, and Rietveld, 1992; Wigle 1992). At the opposite end, transport infrastructure investment is regarded as a negative factor in the process of development. Theoretically this occurs when the investment in transport infrastructure is misdirected and the positive effects of investment in the other sectors exceed that of improved transport. Such "over-investment" is closely associated with the opportunity costs of investment funds and the "crowding-out" of private investment as the government raises funds in the capital market and, hence, pushes up the interest rate; yet, no empirical evidence is provided.

Furthermore, the existing literature shows that different types of transport facilities may have different effects on regional development. For instance, Evers et al. (1987) show that building a conventional railway between Amsterdam, Groningen and Hamburg would have a minimal effect on the spatial economy but the construction of a high-speed railway would create significant polarization effects. Also, road construction would affect industrialization and agricultural development differently (e.g., Botham, 1980; Filani, 1993). Nonetheless, no studies have tapped into this area by taking into account the complex interrelationships between transport and development generally, the ways in which different types of transport facilities may be associated with various dimensions of development, and the spatial consequences of such transport-development interrelationships. By applying the powerful methodological tool of CCA, in the present paper I attempt to shed some light into this relatively neglected area in regional science.

3. METHODOLOGY

Both transport and development are multidimensional in nature so they are much better represented by multiple measures, and the use of single composite variables is highly undesirable. Based on the theoretical underpinnings of the transport-development debate (Loo, 1997a) and the availability of data in the PRC, two sets of transport and development variables are compiled. In the compilation of these indices, a variety of data sources, including major yearbooks, statistical yearbooks, internal documents, company annual reports, and newspapers, were used. Great care has been given to ensure data consistency.

Compilation of Transport Vectors

Railways (TDIR), expressways (TDIX), deep water ports (TDIP), civilian airports (TDIA), local roads (TDIH) and Class I Open Ports (Guojia yilei kouan) (TDIO), are included to reflect the importance of international, regional, and local transport in affecting the relative accessibility of China's Zhujiang Delta under the Open Policy.[4] Transport development indices at the county level are calculated for each of these six types of facilities by taking into consideration their physical densities or availability, design and actual capacities, and detailed construction information. The benchmark year is 1995.

In order to ensure the comparability of different transport variables all weighted transport infrastructure indices are transformed into relational data. The data transformation procedures ensure that these variables initially measured in different measurement units, such as kilometers, throughputs, and carrying capacities, are converted into a single common scale, that is, relative performance within the region.

To illustrate, the railway development index (TDIR) is calculated by the following procedures. First, the length of existing railways rlenr and those under construction rconr, in every city and county are obtained. Second, these raw data are weighted by their carrying capacities rcap (obtained from the technical menu)[5] and the "expectation effects" expe (for lines which are still under construction or expansion). Based on the railway-line carrying capacities, single-track, double-track, and express railway lines are weighted by 1, 3.6, and 8, respectively.[6] From an earlier study it was found that the average length of time for the completion of transport and other capital construction projects in the Zhujiang Delta was roughly two years.[7] Thus, the value of "expectation effects" for any year is estimated to be one-half, expe = 0.5. This weight is introduced to capture the expectation of investors and people on the improved accessibility of an area once the construction works of a project have started. The omission of these effects is highly undesirable as real property and other development in the Zhujiang Delta has always begun prior to the completion of the transport projects (Shi and Qiu, 1993). Third, the weighted length is divided by the area of the respective city or county to obtain the weighted density. Finally, the weighted data are transformed into relational data, that is, expressed as percentages of the city or county with the highest weighted density. In this way, the TDIR of the city or county with the best railway infrastructure facilities is 100.

Mathematically, the compilation of TDIR for the kth county can be summarized by Equation (1)

(1) Multiple line equation(s) cannot be converted to ASCII text.

where rleni is the length of existing railways of type i, rcapi is the line capacity of railways of type i, n is number of types of railway line, rconi is the length of railways of type i under construction, expe is the expectation effects, area is land area, and N is the total number of subunits in a region.

Following the above procedures and rationale, the indices for expressways (TDIX), deep-water ports (TDIP), civilian airports (TDIA), road (TDIH), and Open Ports (TDOO) are compiled by taking into account their unique characteristics. Specifically, TDIX are calculated by Equation (2)

(2) Multiple line equation(s) cannot be converted to ASCII text.

where xlen is length of expressways and xcon is the length of expressways under construction. In the PRC an expressway is defined as a divided arterial highway with full control of access and with a designed average daily traffic (ADT) capacity of 25,000 vehicles per day (vpd) or above.

The indices for TDIP are calculated by Equation (3)

(3) Multiple line equation(s) cannot be converted to ASCII text.

where pnum is the number of existing deep-water berths (of 10,000 tons or above) and pcon is the number of deep-water berths under construction.

The indices for airports TDIA are calculated by Equation (4)

(4) Multiple line equation(s) cannot be converted to ASCII text.

where acapi is design capacity (d.c.) of the ith airport operating below d.c., n is the number of airports operating below d.c.;acapj is d.c. of the jth airport under construction; m is the number of airports under construction; bcapl is the actual operating capacity of the lth airport operating above d.c. and r is the number of airports operating above d.c.

The indices for Class One Open Ports (TDIO) are calculated by Equation

(5) Multiple line equation(s) cannot be converted to ASCII text.

where opas is number of Class One Open Port for passengers only, ofre is number of Class One Open Port for both passengers and freight. Due to the differences of Class One Open Ports for passengers and those for both passengers and freight in affecting regional accessibility they are separated into two classes. Theoretically, there is no justification for weighting the international flows of people and goods differently. Hence, they are weighted equally and opas is assigned a weight half of ofre.

Lastly, the indices for roads (TDIH) are calculated by Equation (6)

(6) Multiple line equation(s) cannot be converted to ASCII text.

where hlen is length of highway. The index is relatively simple mainly because of the lack of systematic data on the breakdowns of road categories by the four classes at the county level. Besides, technological variations in the highway or road standards are relatively small when compared with the other transport modes, especially in an urban context.

Compilation of Development Vectors

Similarly, development is not understood as a unidimensional process. Regional development should at least encompass the income (RDII), structural change (RDIC), living standard (RDIL), and rural poverty (RDIR) components (see discussion below). Although these different dimensions of regional development are highly complex and are subjects of academic interest in their own right, they are included to give development a broader meaning and to reveal the "subtle" aspects inevitably concealed by a few summary indices. The most comprehensive and up-to-date data at the county-level are for 1992 (Loo, 1997a). Hence, it is used as the benchmark year for the study of development. Based on the data available ten development variables are compiled under the four dimensions of development mentioned above.

In general, per capita real income is still considered the single most important indicator of the level of development attained. In China, real National Income (NI) per capita is preferred over Total Product of Society (TPS) per capita because the latter has suffered from the problem of double-counting (Huddleston and Pangotra, 1990). Mathematically, this first component of regional development--income component--is calculated by Equation (7)

(7) Multiple line equation(s) cannot be converted to ASCII text.

where ni is national income, pdef is the inverse of price deflator, and popu is population size.

Although the distinction between economic growth and development was blurred and seen as trivial in the 1950s, it has commonly been accepted since the 1970s that the latter has a much broader connotation that embraces changes other than the mere continuous rise in real income per capita. However, there is no consensus as to what these changes are. In the present study, three major dimensions are highlighted to give a firmer grasp of the concept of development. First, development must be accompanied by structural change which is not only limited to the economy but also includes the wide-ranging geographical, social, and political systems. Industrialization RDIC1, increased participation in the world economy RDIC2, urbanization RDIC3 and RDIC4, and the growth of tertiary industries RDIC5 are some of the most widely recognized changes. Specifically, the industrialization index RDIC1 is obtained by Equation (8)

(8) Multiple line equation(s) cannot be converted to ASCII text.

where gvio is the gross value of industrial outputs and tps is the total product of society. The use of the sectoral composition of NI is preferred over the breakdowns of TPS. However, the former is not systematically available at the county level.

In the Zhujiang Delta, increasing participation in international division of labor, especially in the form of exports to the world market RDIC2, represents another important dimension of the regional structure that is highly valued by the government as a source of foreign exchange (Leung and Loo, 1997). Therefore, the degree of export-orientation is included and is calculated by Equation (9)

(9) Multiple line equation(s) cannot be converted to ASCII text.

where expo is export value in 10,000 US dollars and excr is the exchange rate.

Urbanization is also a major facet of the development process. It is associated with the dual process of an increasing proportion of people living in urban areas (towns and cities) and engaging in urban (nonagricultural) occupations.

Accordingly, RDIC3 calculated by Equation (10) and RDIC4 calculated by Equation (11) measure the degrees of urbanization by the household registration system and occupation, respectively. Separate measures are necessary because of the controversy on the definitions of "urban" under the household registration system in China (see Chan, 1994).

(10) Multiple line equation(s) cannot be converted to ASCII text.

where urbp is the size of urban population.

(11) Multiple line equation(s) cannot be converted to ASCII text.

where nona is size of the nonagricultural population.

Finally, the share of the tertiary sector, including the service and banking industries, would be increasing as the economy diversifies and develops. However, a good measure of income from the sector is not available at the county level so the value of nonagricultural and industrial outputs is used as a surrogate. This residual value reflects the changing share of output generated from nonagricultural and industrial sources. The relative share of the sector in the economy is reflected in RDIC5 which is calculated by Equation (12)

(12) Multiple line equation(s) cannot be converted to ASCII text.

where serv is the value of nonagricultural and industrial outputs.

So far, little if any attention has been paid to the well-being of the people. Largely ignored has been the question of "development for whom?" To address this inadequacy the living standard RDIL and rural RDIR components are used as proximate indicators to reflect the improvement of living standard of the masses.

The real average wage RDIL1 is used to reflect the income flow of the people and is obtained by Equation (13)

(13) Multiple line equation(s) cannot be represented in ASCII text.

where wage is the average wage of workers.

Consumption power is reflected in the retail sales per capita RDIL2 and is shown in Equation (14)

(14) Multiple line equation(s) cannot be converted to ASCII text.

where reta indicates total retail sales.

Savings per capita RDIL3 is used to capture the general economic well-being or wealth of the population. The indices are calculated by Equation (15)

(15) Multiple line equation(s) cannot be converted to ASCII text.

where save is the value of savings.

Finally, net income of the farming population is listed separately in RDIR because rural poverty constitutes one of the major inequality problems. With the economically lagging regions predominantly associated with primary production, peasant income constitutes an important aspect of the regional structure. It is calculated by Equation (16)

(16) Multiple line equation(s) cannot be converted to ASCII text.

where peas is the average income of peasants.

4. CANONICAL CORRECTION ANALYSIS

CCA is an ideal methodological tool for the analysis of the interrelationship between transport and regional development. As mentioned earlier, both transport and regional development are multifaceted phenomena, that cannot be adequately summarized or analyzed by one simplified aggregate measure alone but must be represented by multiple measures. Mathematically they are better conceptualized as vectors, and the real spatial structure of a region and its constituting components, such as counties, are better seen and described by a multitude of variables of different kinds. Thus, each spatial subunit or county can be seen as partitioned vectors. In the Zhujiang Delta there are 31 cities and counties (N = 31).8 Hence, we have a region of 31 partitioned vectors. Such vectors may be conceptualized as consisting of a pair of subvectors made up of p transport variables (p = 6) and q development variables (q = 10). By standardizing the two sets of variables (zero mean, unit variance) z(RDI) and z(TDI), respectively, we can denote the jth subregional unit, or county, in each partitioned vector, by

(17) Multiple line equation(s) cannot be converted to ASCII text.

In this way, all the information about linear relationships within and between the two sets of data can be summarized by the covariance matrix of the vector variables. The data are standardized so the covariance matrix is identical to a correlation matrix and the correlation matrix R of gj may be written as the partitioned matrix

(18) Multiple line equation(s) cannot be converted to ASCII text.

where R11: p x p matrix correlations between the transport variables

R22: q x q matrix correlations between the development variables

R12 = Rt21: p x q matrix correlations between the transport and development variables of each set

We are analyzing the relationship between transport and development so we are primarily interested in R12 and R21. CCA tries to maximize the covariance between the two sets of variables, z(TDI)(N x p) and z(RDI)(N x q), by simultaneously rotating the coordinating frames of each space to new positions. Conceptually, this is similar to thinking of the region as a galaxy of N points in a single space of p x q-dimensions. Mathematically, it involves finding the latent roots of a new matrix M obtained by manipulating the four partitions of the R matrix to highlight the interrelationships between, instead of within, the two sets of transport and development variables. This new matrix is given by

(19) M = R-111 R12 R-122 R21

The purpose of inverting R11 and R22 is to orthogonalize the transport and development variables, respectively, so that the elements of matrix M will express the overlap between the two sets of data. Under the new coordinate systems the relationships with each set of variables are disentangled and there is a reduction in dimensionality. Algebraically, the rotations are equivalent to finding linear transformations of each set of variables, muk = atkz(TDI) and vk = btkz(RDI), where k is the canonical function, and a and b are such that the simple correlation Rck between the transformed variables muk and vk is maximized.

The maximum number of canonical functions extracted is equal to the number of uncorrelated (orthogonal) function equations obtained by conducting a full-rank principal components analysis of matrix M. Altogether, there will be s pairs of such linear transformations, that is, k = 1,..., s, where s = min(p,q). By convention, the smaller set of indices are called criterion variables and the larger set are called predictor variables.[9] Nonetheless, the results of the analysis will not be affected even when development variables are inputted as criterion variables and transport variables as predictor variables. The term predictor does not denote the assumption of a dependency relationship between the two sets of data as would the case in multiple recession. This is a very important characteristic of the present analysis because the relationship between transport and development is seen to be one of interdependency and their characteristics are interwoven to produce the real structures in space. Another major difference of CCA with multiple regression analysis is that whereas the latter does deal with multiple predictor variables, it deals with one criterion (dependent) variable only. The multiple regression equation for a research question with one dependent variable y and four independent variables x1, x2, x3, x4, is y = a + beta1x1 + beta2x2 + beta3x3 + beta4x4, where a, beta1, beta2, beta3, and beta4 are constants. Thus, for the present research question with multiple transport variables p and development variables q, p + q regression equations are required. Besides, there is no direct way of analyzing the relationships among the p + q regression equations.

The above comparison is not to understate the importance and powerfulness of multiple regression analysis but this does point to the different uses of the two methodological tools in analyzing various types of research questions and according to the restrictions that the researcher chooses to incorporate into the model. For instance, the proposition that transportation is a catalytic factor in development would lead the researcher to develop multiple regression models using the q development variables as dependent variables. Under CCA, no such a priori assumptions are required. As such, CCA imposes fewer constraints on the multivariate statistical model and is therefore complementary to multiple regression analysis. For instance, the subsets of most closely related transport and development variables identified by CCA may provide an objective and scientific basis for the researcher to develop more vigorous statistical or econometric models to address questions related to directions of causality.

After the principal component analysis of matrix M the sum of the eigenvalues can be divided by its rank to arrive at the roots (lambda) of the matrix. These eigenvalues give the proportion of variance contained in each of the canonical functions (R2ck), and are calculated by

(20) (M - lambdaI) = 0

where lambda are the canonical roots R2ck and I is an identity matrix. In the above transformation, all within-set correlation is reduced to zero and all linear correlation between sets is channeled through the canonical correlation coefficients, RCk that is, square root of lambda. Therefore, CCA does not alter the intrinsic correlation structure of the data but provides a convenient coordinate system within which the correlation of interest is clearly revealed. The new variables muk and vk which correspond to the rotated axes of the coordinate frames, are called canonical variates and the familiar product-moment correlation coefficient RCk between the canonical variates muk and vk is the canonical correlation coefficient. Upon understanding the correlation between the transport and development variates (muk and vk), the next logical step is to interpret the relationships between the individual variables (p + q in total) and their respective canonical variates for each canonical function. Analytically, we are moving beyond the examination of the "imaged" transport and development variates which are derived mathematically in the abstract statistical space to the interpretation of "real" transport (TDI) and development (RDI) variables which are included in our model based on theoretical and practical considerations.

To recall, each canonical variate is derived subject to the restriction of maximizing the relationship between the two sets they represent. This optimality is achieved by weighting the data of each subarea in the region and then calculating the weighted sum of the variables for each variate. These weights are called canonical weights or function coefficients. For every function there are two associated vectors of canonical weights for transport Tk and development Dk. As the transport variables are fewer in number Tk may be more easily calculated by the formula

(21) (M - lambdak)Tk = 0

and Dk may be obtained by substituting Tk into the following equation

(22) Multiple line equation(s) cannot be represented in ASCII text.

For a single canonical variate, canonical weights are similar to beta weights in multiple regression analysis (Levine, 1977). They can take on positive and negative values and are not constrained to be less than one. As such, the interpretation of canonical weights suffers from similar criticisms as beta weights in regression analysis. Most importantly, a small canonical weight may result either because the variable is irrelevant in determining the transport-development relationship or because its effects have been partialed out of the relationship due to a high degree of multicollinearity (Hair et al., 1995).

The use of the structure coefficients overcomes the above inherent weakness in function coefficients. Hence, the former are chosen to interpret the structural dimension of the interrelationships among the variables and canonical variates extracted. The structure coefficients are the correlation coefficients between the standardized variables (z(TDI), z(RDI)) and their own canonical variates (muk, vk). For each canonical function, there are two canonical structure matrices S, one for transport ST and the other for development SD). Mathematically, the element of the canonical structure matrix can be denoted by skj, where j = 1 ... p for the transport set and q for the development set. Conceptually, structure coefficients are similar to the R2 in regression analysis and factor loadings in factor analysis. Hence, they are also called canonical loadings. Structure coefficients are much more interpretable because their values only vary between -1 and +1.

As mentioned earlier, CCA is particularly suitable for the analysis of geographical issues because it is able to produce spatial meanings. The degree of participation of each spatial unit in a particular canonical variate can be obtained simply by premultiplying the associated vector of canonical weights with the standardized raw data to arrive at the canonical scores. For the kth canonical function the vector of canonical scores for transport St is given by

(23) Stk = z(TDI)Tk

and the canonical scores for development Sd is given by

(24) Sdk = z(TDI)Dk

In sum, the analysis aims to explore the extent and nature of overlap between different aspects of the spatial structure by linking the most closely related variables from the transport and development data sets. CCA combines the two variable sets in different ways that reflect the complexity of their interrelationship. Upon analyzing each of the interrelationships in turn one would be able to identify several broadbrush tendencies of how transport and development variables are integrated in the Zhujiang Delta.

5. RESULTS OF THE CANONICAL CORRELATION ANALYSIS

Summary results of the canonical correlation analysis are shown in Table 1. In the existing application CCA identifies the first canonical function (k = 1) by transforming the set of p transport variables and the set of q development variables into the transport and development variates (muk and vk), respectively, so that the correlation (Rck) between these two variates is maximized. In the p x q-dimension statistical space, the next pair of transport and development variates (k = 2) are identified by placing them at right angles to the first pair and rotating them until the next highest correlation between the two sets of variables is achieved. Orthogonality ensures that Rc between successive pairs of canonical variates decreases as k increases. This process of factoring (finding lambda) is carried out until all possibilities are exhausted, that is, when there are as many canonical functions as s.

Three criteria are used to determine the number of canonical functions (pairs of variates) for detailed interpretation. They are the level of statistical significance of the function, the magnitude of the canonical correlation, and the redundancy measure for the percentage of variance accounted for from the two data sets. In applying CCA, the researcher is interested to test whether the relationships between transport and development identified by the canonical functions are due to chance. The null hypothesis is that there is no relationship between the transport and development variable sets in the Zhujiang Delta. The level of significance is set to be .01 (alpha = .01). Among the test statistics available (Clark, 1975; Levine, 1977; Thompson, 1984), Bartlett's chi-square test is used to test the null hypothesis. This test may be seen to be divided into two parts as the x2 is not computed directly from the data but from another test statistic called Wilk's Lambda (Lambda) which is calculated by the formula

(25) Multiple line equation(s) cannot be represented in ASCII text.

If the null hypothesis is true, a particular function of A will be distributed approximately as a chi-squared variate, with pq degree of freedom (df). Thus, the test statistics x2 is given by

(26) x2 = -[(N-1) - 0.5 (p + q + 1)]ln Lambda

Through counter-checking with the theoretical x2 distribution, the level of significance (Prob.) for each canonical function can be calculated. These useful test statistics (X2, df, Prob. and Lambda) are shown in Table 1A. Based on these results, the null hypothesis is rejected for the first two roots (Prob < .01); and the common patterns between transport and development in the Zhujiang Delta are statistically significant for the first two canonical functions.

Nonetheless, statistical significance should not be used alone. Thompson (1985) and Hair et al. (1995) suggest that the practical significance of the canonical functions, represented by R2c, should also be considered. As discussed earlier, this squared canonical coefficient R2c represents the amount of variance linearly shared by the transport and development composites. Table 1A shows that the R2c of the first three canonical functions (i.e., k = 1,2, and 3) are relatively high at 0.966, 0.906, and 0.679, respectively. Lastly, redundancy analysis is conducted because high R2c may have arisen from a pair of transport and development variates which do not extract significant portions of variance from their respective sets of variables. In order to examine the latter, two steps are taken. First, the total variance of variates explained by the within-set variables is obtained by summing up the square of the respective canonical structure matrix. To recall, the element of the canonical structure matrix S may be denoted by skj, where j = 1 ... p for the transport set and q for the development set. Thus, the proportion of the transport set trace (variance) extracted by the kth variate, VTk, can be given by Equation (27). Similarly, the variance of the kth development variate is calculated by Equation (28)

(27) Multiple line equation(s) cannot be represented in ASCII text.

(28) Multiple line equation(s) cannot be represented in ASCII text.

These results of shared variance are shown in Table 1B, (i) and (ii), respectively.

In CCA, the research focus is primarily on the interrelationships between the two data sets. Thus, information on the within-set shared variance is not of direct interest. These measures are further transformed to show how much of the shared variance in a set can be accounted for by a variate from the other set. Thus, we take a second step of multiplying the shared variance with R2c, which represents the amount of variance of one variate which overlaps the other, to arrive at the Stewart-Love redundancy coefficient. The redundancy coefficient for the transport variate (RdTk = VTk R2ck) answers the question of how redundant the transport variate is, given the development variate. Similarly, the redundancy measures for the development set RdDk = VDkR2ck may be found. The redundancy coefficients for transport and development are not symmetric so they are shown separately in Table 1B. At first glance, the redundancy indices for neither the transport nor the development variates of the first (0.404 and 0.366) and the second (0.220 and 0.161) functions can be considered very high. Nonetheless, there is no generally acceptable rule on the level of redundancy used for retaining the canonical functions for further analysis. In fact the redundancy coefficients in this application are found to be relatively high when compared with other applications in social sciences (Levine, 1977). Besides, "redundancy analysis should be treated as evaluating adequacy of regression (prediction) and not association" (Muller, 1981, p. 142). Because the primary focus in the present research is "association" and the results of the analysis are not used for prediction, the redundancy measures for the first and second functions are considered to be satisfactory.

Based on the above three criteria, the first two roots are of high statistical and practical significance in understanding the underlying structural and spatial patterns of the Zhujiang Delta region. Hence, the discussion below will concentrate on these two roots which show the dominant interdependencies underlying the same spatial structure of the region. For the sake of comparison, results of the canonical functions three to six are also shown. These remaining functions are of lower statistical and practical significance. Nevertheless, they are still reported very briefly as they may point to the "sub-dominant interdependencies" (Clark, 1975) in the Zhujiang Delta during the study period.

The ways in which the canonical functions link the transport and development variables together are to be seen by the structure coefficients displayed in Table 2 and the canonical scores displayed in Table 3. Two dominant and four subdominant interdependencies are identified and they are listed below in order of importance.

National Income, Consumption, and Savings were Most Highly Correlated with Deep-water Port Facilities, Customs Check-points, and Expressways

In the present analysis CCA shows that transport and development in China's Zhujiang Delta are very closely associated with each other. The canonical correlation of the first canonical vector is close to one (R2C1 = 0.966). Statistically, the structure coefficients of TDIP (0.968), TDIO (0.965) and TDIX (0.681) contribute most significantly to the first transport variate mu1. The development variables having the highest correlation with its own canonical variate v1 are RDIL3 (0.920), RDIL2 (0.881), and RDII (0.806).

CCA indicates that the basic transport and development dimension in the regional structure of the Zhujiang Delta is the association of savings, consumption, and national income with deep-water ports, open ports, and expressways. These major transport infrastructure facilities have been associated with the movement of people, especially between the Zhujiang Delta and Hong Kong. Many Class I Open Ports are only open for ferry passengers to and from Hong Kong.[10] Such cross-border interchange of people and freight has been very important in affecting the overall economic performance, that is, real national income, of the cities/counties. Cross-border movement of people between Hong Kong and the Zhujiang Delta has been an essential and indispensable part of the economic "take-off" of the latter because it is necessary not only for conducting business but also for developing personal acquaintance of the local business environment. In 1997 the sum of foreign capital actually used in Guangdong was 14 billion US dollars. Of this amount, 68.90 percent came from Hong Kong (Guangdong tongji nianjian, 1998). In order to facilitate the economic development of the region such growing transport demand should be encouraged and satisfied.

In addition, CCA is particularly useful in identifying the overlap of transport and development variables over space. The canonical scores which can be interpreted as the degree of participation of each spatial unit in the canonical pattern (Clark, 1975) are shown in Table 3. From Table 3 one finds that the degree of participation for each city or county in transport and development scores tends to be of the same sign and of similar magnitude. This is particularly the case for the first canonical pattern.[11] In order to aid understanding, a map showing the administrative divisions of the Zhujiang Delta is shown in Figure 2A. In addition, the canonical scores for the first canonical function are displayed in Figure 2B.

The degree of participation of Guangzhou, Shenzhen, Zhuhai, and Foshan in the first canonical function is positive for both the transport and development variates, St1 > 0 and Sd1 > 0. These positive scores imply a high degree of association between transport and development in these most developed municipalities in the region. In other words, we have a concentration of savings, consumption, and income in cities having high densities of deep-water ports, open ports, and expressways already in operation or under construction.

Six cities and counties (Huizhou, Qingyuan, Doumen, Huiyang, Taishan, and Enping) have negative transport but positive development scores St1 < 0 and Sd1 < 0. Such negative transport scores denote that deep-water ports, direct customs check-points, and expressways were lagging behind development. In these municipalities and counties the development of deep-water ports, designation of National Customs, and construction of expressways may act as powerful stimuli to the economic growth of these areas.

The close relationship between the lack of direct international transport facilities and poor economic performances in most cities or counties in the Zhujiang Delta is manifested in their negative transport and development scores St1 < 0 and Sd1 < 0.[12] Within this group, seven cities or counties have transport scores lower than development scores, St1 < Sd1 < 0. In other words, transport is lagging behind development. However, 14 other cities and countries have development scores higher than transport scores, Sd1 < St1 < 0. For these cities or counties, transport is not the lagging sector in the local economies. On the contrary, the bottleneck lies with the other industries or infrastructure. The findings highlight the need to avoid the pitfall of making sweeping generalizations regarding the "magical" power of transport improvement to stimulating development. Instead, there needs to be more careful studies on the spatial location of transport investment, taking into account not only the existing transport demand but also the possible propensity for future transport demand. The latter is strongly affected by the specific economic characteristics and policies of the cities or counties in question. Further research is required for us to gain a better understanding of the possible causal relationships.

Urbanization Was Most Closely Associated with the Provision of Railway Network and Airport Facilities

CCA suggests that the regional structure of the Zhujiang Delta is integrated in a second way by a high level of urbanization and, to a lesser extent, real wage level with the concentration of railways and airports. The structure coefficients are mostly negative but the magnitude of correlation remains high for TDIA (-0.733) and TDIR (-0.700) with the transport variate mu2, and RDIC3 (-0.688), RDIC4 (-0.650) and RDIL1 (-0.508) with the development variate v2. Although railways and airports have not been the most important dimensions of the economic performance of the Zhujiang Delta, they are particularly important in moving people away from rural towns and agricultural occupations and, thus, in raising their real wage levels. Conversely, the relatively high population and economic thresholds for railways and airports may have made them spatially concentrated in the predominantly urban areas, especially large cities.

The canonical scores show that the degree of positive participation of cities or counties in the second canonical pattern is much higher than the first one. This may be due to the wider spatial incidence of urbanization and the development of railways and airports in many parts of the Zhujiang Delta (Table 3). Most notably, the rapid urbanization process on the western flank of Zhujiang River, especially in Taishan, Enping, and Kaiping has been closely associated with the expectation effects of the construction of Guangzhou-Zhuhai express railways and its branch lines in the 1990s (Loo, 1999). The high negative transport and development scores of Guangzhou, Foshan, Zhuhai, and Jiangmen highlight the relative inadequacy of railway and airport facilities in relation to the levels of urbanization reached. With the much publicized projects of Guangzhou Subway Number One and the New Guangzhou Airport, the poor performance of Guangzhou requires some explanations. Despite the fact that many newly-built railways will have Guangzhou as one of their terminals, the actual construction usually only took place outside the city. There has been a relatively low increase in the actual railway mileage built within the municipality. The fact that the construction of Guangzhou Subway only began in 1995 points to the slow development of mass transit in Chinese cities.[13] Moreover, the New Guangzhou International Airport is located outside the city and instead is in Huadu. The highest positive transport and development scores are recorded in Shenzhen and Qingyuan.

In addition, CCA specifies four subdominant common patterns suggesting further ways that the Zhujiang Delta may be integrated through the transport and development variables.

Industrialization in the Zhujiang Delta was Most Closely Related to the Extension of Highways over Space

The third interdependency in the regional structure combines the highway density variable with industrialization. Table 2 shows that the highest structure coefficient of mu3 is recorded in TDIH (0.533) and the highest structure coefficients of v3 are recorded in RDIC1 (0.471) and RDIC2 (0.373). This relationship points to the extension of highways in cities or counties undergoing relatively rapid industrialization. Indeed, the need for highway extension is obvious with the spatial sprawl of factories and relatively low land prices in the region. On the third canonical pattern, the involvement of Zhongshan, Nanhai, Shunde, Gaoming, and Sanshui in both scores testifies to a close overlap of highway and industrialization patterns in these areas. Most of them, including Zhongshan, Nanhai, and Shunde, were the most rapidly industrializing municipalities in the Delta, nicknamed the Four Little Tigers, the other being Dongguan.

Export-orientation Tended to Move in the Same Direction as Railway Density

Vector 4 points to the fact that export-oriented cities or counties tend to be areas of high railway density. The structure coefficients for canonical function 4 have been relatively clear-cut with mainly TDIR (-0.429) and RDIC2 (0.569) contributing to mu4 and v4 respectively. In other words, it signified that low export-orientation was associated with low railway density. This vector underlines the relatively high freight-generating intensity of export production and the low value of these products which are still heavily dependent on railway transport to Hong Kong or nearby ports. On the fourth canonical patterns, the canonical scores of Guangzhou, Nanhai, and Shunde are highly positive. Huizhou has a positive transport but negative development score for this and the next canonical scores. This implies the failure of the local economy (at least at this stage) to take full advantage of the transport facilities by investing in the other industries to boost development.

Rural Development and Service Sector Production in the Region Have Been Most Closely Associated with the Improvement in Railway and Highway Densities

Canonical loadings on Vector 5 further link the rural and tertiary activity development with the network of railways and highways. The highest structure coefficients for the fifth transport variate mu5 are TDIR (0.487) and TDIH (-0.480) and the highest ones for the fifth development variate v5 are R.DIC5 (0.517) and RDIR (0.487). In this respect the tertiary sector probably includes the informal sector in the rural areas which thrives in rural-based counties lacking in direct railways and highways. In this canonical pattern, Panyu and Baoan have the highest scores. They are the most important rural counties supplying agricultural produce to the two largest municipalities in the Zhujiang Delta--Guangzhou and Shenzhen (Loo, 1997b). Again, this points to the close association of low railway and highway network with the agricultural-based economy of the rural counties.

Industrial Production and Industrial-supporting Tertiary Sector Were Related to the State of Development of Airport and Highway Facilities

Vector 6 joins the tertiary and industrial production indicators with airport and expressway densities. For this last canonical function, the structure coefficients for TDIA (0.443) and RDIC5 (0.691) are the highest. In this function, the tertiary sector is most likely to be associated with commercial development and tourism in the major cities with airport facilities. Furthermore, the loadings for TDIX (-0.421) and RDIC1 (-0.499) are negative. This reflects the lack of expressways with the relatively low industrialization level. Zhuhai has the highest score in this last canonical pattern. In particular, the attractiveness of Zhuhai as a tourist city after the opening of the Zhuhai International Airport is noteworthy.

6. VALIDATION OF RESULTS

As in the application of other statistical techniques, the researcher is concerned with the validation of CCA results. Among the available approaches for validating the results, a sensitivity analysis of the predictor variable set for the most important canonical function is used by Hair et al. (1995).[14] In essence, the sensitivity analysis examines the stability of different CCA statistics, including canonical roots, shared variance, redundancy, and canonical loadings when individual development variables are deleted. The results of the analysis for the first canonical vector are shown in Table 4. It can be seen that the overall canonical correlation, ranging from 0.968 to 0.983, and root, ranging from 0.936 to 0.966, are remarkably stable in each of the cases where a development variable is deleted.

More importantly, the canonical loadings for both the transport and development variates remained stable and consistent throughout the analysis. In each of the cases, the basic structural dimension of the transport-development relationship, as reflected by the canonical loadings, is maintained. In other words, the association of national income, consumption, and savings with deep-water port facilities, customs check-points, and expressways is clearly discernable throughout the test. Such a robust relationship is worthy of further research with the application of more vigorous statistical models including multiple regression models. Finally, the shared variance and redundancy of the transport and development variables are also fairly resistant to changes in the model specifications.

7. CONCLUSION

In sum, the transport-development relationship should not be treated as fixed or uniform over space. The application of CCA in the Zhujiang Delta reveals substantial information on the strength of the underlying transport-development interrelationship, the ways in which the six major transport facilities have been associated with the ten dimensions of regional development, and the spatial characteristics of such complex transport-development interrelationships. The six major trends identified reinforce the proposition that the nature of transport investment and the modal and locational choices of transport infrastructure projects would affect the de facto relationships between transport and development (Loo, 1997a). In other words, different types of transport infrastructure and facilities have different relationship with various dimensions of development. Although CCA cannot answer all questions about the transport-development relationship, its application has improved our understanding of the intertwined relationship between different types of transport infrastructure and development dimensions within the regional structure of China's Zhujiang Delta. It is hoped that the limited findings of the present paper may encourage more applications of this methodological tool in regional science.

* I wish to express my sincere gratitude to Professors Gordon F. Mulligan, David A. Plane, and the four anonymous referees for their insightful comments and criticisms.

Received November 1998; revised April 1999; accepted July 1999.

1 They are Guangzhou, Shenzhen, Zhuhai, Dongguan, Zhongshan, Huizhou, Jiangmen, Foshan, Zhaoqing, and Qingyuan municipalities at the prefectural level, and Panyu, Taishan, Nanhai, and Shunde municipalities at the local level.

• 2 They are Huadu, Conghua, Zengcheng, Baoan, Doumen, Huiyang, Boluo, Huidong, Xinhui, Enping, Kaiping, Heshan, Sanshui, Gaoming, Gaoyao, Guangning, Sihui, and Qingxin county.
• 3 Recently this area has received renewed academic interest and special issues of the Annals of Regional Science (23) and Applied Geography (45/46) are devoted to infrastructure and development. For discussion see Loo (1997a).
• 4 Class I Open Ports are designated by the State Council. They refer to the passenger and freight interchange ports opened to foreign vessels, airplanes, and vehicles; or passenger and freight ports used only for outgoing Chinese vessels, airplanes, and vehicles; or freight ports used for the entry of foreign vessels for goods delivery. They are administered directly either by the central or provincial government. (Tang and Zhao, n.d., pp. 1-4)
• 5 The technical menu lists the technologies and line capacities for different types of railway lines. In the PRC, the railway line capacities for a single-track, double-track, and express railway line were 45 (42-48), 160 (140-180), and 360 tonnes per kilometers, respectively (Hao, 1988).
• 6 Ibid.
• 7 For the lengths of time taken to complete individual transport and capital projects in the region, see Loo (1997a, Appendices V. 1-6 and VII). Because variations in the construction period of individual projects are common (usually within the range of 6 months to 4 years) and the construction period for some individual projects cannot be determined, the average of approximately two years is used for all projects.
• 8 Because Qingxin county was only separated from Qingyuan municipality in May 1992 it is still considered as part of the latter in the present analysis.
• 9 In the more classical reference books, such as Clark (1975) and Levine (1977), the smaller data sets are named predictor variables. However, in more modern reference books such as Hair et al. (1995) and Johnson and Wichern (1998) the smaller data sets are named criterion variables.
• 10 They included Foshan Port in Nanhai, Heshan Port in Heshan, Jiangmen Port in Jiangmen, Meisha Port in Shenzhen, Rongqi Port in Shunde, Sanfu Port in Kaiping, Taiping Port in Dongguan, Wanji and Zhuhai Ports in Zhuhai, and Zhaoqing Port in Zhaoqing (Tang and Zhao, n.d.).
• 11 When the canonical root (R2C) is one, the two canonical scores are equal. The closer is R2C to one, the smaller is the difference between the two canonical scores. Therefore, the deviation of the two canonical scores may be interpreted as the degree of contribution of the city or county to the canonical root (Clark, 1975).
• 12 This is partly due to the relative high polarization of transport investment and regional development in the Zhujiang Delta during the study period (Loo, 1997b, 1998, 1999).
• 13 Railway construction in a heavily urbanized area like Guangzhou has faced many problems including residential and business relocations, demolition of buildings, and traffic diversion. The actual construction works, first started in 1993, have lasted for over five years and the Guangzhou Subway was only opened to traffic in February 1999.
• 14 This test is also recommended by one of the referees.

TABLE 1: Summary Results of Canonical Roots between Multiple Transport and Development Variables

A. Canonical Structure Legend for Chart: A - Number of Roots Removed B - k C - RC,k D - RC, k2 E - Barlett X2 F - degrees of freedom G - Probability H - Lambda A B C D E F G H 0 1 .983 .966 167.080 60 .000 .000 1 2 .952 .906 94.262 45 .000 .012 2 3 .824 .679 43.423 32 .086 .133 3 4 .602 .363 18.987 21 .586 .413 4 5 .529 .280 9.295 12 .678 .649 5 6 .314 .099 2.237 5 .815 .901 B. Redundancy Analysis

(i) Standardized Variance of Transport Variables Explained by:

Legend for Chart: A - Canonical Function B - Their Own Canonical Variate (Shared Variance, VTk), Percentage C - Their Own Canonical Variate (Shared Variance, VTk), Cumulative Percentage D - The Opposite Canonical Variate (Redundancy; RdTk), Percentage E - The Opposite Canonical Variate (Redundancy; RdTk), Cumulative Percentage A B C D E 1 .419 .419 .404 .404 2 .243 .662 .220 .624 3 .101 .763 .069 .693 4 .071 .834 .026 .719 5 .085 .919 .024 .743 6 .083 1.002[*] .008 .751

(ii) Standardized Variance of Development Variables Explained by:

Legend for Chart: A - Canonical Function B - Their Own Canonical Variate (Shared Variance, VDk), Percentage C - Their Own Canonical Variate (Shared Variance, VDk), Cumulative Percentage D - The Opposite Canonical Variate (Redundancy, RdDk), Percentage E - The Opposite Canonical Variate (Redundancy, RdDk), Cumulative Percentage A B C D E 1 .378 .378 .366 .366 2 .178 .556 .161 .527 3 .080 .636 .054 .581 4 .059 .695 .022 .603 5 .067 .762 .019 .622 6 .079 .841 .008 .630

* Note: Cumulative percentage should add up to 1.000. The slight discrepancy is due to the rounding up of variance to three decimal places.

TABLE 2: Structure Coefficients between Multiple Transport and Development Variables

Legend for Chart: A - Variate/Variable Name B - Brief Description C - Canonical Vectors, One (k = 1) D - Canonical Vectors, Two (k = 2) E - Canonical Vectors, Three (k = 3) F - Canonical Vectors, Four (k = 4) G - Canonical Vectors, Five (k = 5) H - Canonical Vectors, Six (k = 6) A B C D E F G H Transport Variables and their Canonical Variates (uk) TDIR Weighted Railway .147 -.700 .075 Density -.429 -.487 -.249 TDIX Weighted Expressway .681 -.492 .332 Density -.061 .054 -.421 TDIH Weighted Highway .386 -.419 .533 Density .390 -.480 -.099 TDIP Weighted Port .968 -.105 -.053 Density .144 -.041 .164 TDIA Weighted Airport .096 -.733 -.426 Density .225 .161 .443 TDIO Weighted Open .965 -007 .150 Port Density -.110 -.102 .152 Development Variables and their Canonical Variates (vk) RDII real income .806 -.386 .252 indicator -.143 .179 .093 RDIR rural development .592 -.223 .303 indicator -.028 .487 .055 RDIL1 real wage .459 -.508 .368 indicator .074 .070 -.073 RDIL2 real consumption .881 -.318 .128 indicator -.177 .133 .057 RDIL3 real savings .920 -.166 .218 indicator -.002 -.072 -.013 RDIC1 industrialization .096 -.419 .471 indicator .040 -.271 -.499 RDIC2 export-orientation .499 -.351 .373 indicator -.569 .145 -.178 RDIC3 urbanization .594 -.650 .098 indicator 1 -.339 -.123 .102 RDIC4 urbanization .560 -.688 .041 indicator 2 -.299 .007 -.045 RDIC5 tertiary sector .156 .030 .270 indicator -.072 .517 .691

Note: Leading structure coefficients are typed in italics.

TABLE 3: Summary Results of Canonical Scores

Legend for Chart: A - First Canonical Pattern, Transp. (St1) B - First Canonical Pattern, Dev. (Sd1) C - Second Canonical Pattern, Transp. (St2) D - Second Canonical Pattern, Dev. (Sd2) E - Third Canonical Pattern, Transp. (St3) F - Third Canonical Pattern, Dev. (Sd3) G - Fourth Canonical Pattern, Transp. (St4) H - Fourth Canonical Pattern, Dev. (Sd4) I - Fifth Canonical Pattern, Transp. (St5) J - Fifth Canonical Pattern, Dev. (Sd4) K - Sixth Canonical Pattern, Transp. (St6) L - Sixth Canonical Pattern, Dev. (Sd6) A B C D E F G H I J K L City at Prefectural Level (Excl. Administered Cities/Counties) Guangzhou 0.554 0.394 -3.459 -3.239 -2.348 -2.173 2.143 1.556 -0.244 -0.613 1.515 -0.056 Shenzhen 5.346 5.264 0.791 0.740 0.631 0.550 0.262 0.048 -0.386 -0.016 0.121 0.034 Zhuhai 0.183 0.440 -1.529 -1.556 -0.854 -0.420 -1.273 -0.934 1.585 0.726 2.232 1.428 Huizhou -0.077 0.178 -0.268 -0.148 0.595 1.114 0.210 -2.132 1.161 0.256 -1.030 -0.619 Dongguan -0.317 -0.185 -0.367 0.163 0.424 0.698 0.467 0.118 -1.268 0.571 -0.556 -1.878 Zhongshan -0.030 -0.332 -0.065 0.074 0.955 0.931 -0.238 0.292 2.037 0.262 -0.450 -0.668 Jiangmen -0.123 -0.192 -1.380 -1.219 2.283 -1.755 -3.539 -1.755 -1.635 -1.557 1.680 0.590 Foshan 0.158 0.206 -2.610 -2.751 0.262 -0.122 -0.439 -0.504 -0.931 -1.071 -3.966 -0.421 Zhaoqing -0.129 -0.185 0.711 -0.270 -1.008 -0.957 -0.907 -1.870 -0.043 1.175 0.065 0.207 Qingyuan -0.050 0.079 0.742 0.877 -1.389 -0.994 -0.786 0.143 0.420 0.646 -0.497 0.547 County/City at County Level Huadu -0.309 -0.562 0.249 -0.264 0.133 0.928 0.424 1.467 -0.493 0.111 -0.078 0.683 Conghua -0.447 -0.405 0.546 0.362 0.551 -0.997 0.876 0.668 -0.573 0.793 0.644 0.197 Zengcheng -0.396 -0.540 0.164 0.474 -0.155 -0.121 0.454 0.700 -1.726 0.711 -0.043 0.873 Panyu -0.022 -0.046 0.095 -0.143 0.397 -0.076 -0.214 0.845 1.806 0.829 -0.652 -0.938 Baoan -0.301 -0.267 -0.953 -0.878 0.791 1.067 -0.165 -0.898 1.828 3.591 0.414 0.667 Doumen -0.021 0.009 0.499 0.800 -2.340 -1.750 -1.921 -1.356 -1.387 -0.483 -0.586 -0.804 Huidong -0.178 -0.350 0.635 0.385 -0.436 -1.353 0.096 -0.010 0.465 -0.167 -0.097 1.414 Huiyang -0.015 0.169 0.460 0.697 -0.333 0.098 0.302 1.561 0.387 0.024 -0.489 2.556 Boluo -0.333 -0.222 0.632 0.759 -0.094 -1.026 0.357 -0.172 -0.353 -0.920 0.326 1.000 Xinhui -0.295 -0.341 0.541 0.205 -0.678 0.113 0.012 -0.001 -0.967 -0.551 0.005 -1.232 Taishan -0.191 0.063 0.784 0.750 -0.650 -1.221 0.266 0.288 0.260 0.082 0.107 -1.244 Kaiping -0.155 -0.279 0.389 0.707 0.020 0.631 0.078 0.825 0.846 0.172 -0.299 -0.105 Enping -0.185 0.032 0.407 0.786 0.069 -0.750 0.158 0.074 0.699 -0.137 -0.201 -0.436 Heshan -0.085 -0.294 0.158 0.460 0.066 -0.008 -0.296 0.564 0.938 1.447 -0.495 -1.404 Nanhai -0.559 -0.106 0.017 -0.309 1.590 1.868 1.585 1.800 -0.993 -0.638 0.585 -0.145 Shunde -0.356 -0.496 -0.403 -0.571 1.783 1.126 0.931 0.703 0.001 -0.125 0.002 -0.848 Gaoming -0.503 -0.718 0.493 0.854 0.831 0.616 1.115 -1.195 -0.749 -0.679 0.780 1.762 Sanshui -0.369 -0.293 0.596 0.440 0.083 1.246 0.508 0.290 -0.473 -1.373 0.411 0.723 Gaoyao -0.251 -0.431 0.716 0.423 -0.485 -0.192 0.017 -0.186 -0.061 -0.794 0.139 -0.868 Guangning -0.260 -0.517 0.725 0.922 -0.383 -0.056 0.082 -0.960 0.014 -1.135 0.194 -0.299 Sihui -0.284 -0.075 0.684 0.468 -0.314 -0.472 0.161 0.033 -0.164 -1.136 0.221 -0.718

TABLE 4: Sensitivity Analysis of the First Canonical Root to the Removal of a Predictor Variable

Legend for Chart: A - Results after Deletion of, Complete Variate B - Results after Deletion of, RDII C - Results after Deletion of, RDIR D - Results after Deletion of, RDIL1 E - Results after Deletion of, RDIL2 F - Results after Deletion of, RDIL3 G - Results after Deletion of, RDIC1 H - Results after Deletion of, RDIC2 I - Results after Deletion of, RDIC3 J - Results after Deletion of, RDIC4 K - Results after Deletion of, RDIC5 A B C D E F G H I J K Canonical Correlation (Rc) .983 .980 .968 .981 .980 .972 .981 .983 .981 .982 .980 Canonical Root (Rc2) .966 .960 .936 .962 .960 .945 .963 .966 .962 .964 .960 Transport Variate (uk), Canonical Loadings TDIR Weighted .147 .175 .168 Railway Density .279 .186 .404 .119 .153 .037 .122 .112 TDIX Weighted .681 .718 .711 Expressway Density .756 .725 .781 .677 .686 .605 .679 .676 TDIH Weighted .386 .451 .457 Highway Density .447 .459 .432 .383 .390 .323 .385 .382 TDIP Weighted .968 .961 .945 Port Density .971 .964 .923 .966 .969 .927 .964 .967 TDIA Weighted .096 .068 .016 Airport Density .250 .086 .420 .084 .103 -.059 .071 .087 TDIO Weighted .965 .978 .984 Open Port Density .940 .976 .859 .964 .965 .961 .965 .964 Shared Variance .419 .439 .434 .456 .443 .454 .415 .421 .376 .415 .415 Redundancy .404 .421 .407 .439 .426 .430 .399 .407 .362 .400 .398 Development Variate (vk), Canonical Loadings RDII Real .806 omitted .838 Income Indicator .859 .837 .871 .805 .810 .744 .802 .808 RDIR Rural .592 .618 omitted Development Indicator .618 .620 .609 .599 .595 .561 .596 .604 RDIL1 Real .459 .499 .500 Wage Indicator omitted .507 .582 .458 .464 .383 .456 .461 RDIL2 Real .881 .896 .898 Consumption Indicator .923 omitted .927 .879 .884 .824 .876 .881 RDIL3 Real .920 .940 .950 Savings Indicator .930 .942 omitted .921 .922 .888 .920 .922 RDIC1 .096 .145 .153 Industrialization .163 .150 .200 Indicator omitted .100 .044 .094 .093 RDIC2 .499 .577 .563 Export-Orientation .680 .588 .783 Indicator .547 omitted .444 .543 .548 RDIC3 Urbanization .594 .537 .553 Indicator 1 .549 .539 .572 .496 .503 omitted .497 .498 RDIC4 Urbanization .560 .616 .609 Indicator 2 .705 .626 .793 .581 .600 .487 omitted .582 RDIC5 Tertiary .156 .129 .118 Sector Indicator .153 .129 .165 .158 .155 .149 .153 omitted Shared Variance .378 .373 .411 .461 .366 .440 .416 .389 .327 .377 .417 Redundancy .366 .358 .384 .444 .352 .416 .401 .376 .314 .364 .400

Note: Leading structure coefficients of the complete variate are typed in italics.

MAP: FIGURE 1: Geographical Location of China's Zhujiang Delta.

MAPS: FIGURE 2: Internal Regional Structure of China's Zhujiang Delta.

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By Becky P.Y. Loo, Department of Geography and Geology, The University of Hong Kong, Pokfulam, Hong Kong. E-mail: bpyloo@hkucc.hku.hk