GIS and Spatial Modeling in Regional Development Studies:
Case Study on the Greater Beijing Area
Danlin Yu
Ph.D. Candidate
Department of Geography
University of Wisconsin – Milwaukee
Milwaukee, Wisconsin, 53201
Tel: (414) 229-5818
Fax: (414) 229-3981
Email: danlinyu@uwm.edu
1 INTRODUCTION
GIS application in regional studies has recently attracted scholars’ interests. However,
most of the studies focused on GIS’s mapping and monitoring functionalities. As a spatial data
management system, its spatial analytical aspects remained largely unexploited. This study
intends to integrate spatial modeling into GIS to investigate the regional development
mechanisms in the Greater Beijing Area, China.
In the literature, investigation of development mechanisms is primarily conducted
through regression analysis. Non-spatial (OLS regression) or global spatial (spatial lag or error
regression) approaches were most commonly employed. The non-spatial approach is best suited
for larger scale study, such as provincial level spatial units, since high-level of data aggregation
intends to mask subtle spatial effects among spatial units. The global spatial approaches, on the
other hand, are able to handle the spatial effects, especially the spatial dependence by explicitly
including a spatial factor (either a spatial lag or a spatial error) in the model construction and
calibration. However, another closely related spatial effect, the spatial heterogeneity, is not fully
addressed in the global spatial approaches. In addition, due to its global nature, the spatial
regression only gives a general picture of development mechanisms in practice. Although GIS is
closely integrated in developing a global spatial model for spatial information retrieving and
manipulation, the calibration of the model cannot be returned to GIS for visualization.
To this end, this study intends to employ a recently developed GIS alternative, the
geographically weighted regression (GWR) to investigate the spatial heterogeneity in regional
development mechanisms. The followed section will introduce the methodology and data.
Section 3 describes major findings of this study. The paper concludes with a summary and future
research foci.
1
2 METHODOLOGY AND DATA
The essence of the geographically weighted regression (GWR) is to treat the regression
coefficients as functions of location instead of fixed constants:
Y = X  f (ZE, ZN) + ε
(1)
where  is a matrix operator that multiply corresponding elements of the two matrixes.
Y is an (n * 1) vector of dependent variable; X is an (n * k) matrix of explanatory variables; f(ZE,
ZN) is an (n * k) matrix of functions, representing the locally varying model coefficients; and ε is
a well-behaved disturbance term (normally distributed, with zero-mean and constant variance).
The varying relationship is usually determined by spatial factors, such as distance. Bearing this
in mind, one can approximate the GWR model in the region of i by weighted linear regression
using a subset of the spatial units in the dataset that are close to location i, and calibrate the
coefficients using weighted least square (WLS) technique. The weights are determined by a
spatial unit’s proximity to location i (the weighting schemes). In calibration, spatial units closer
to i are weighted more than the ones farther away. The most commonly used weighting schemes
include Gaussian distance-decaying function, bi-square function and tri-cube function. All the
weighting schemes involve a variable called bandwidth. Usually an out-of-sample crossvalidation procedure is employed to obtain an optimal bandwidth for calibration.
However, the ordinary calibration of the GWR model has three potential problems. First,
the outliers may contaminate the local regressions. Second, the local regressions based on a
distance-weighted subset of observations may suffer from “weak data” problems. That is, the
effective number of observations used to produce estimates for some points in space may be very
small. Third, valid statistic inferences cannot be drawn because the reuse of sample data
observations in the process of calibration (a Bonferroni problem). Given a lack of independence
2
between estimates for each location in the GWR model, conventional regression measures of
dispersion for the estimates will likely be inaccurate and misleading.
For this purpose, this study then modified the ordinary GWR with a simulation-based
Bayesian GWR and an adaptive bandwidth to try to overcome these problems. With an adaptive
bandwidth, the weak data problem could be effectively eliminated since all the local regressions
will have the same amount of spatial units participating in the calibration. The Bayesian
approach employs simulation techniques to produce the distribution of the model coefficients.
With a relatively large number of random simulations, it can ameliorate the outlier’s
contamination and the Bonferroni problem. Hence, statistically valid inference can be produced
from the Bayesian GWR.
The data used in this project are the socioeconomic data from the Greater Beijing Area,
China, at county level. The Greater Beijing Area is located in the northern coastal China,
including Beijing, Tianjin and Hebei province. It has 170 county-level spatial units (Fig. 1) and
occupies about 2% of the total territory of China. Limited by data availability, this study will
analyze the data for 1995 and 2001. The dependent variable used in the study is per capital GDP,
which represents the level of a spatial unit’s (county) development. By studying the literature of
geography, economy, and regional studies, and the author’s personal working experiences and
fieldwork in the Greater Beijing Area, five independent variables are identified as follow: 1) the
force of globalization represented by foreign direct investment per capita (FDIPC); 2) the
national support represented by fixed asset investment per capita (FIXINV); 3) local state
support represented by the local financial expense per capita (FINEXP); 4) marketization factor
represented by the share of State-Owned-Enterprises in fixed asset investment (SOEPCT); and 5)
a quality of life indicator represented by urbanization (URB). To insure the final coefficients for
individual independent variables are comparable, all the data are log-transformed.
3
3 MAJOR FINDINGS
After deriving the spatial information from GIS, the Bayesian GWR models are run with
the MATLAB BGWR routine. To ameliorate the outliers’ contamination and produce valid
statistical inference, the routine is programmed to run 2500 random simulations with the first 500
simulation discarded as “burn-ins” (to smooth the distribution since the simulations begin with
arbitrary values). A set of six maps for each year, 1995 and 2001, were produced for the five
independent variables and the constant term. The maps are attached as figure 2 to 13. Each map
only show the variations of individual development mechanisms of the spatial units that are also
statistically significant at 10% level. For the non-significant spatial units, it is blanked out.
From the analytical results, six impressions may be taken away. First, except for the
factor urbanization in 1995, significant variations of these regional development mechanisms
present in the Greater Beijing Area for both 1995 and 2001. The result supports the hypothesis
that regional development mechanisms vary across space. Such varying development
mechanisms formed the spatial pattern of current regional development in the Greater Beijing
Area.
Second, since the regression slope usually refers to the “basic development factor”, the
variation in the regression slope indicates a significant core-periphery spatial structure in the
Greater Beijing Area, with Beijing-Tianjin as the core region, and counties in Hebei province the
periphery. Such core-periphery spatial structure persists throughout the study period (Fig. 2 and
3).
Third, globalization, although projects relatively small influence on regional development
in the Greater Beijing Area, seems to favor counties in the core region and its immediate vicinity.
Surprisingly, globalization’s influence on regional development was quite uniform, especially in
2001. The core-region’s specific geopolitical position, especially considering Beijing is the
capital of the nation, is the primary reason for such spatial consistency.
4
Fourth, the government, especially the central government, still plays significant role in
local regional development in Hebei province, but no significant influence was found in the coreregion. Specifically, it seems in 1995, the southern part of Hebei, especially Shijiazhuang,
Handan, Xingtai, Baoding and Cangzhou relied more heavily on the central government’s
support (Fig. 6), while local government also projects significant positive influence on Baoding’s
development (Fig. 8). In 2001, however, the central government’s support was specifically
important for the periphery region’s development (Fig. 7). Baoding, again sees local
government’s support as an important factor in its development (Fig. 9).
Fifth, this study finds that the state-owned-enterprises does not play a much significant
role in the Greater Beijing Area’s regional development. In both years, it seems that Baoding
suffers from its relatively large portion of SOEs in its economy (Fig. 10 and 11). However, it is
worth noting that the change of significant positive roles of SOE on regional development from
1995 to 2001. In 1995, SOEs seemed to play significant positive role in counties of Tianjin. This
may be a residual effect of the previous reform efforts, since Tianjin was one of China’s most
important industrial bases. After the Chinese government launched its economic reform policies
in the late 1970s, and as Tianjin was elected as one of the coastal open cities in 1984, efforts of
revitalizing its SOEs were taken. However, as the reform deepened, Tianjin’s economy became
more and more external-oriented. In the meantime, SOEs were largely moved to Hebei’s capital
city, Shijiazhuang and its vicinity. Hence a significant SOE influence was observed in this area
in 2001 (Fig. 11).
Sixth, as aforementioned, urbanization did not play a much significant role in the Greater
Beijing Area in 1995. Nearly no significant variation of this development mechanism can be
identified in that year (Fig. 12). However, it seems in 2001, urbanization projects a relatively
significant role on regional development of the counties of Zhangjiakou and Chengde, two
prefectures north to Beijing. It is also quite interesting that the influence of urbanization in this
5
area does not vary much (Fig. 13). This pattern can be attributed to the traditional relationship
between these two prefectures and Beijing. Zhangjiakou and Chengde are usually deemed the
northern guards of the nation’s capital, both militarily and ecologically. Such relationship, on one
hand, prevents counties in these two prefectures from taking off too rapidly since there are
limitations of what sort of industries they can develop; on the other hand, it also connect them
morel closely to the core-regions than other counties. Beijing’s metropolitan effect hence plays a
relatively significant role in their regional development.
4 SUMMARY AND CONCLUSION
Employing the newly developed GIS technique, the geographically weighted regression,
this study investigates the spatially varying regional development mechanisms in the Greater
Beijing Area, China, at the county level. Data from 1995 and 2001 were examined and
compared. Significant variations among the listed development mechanisms were identified.
This study indicates that application of GIS and spatial modeling techniques yields thorough
understanding of the spatial pattern in regional development. Moreover, following the similar
procedures, the techniques discussed in this study are readily applicable to studies other than
regional development mechanism investigation. The future research will try to further explore
the capability of GIS and spatial modeling in other areas, such as transportation planning, urban
housing research, remote sensing analysis, etc.
6
Fig. 1 The Greater Beijing Area
Neimenggu
Liaoning
Chengde
Zhangjiakou
Qin
h ua
ngd
ao
Beijing
Tangshan
Langfang
Tianjin
Shanxi
Baoding
-
Cangzhou
Shijiazhuang
Hengshui
Shandong
Xingtai
Prefecture
County
Handan
120
60
0
120 Kilometers
Fig. 2 BGWR result for the variation of regression slope in 1995
Neimenggu
Liaoning
Shanxi
-
Constant 1995
2.35 - 3.77
3.78 - 4.98
Shandong
4.99 - 5.76
5.77 - 6.44
120
60
0
120 Kilometers
6.45 - 7.27
Fig. 3 BGWR result for the variation of regression slope in 2001
Neimenggu
Liaoning
Shanxi
-
Constant 2001
.93 - 2.42
2.43 - 4.01
Shandong
4.02 - 5.84
5.85 - 7.73
7.74 - 9.18
120
60
0
120 Kilometers
Fig. 4 BGWR result for the variation of foreign direct investment per capita in 1995
Neimenggu
Liaoning
Shanxi
-
FDI 1995
-.04 - -.02
-.01 - .01
Shandong
.02 - .04
.05 - .10
120
60
0
120 Kilometers
.11 - .22
Fig. 5 BGWR result for the variation of foreign direct investment per capita in 2001
Neimenggu
Liaoning
Shanxi
-
FDI 2001
-.10 - -.07
-.06 - -.03
Shandong
-.02 - .01
.02 - .05
.06 - .20
120
60
0
120 Kilometers
Fig. 6 BGWR result for the variation of fixed asset investment per capita in 1995
Neimenggu
Liaoning
Shanxi
-
FIXINV 1995
.04 - .12
.13 - .19
Shandong
.20 - .25
.26 - .36
120
60
0
120 Kilometers
.37 - .61
Fig. 7 BGWR result for the variation of fixed asset investment per capita in 2001
Neimenggu
Liaoning
Shanxi
-
FIXINV 2001
-.04 - .05
.06 - .12
Shandong
.13 - .18
.19 - .51
.52 - .92
120
60
0
120 Kilometers
Fig. 8 BGWR result for the variation of financial expense per capita in 1995
Neimenggu
Liaoning
Shanxi
-
FINEXP 1995
-.15 - .00
.01 - .15
Shandong
.16 - .35
.36 - .66
120
60
0
120 Kilometers
.67 - 1.15
Fig. 9 BGWR result for the variation of financial expense per capita in 2001
Neimenggu
Liaoning
Shanxi
-
FINEXP 2001
-.32 - -.18
-.17 - -.03
Shandong
-.02 - .13
.14 - .33
.34 - .69
120
60
0
120 Kilometers
Fig. 10 BGWR result for the variation of the share of SOE in fixed asset investment in 1995
Neimenggu
Liaoning
Shanxi
-
SOEPCT 1995
-.20 - -.11
-.10 - -.02
Shandong
-.01 - .05
.06 - .13
120
60
0
120 Kilometers
.14 - .22
Fig. 11 BGWR result for the variation of the share of SOE in fixed asset investment in 2001
Neimenggu
Liaoning
Shanxi
-
SOEPCT 2001
-.24 - -.18
-.17 - -.09
Shandong
-.08 - .04
.05 - .18
.19 - .38
120
60
0
120 Kilometers
Fig. 12 BGWR result for the variation of urbanization in 1995
Neimenggu
Liaoning
Shanxi
-
Urbanization 1995
-.31 - -.30
-.29 - -.20
Shandong
-.19 - .01
.02 - .09
120
60
0
120 Kilometers
.10 - .17
Fig. 13 BGWR result for the variation of urbanization in 2001
Neimenggu
Liaoning
Shanxi
-
Urbanization 2001
-.27 - -.17
-.16 - -.07
Shandong
-.06 - .04
.05 - .20
.21 - .41
120
60
0
120 Kilometers