Modeling Urban Growth Using GIS and Remote Sensing

Transcription

1 Modeling Urban Growth Using GIS and Remote Sensing Jun Luo 1 Department of Geography, Geology and Planning, Missouri State University, 901 South National Avenue, Springfield, Missouri Danlin Yu Department of Earth and Environmental Studies, Montclair State University, Montclair, New Jersey Miao Xin Department of Geography, Geology and Planning, Missouri State University, 901 South National Avenue, Springfield, Missouri Abstract: Based on remote sensing and GIS, this study models the spatial variations of urban growth patterns with a logistic geographically weighted regression (GWR) technique. Through a case study of Springfield, Missouri, the research employs both global and local logistic regression to model the probability of urban land expansion against a set of spatial and socioeconomic variables. The logistic GWR model significantly improves the global logistic regression model in three ways: (1) the local model has higher PCP (percentage correctly predicted) than the global model; (2) the local model has a smaller residual than the global model; and (3) residuals of the local model have less spatial dependence. More importantly, the local estimates of parameters enable us to investigate spatial variations in the influences of driving factors on urban growth. Based on parameter estimates of logistic GWR and using the inverse distance weighted (IDW) interpolation method, we generate a set of parameter surfaces to reveal the spatial variations of urban land expansion. The geographically weighted local analysis correctly reveals that urban growth in Springfield, Missouri is more a result of infrastructure construction, and an urban sprawl trend is observed from 1992 to INTRODUCTION Understanding the spatial pattern of urban growth and land use change is of particular importance in the study of urban geography. Various approaches have been developed to model and simulate the patterns of urban growth and land use changes (e.g., Clare et al., 1997; Wu and Yeh, 1997; Landis and Zhang, 1998; Cheng and Masser, 2003; Arai and Aiyama, 2004; Liu and Zhou, 2005). The dominant ones 1 junluo@missouristate.edu. 426 GIScience & Remote Sensing, 2008, 45, No. 4, p DOI: / Copyright 2008 by Bellwether Publishing, Ltd. All rights reserved.

2 MODELING URBAN GROWTH 427 include the cellular-automata (CA) based simulation models (Clare et al., 1997; Batty et al., 1999) and multivariate analysis based statistical models (Wu and Yeh, 1997; Hu and Lo, 2007). Such models provide quite fruitful analytical and theoretical insights for the development of urban geography. With the rapid development of GIS and spatial analytical techniques and the availability of remote sensing data during the recent decades, research in urban geography has been greatly enriched (e.g., Yu, 2007; Yu et al., 2007). Among the trends of urban GIS/remote sensing studies, one particular approach is to examine the spatial patterns of urban growth in greater detail through local analysis (Fotheringham et al., 2002; Luo and Wei, 2006). Previous urban growth and land use models primarily focus on revealing the urban growth pattern from a global or whole-map view. For instance, the transition rules of CA models or the parameters of the explanatory variables of the statistical model, which indicate the influences of various factors on urban land expansion, are deemed invariant across space. From a modeling and general perspective, such models certainly yield crucial nowledge for understanding the trends, patterns, and mechanisms of urban development. However, the complexity of urban dynamics, as revealed by the CA models, indicates that relationships between urban growth and its underlying factors tend to have more of a non-stationary character over space than an invariant one. In multivariate statistical analysis models, such potential non-stationarity implies that the same set of factors might lead to different responses in different parts of the study area. Understanding, exploring, and modeling such potential spatial non-stationary relationships hence provide an alternative venue for better understanding the details of the urban growth pattern. In this regard, the current study intends to examine the detailed urban growth pattern in the Springfield, Missouri metropolitan area from 1992 to 2005 through a geographically weighted local analysis approach. In particular, the research attempts to reveal the spatially varying relationships between determinant variables (the underlying factors of urban growth) and urban land expansion by developing and employing a logistic geographically weighted regression. Geographically weighted regression (GWR) is a recently developed geographic data analysis methodology that provides an alternative way of examining relationships in greater details (Fotheringham et al., 2002). In general, GWR assumes the relationship obtained from conventional global regression models is an average of varying local spatial processes. Using nonparametric ernel functions, researchers are able to create local samples for a particular location from geographically weighing the neighboring data to simulate the local process. Although the introduction of potential multicollinearity of the explanatory variables or correlation among locally estimated coefficients could pose a potential problem of the application (Wheeler and Tiefelsdorf, 2005), the trade-off of reduced estimation variance renders the methodology an appealing one when it comes to examining possible spatial non-stationarity (Fotheringham et al., 2002). In our current study, which intends to examine the fine-scale interactions among various factors and urban growth and land use change, the application of GWR is suitable and may lead to better understanding of the urban development mechanism. The study will employ a logistical regression to model the impacts of locational attributes and socioeconomic factors on urban land use expansion. In particular, we intend to extend the regular logistic regression and establish a logistic GWR. Our

3 428 LUO ET AL. current research intends to contribute to the literature in three primary aspects. First, we propose that the probability of future urban land use change is associated with current land use, geographic location, and neighborhood socioeconomic characteristics, and model such association using Springfield, MO as a case study. Second, we examine this association in greater detail via geographically weighted analysis, which attempts to present local patterns that are complimentary to the global pattern of urban growth. Third, we continue the effort of incorporating remotely sensed information in urban studies, which is potentially more informative and may provide a better understanding of the dynamics of urban development. The paper is organized as follows. The next section briefly discusses the study area and data issues, followed by a third section that develops a global logistic regression model for urban land change and growth. A fourth section applies a logistic GWR to an examination of the relationship established in the third section in greater detail. The fifth section presents the results and discussion, and a sixth concludes the research with a summary and description of future research foci. Study Area STUDY AREA AND DATA BASES Springfield is the third-largest metropolitan area in Missouri. It is located southwestern Missouri, includes five counties (Pol, Dallas, Webster, Greene and Christian), and encompasses roughly 7821 m 2 (Fig. 1). The paper focuses on the urban growth of the Springfield metropolitan area from 1992 to 2005, and its possible causes. Urban growth mainly occurred in the areas surrounding the City of Springfield (Fig. 2). Land Use Data The original m grids of land use data used in this study were created by the land cover projects of MoRAP (Missouri Resource Assessment Partnership). MoRAP s land cover projects used Landsat TM images to derive land cover/use information of Missouri based on remote sensing and GIS technologies. The outcomes of the projects were made available to the public through the Missouri Spatial Data Information Service ( The original land use data used for the research have 16 and 15 land cover classes, used in grids for 1992 and 2005, respectively. The classification scheme follows the hierarchical scheme outlined in the National Vegetation Classification (see but it is not appropriate for our current research, as it has too many detailed land cover subcategories. Therefore, we conducted a reclassification to merge similar subcategories. The merge operation was performed in ArcGIS TM using the Reclassify tool of the Spatial Analyst module. Five land use types were initially identified: urban, barren land, crop or grass land, forest or woodland, and water. Because we were only concerned with conversion from non-urban to urban uses, we further reclassified the two land use grids so that they only have two types of land use (urban or non-urban), as indicated by cells with attributes of 1 or 0. After generating the final land use grids, we performed a raster minus calculation using Spatial Analyst s raster calculator i.e., 1992

4 MODELING URBAN GROWTH 429 Fig. 1. Map of the study area. grid minus 2005 grid. The cells in the resulting grid with a -1 cell value would be those that experienced non-urban to urban land use conversion. The original land use data and the final reclassified grid are all georeferenced to NAD 1983 UTM Zone 15N coordinate system. Figure 2 depicts the expansion of urban land in the study area from 1992 to Urban land increased by about 170%, from about 145 m 2 in 1992 to about 392 m 2 in Land Use Data Sampling The classified image has 8,686,408 cells with 30 m resolution. Most spatial modeling pacages cannot handle such a large data set, and thus data sampling is needed

5 430 LUO ET AL. Fig. 2. Urban growth in the Springfield metropolitan area, for the research. However, while spatial sampling can reduce spatial dependence for the classical multivariate models, small sample size tends to lead to unreliable multivariate analysis (Cheng and Masser, 2003). To obtain an adequate yet manageable sample size, we applied a stratified random sampling scheme for land use data sampling. The sampling scheme selected 4473 sample points, among which 191 points experienced non-urban to urban land use conversion and 4282 points were in non-urban land use in 1992 and experienced no urban growth. For the entire study area, the cells undergoing non-urban to urban conversions account for 4.08% of the non-urban cells in 1992, whereas in the samples the percentage is 4.27%, indicating good correspondence with the full data set. Quantifying Urban Growth and Growth Mechanisms To examine the possible causes for urban growth, we first define urban growth as a choice of a particular location changing from non-urban land use to urban land use.

6 MODELING URBAN GROWTH 431 Specifically, we intend to model the factors that have an impact on the possibility of non-urban to urban use conversion. Various geographic and socioeconomic factors were identified in previous studies, such as proximity to road infrastructure, attributes of the specific land use site, and attributes of neighborhoods of the land use site. The majority of the literature in urban land change demonstrates that proximity factors are important in accounting for land use transition (e.g., White and Engelen, 1997; Wu and Yeh, 1997; Cheng and Masser, 2003). Lie other metropolitan areas in the U.S., Springfield s urban sprawl has been transportation oriented. Major roads, including highways, local arteries, etc. form the cadastre of the transportation networ in the Springfield area and hence have a great impact on urban growth. New land development sites are usually located close to an existing urban cluster because such a location can reduce the construction cost of infrastructure and provide conveniences for future occupants. Springfield s downtown, although no longer an economic center, still remains an administrative center, and has many cultural amenities. Therefore, it was desirable for us to test its role, if any, in urban growth within the broader metropolitan region. Consequently, we selected the distance to major roads, the nearest urban cluster, and Springfield s downtown (urban center) as our primary proximity factors. To obtain values for these proximity variables for the sample points, we first generated a set of distance raster surfaces (30 30 m cell size) using the Euclidean Distance geoprocessing tool in ArcGIS TM ; we then extracted variable values for each sample point from the generated distance raster surfaces. We also noted that the character of land use development at a site is strongly dependent on neighborhood land use conditions (White and Engelen, 1997; Wu and Yeh, 1997; Cheng and Masser, 2003). We tested the global logistic regression model (see the next section) with a series of neighborhoods from a 3 3 cell to a cell, and found that the number of urban cells in a 9 9 cell neighborhood has the strongest impact on the particular site s land use change, and hence is selected to represent the neighborhood impact. In addition, Clare et al (1997) found that topography plays an important role in determining the land use transition. We hence generated the slope of each sample location as a proxy for topography for our current study. Needless to say, except for the geographic conditions that might influence urban growth, the dominant forces behind urban growth are socioeconomic factors (Hu and Lo, 2007). From the literature review and the specific case of Springfield, we selected five socioeconomic variables: population density, income, race, poverty rate, and employment rate. All the variables used to establish the model, and their characteristics, are listed in Table 1. GLOBAL LOGISTIC REGRESSION MODEL The transition from non-urban to urban land uses has been modeled by classic multivariate statistic analysis. For example, Wu and Yeh (1997) used a logistic regression model to detect the changing determinants of land use change in Guangzhou, China before and after urban land reform in Arai and Aiyama (2004) used liner regression and discriminant analysis to identify significant explanatory factors of land use transition potentials in a suburban district of Toyo.

7 432 LUO ET AL. Table 1. Variables Used in the Land Use Conversion Models Variables Type Descriptions Dependent variable Land use conversion Nominal Non-urban to urban land use conversion Independent variable Dis2Mjrd Continuous Distance to major roads (m) Dis2UC Continuous Distance to nearest urban cluster (m) Dis2Downtown Continuous Distance to downtown Springfield (m) Slope Continuous Slope (%) Urban Continuous Number of urban cells in a 9 9 cell window PopDense Continuous Population density (1000 person/m 2 ) Income Continuous Per capital income ($10,000) White Continuous Percentage of white people Poverty Continuous Poverty rate Employment Continuous Employment rate Following similar studies, we establish a logistic regression model to examine the influences of the identified proximity and socioeconomic factors on urban growth. Logistic regression is well suited for analyzing relationships between a binary dependent variable and a set of explanatory variables. In short, logistic regression first transforms the binary dependent variable to a probability measure of its status (urban or non-urban land use). The probability measure usually follows a logistic distribution, as shown in the following equation: ChangeProb i = C + β X i e C + β X 1 + e (1) The probability measure is further transformed to a continuous odds ratio, which represents the odds of status change for a dependent variable. In our research, it represents the odds that a particular location will change from a non-urban to urban land use. It can be clearly shown that the odds ratio taes the form: C + β X i ChangeProb i = e 1 ChangeProb i (2)

8 MODELING URBAN GROWTH 433 Table 2. Global Logistic Regression Model for Non-urban to Urban Land Conversion Probability Explanatory variables B S.E. t value Exp(B) Constant Dis2Mjrd ** Dis2UC ** Dis2Downtown Slope Urban ** PopDense ** Income * White Poverty Employment Sample size 4473 Log lielihood PCP a 85.6 a PCP = percentage correctly predicted with cut value 0.5. * Significance at 0.05 level. ** Significance at 0.01 level. By taing the logarithm on both sides, we obtain: ChangeProb i In ChangeProb i = C + β X i (3) in which ChangeProb is the probability of land use change, C is a constant, and β is the parameter for the individual explanatory variable X ( = (1,2,3 n). We can see that logistic regression is actually a transformation of a linear regression. The global logistic regression model is usually estimated by the maximum lielihood method and the results are presented in Table 2. The global logistic model is significant at the 99% confidence level. The Log lielihood value and percentage correctly predicted (PCP) are and 85.6%, respectively, which indicate a moderate goodness of fit of the model and a moderate level of prediction accuracy. The result of the global model is quite intuitive and follows the common wisdom in urban land use studies. In particular, among the proximity variables, distance to major roads (Dis2Mjrd) has the strongest negative effect on land conversion probability, followed by distance to nearest urban cluster (Dis2UC), which suggests that urban growth in Springfield has been largely dependent on road infrastructure and existing

9 434 LUO ET AL. urban agglomerations. Although not statistically significant, distance to downtown Springfield (Dis2Downtown) had somewhat of a negative influence on land use conversion, which might indicate that urban growth in the Springfield metropolitan area mainly occurred in the areas surrounding the City of Springfield. The topography factor (slope) has a negative effect on urban growth, although not significant, whereas neighborhood condition (Urban) certainly projects a very strong influence on land use changes. Population density (PopDense), however, has the strongest positive effect on urban growth, which implies that large-scale residential land development has been dominating the urban growth pattern in Springfield. In the meantime, although per capita income is positively associated with urban growth, in general, race, poverty level, and employment status seem to have a rather insignificant impact on urban growth. Although the classic logistic regression model has explained well the determinants of the probability of urban land change and growth, the results of our study present a general, averaged picture of the urban growth mechanisms in Springfield. Specifically two potential problems might prevent us from fully understanding these mechanisms. First, it is noted that land use transition as a spatial process usually involves high spatial dependency among observations (the strong impact of the urban factor implies as much). Analysis that does not consider such spatial dependency might lead to misspecifications of proposed model and unreliable inference. Second, the classical statistical analysis of urban land expansion implicitly assumes that urban growth mechanisms are spatially stationary that the same set of factors always invoes the same response everywhere. Such an assumption of spatial stationarity often may be untenable (Anselin, 1988, 1995; Fotheringham et al., 2002), especially for urban growth studies that usually involve large spatial data sets from remote sensing or other sources at relatively small scale. With this in mind, we examined the above-established logistical regression model using a geographically weighted analysis, termed logistic GWR (Fotheringham et al., 2002). Because the logistic GWR allows the estimated coefficients of the explanatory factors to vary across space, the analysis can provide insightful information that is complementary to the global analysis. LOGISTIC GEOGRAPHICALLY WEIGHTED REGRESSION MODEL GWR is a local regression technique for investigating spatial non-stationarity. GWR is built on the spatial expansion method (Fotheringham et al., 1998), which sees to estimate parameters of a global regression model with a function of some other attributes representing spatial variation (Casetti, 1972, 1997). The expansion method only represents the broad spatial trends (Fotheringham et al., 2000) and may mas the significant local variation (Fotheringham et al., 2002). In contrast, GWR is suitable for modeling the complex local variation of regression parameters and has been recently applied in various studies (e.g., Fotheringham et al., 2001; Longley and Tobón, 2004; Yu and Wu, 2004; Lloyd and Shuttleworth, 2005; Mennis and Jordan, 2005; Páez, 2006). Basically, the GWR model taes the following form (Brunsdon et al., 1996; Fotheringham et al., 2002):

10 MODELING URBAN GROWTH 435 Y i = C i + β i X i + ε i (4) C i is the constant parameter that is specific to location i; β i is the parameter of independent variable X at location i. Based on Equation (4), Equations (1), (2), and (3) can be modified to the following forms in a GWR environment: ChangeProb i = C i + β i X i e C i + β i X i 1 + e (5) ChangeProb i = e 1 ChangeProb i C i + β i X i (6) ChangeProb i In ChangeProb i = C i + β i X i (7) where β i represents the parameter estimate for explanatory variable at land use sample point i. GWR estimates the parameters for each observation at location i using a local sample that is generated through a nonparametric ernel weighting scheme. The weighting scheme assigns weights to data points at other locations according to their spatial proximity to location i (Fotheringham et al., 2002). The ernel function usually taes a Gaussian-lie shape, which would ensure that near locations gain higher weights and vice versa. Various ernel functions have been developed and applied in practice, such as the bi-square function, Gaussian function (Fotheringham et al., 2002), and tri-cube function (McMillen, 1996). Surprisingly, although different ernels certainly generate different estimates, the variation patterns of the coefficients tend to remain less influenced by the ernel used. In addition, both bi-square and tri-cube functions would potentially generate a local sample in which all the observations have the same value for the dependent variable. To avoid such local non-variance trap, a Gaussian ernel is used to guarantee that all samples are included for each of the estimations. The Gaussian function is written as follows (LeSage, 1999): W i = φ( d i σθ) (8) where θ denotes the standard normal density and σ denotes the standard deviation of the distance vector d i..θ is a bandwidth that is a ey for the weighting function. In this

11 436 LUO ET AL. Table 3. Comparison between Global Logistic and Logistic GWR Global logistic model Logistic GWR PCP a Residual sum of squares Log lielihood to Moran's I of residuals 0.76 ** 0.41 a PCP = percentage correctly predicted with cut value 0.5. Table 4. Summary Statistics of Logistic GWR Estimates Minimum Maximum Mean Std. deviation Dis2Mjrd Dis2UC Dis2Downtown Slope Urban PopDense Income White Poverty Employment research, a cross-validation method is used to determine the optimal bandwidth (LeSage, 1999; Fotheringham et al., 2002): M [ 1 P ij ( θ) ] 2 i = 1 (9) SPATIAL VARIATIONS OF THE URBAN GROWTH PATTERN The same set of 4473 sample point data was used to construct the logistic GWR model. The model is calibrated using LeSage s spatial econometrics toolbox for Matlab ( The solved optimal bandwidth is The results of the logistic GWR are reported in Tables 3 and 4 and Figures 3 5. Table 3 presents a comparison between the global logistic regression model and the logistic GWR model. Table 4 summarizes the varying coefficients across the study area. Figures 3 5 present the surfaces of the varying coefficients; however, only the

12 MODELING URBAN GROWTH 437 Fig. 3. Parameter surfaces of distance to major roads (A), distance to urban clusters (B), and distance to Springfield downtown (C). Areas not statistically significant areas have white tone. ones with significant pseudo-t test values are mapped. The surfaces are generated using an Inverse Distance Weighted (IDW) interpolation with a m cell size. Figure 3 includes the coefficient surfaces of the three proximity variables; Figure 4 contains the coefficient surfaces of topography and neighborhood effect; and Figure 5 details the varying coefficients of the socioeconomic factors. Because we did not find the employment rate, racial factor, and poverty level to be pseudo-significantly related to land use change in most places, we dropped these coefficient maps and concluded that population density and per capita income are the only significant socioeconomic mechanisms for urban land use change in Springfield. From the tables and figures, and comparing with the results of the global model, a few ey conclusions can be drawn. First, although due to the lac of appropriate testing software, a formal improvement test of logistic GWR over global logistic regression is not performed here, Table 3 summarizes nicely the potential improve-

13 438 LUO ET AL. ments in terms of prediction accuracy, goodness-of-fit, and reduced residual autocorrelation. Specifically, when the model is locally calibrated, all the local models achieve higher log lielihoods than the global model. The range of log lielihood of the 4473 local estimations is between and , whereas the global model scores at Furthermore, the reduced residual sum of squares indicates a better fit of the GW model than the global model. More importantly, the logistic GWR model generates a 95.8% PCP, a 12% improvement from the global model. The results clearly suggest that the logistic GWR predicts land use change much better than the global model. Moreover, the residuals of the logistic GWR are no longer spatially autocorrelated, indicating that by allowing the coefficients to vary across space, the local models effectively capture the mased spatial effects. Second, from Figure 3A, it is clear that distance to major roads has more influence in the western parts of the study area than in the east, and exhibits a concentric pattern of influence. The weaest influences can be found in southeast and northeast parts of the study area, from where the influences increase concentrically toward the west. The coefficient surface of the distance to urban clusters (Fig. 3B) shows a rather similar pattern as the distance to road. This result indicates that in the western part of the metropolitan area, urban growth is more a result of urban infrastructure construction than elsewhere from 1992 to Distance to downtown, however, exhibits a different pattern (see Fig. 3C). It has the highest level of influence on land use development in the south-central part of the study area, decreasing toward the north, and becoming insignificant in large portions in the north of the study area. This is not a surprising result, considering that the current urban expansion direction is more toward the south than any other direction (Fig. 2). In addition, the positive sign of the coefficients in the north of the study area may indicate that a potential polycentric urban growth pattern exists in the Springfield metropolitan area, as land use in the north tends to be more urbanized when it is more distant from downtown Springfield. Third, topography (Fig. 4A) in general exerts a negative impact on urban growth; the greater the slope, the lower the possibility of non-urban to urban land use conversion. This is reasonable, as the cost of non-urban to urban land conversion would be greater on parcels with higher slope. More importantly, the changing pattern of the coefficient in Figure 4A also indicates that topography s negative impact is more pronounced in the less urbanized areas (north) than in the more urbanized areas (south). This again appears to be correct, as the costs of conversion from non-urban to urban land use would be greater in less urbanized areas, even if topographic conditions are identical. The influence of neighborhood urban cells exhibits a concentric spatial pattern, with the lowest levels around the City of Springfield, the urban core of the study area, and increasing outward from there (Fig. 4B). This indicates that outer areas urban growth relies more on the density of surrounding urban land than the more urbanized areas. This result agrees with the theory of urban sprawl that specifies that land use tends to change from non-urban to urban in the relatively less urbanized areas, and provides solid evidence that Springfield has experienced urban sprawl during the period from 1992 to Fourth, urban sprawl in Springfield, Missouri is further supported by the varying coefficients of population density and per capita income level. Figure 5A indicates that in the suburban areas, higher population density tends to increase the chance of

14 MODELING URBAN GROWTH 439 Fig. 4. Parameter surfaces of slope (A) and urban cells (B). Areas not statistically significant areas have white tone. Fig. 5. Parameter surfaces of population density (A) and per capita income (B). urban growth more than in the urban center. This result indicates that once sprawl starts, it tends to accelerate in the less urbanized rather than more urbanized areas. Figure 5B presents a pattern indicating that income level is more positively and strongly related to urban growth in the suburbs than in the downtown areas. This observation accords with the theory that urban sprawl and suburbanization are associated with increased income (Blac and Henderson, 1999). CONCLUSIONS In this study, based on remote sensing and GIS, we have developed global and a local logistic regressions models, which integrate a set of spatial and socioeconomic variables, to reveal the mechanisms of urban growth in Springfield, Missouri from

15 440 LUO ET AL to We found that logistic GWR improves the global logistic regression in terms of prediction accuracy, data fitness, and reduced residual spatial autocorrelation. More importantly, the logistic GWR model allows the model parameters to vary across space, which provides in-depth understanding of the spatial variations of urban development dynamics. It has been demonstrated that urban growth in Springfield is more a result of urban infrastructure construction and exhibits typical sprawl characteristics. Moreover, through logistic GWR analysis, we have a more detailed understanding of the urban development mechanisms in the metropolitan area. Although we need to interpret the results with caution, as GWR is not an unbiased estimation, and coefficients might exhibit strong correlation with one another (Wheeler and Tiefelsdorf, 2005), it is still worth noting that the GW analysis indicates that urban growth is a rather complex process, which involves a variety of spatial and socioeconomic factors. Those factors, however, might not all be that important in different parts of the study area. Depending on the actual locations, urban development dynamics can be quite different from one another. From a methodological standpoint, the current study extends previous urban land use models with a geographically weighted analysis. Our study does not mae strong efforts to strengthen the model itself. Future studies should incorporate more environment-related variables, which might be generated through more rigorous analyses of remote sensing imagery, into the logistic GWR model. In addition, similar applications to other metropolitan areas would certainly help verify the conclusions developed from our current study. We hope that this study, however, has broadened our understanding of the urban development process through the combined application of GIS and remote sensing techniques. ACKNOWLEDGMENTS This research is financially supported by the Faculty Research Grant the first author received from Missouri State University in REFERENCES Anselin, L., 1988, Spatial Econometrics: Methods and Models, Dordrecht, The Netherlands: Kluwer Academic. Anselin, L., 1995, Local Indicators of Spatial Association LISA, Geographical Analysis, 27(2): Arai, T. and T. Aiyama, 2004, Empirical Analysis for Estimating Land Use Transition Potential Functions Case of the Toyo Metropolitan Region, Computers, Environment, and Urban Systems, 28(1-2): Batty, M., Xie, Y., and Z. Sun, 1999, Modeling Urban Dynamics through GIS-Based Cellular Automata, Computers, Environment, and Urban Systems, 23(3): Blac, D. and V. Henderson, 1999, A Theory of Urban Growth, Journal of Political Economy, 107(2): Brunsdon, C., Fotheringham, A. S., and M. E. Charlton, 1996, Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity, Geographical Analysis, 28(4):

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