GIS Based Studies in the Humanities and Social Sciences - Chpater 9

9 A Toolbox for Examining the Effect of Infrastructural Features on the Distribution of Spatial Events Atsuyuki Okabe and Tohru Yoshikawa CONTENTS 9.1 Introduction................................................................................................127 9.2 General Setting...........................................................................................128 9.3 Procedure for Examining the Effect .......................................................129 9.3.1 The Procedure for Using the Goodness-of-Fit Test Method............................................................................................130 9.3.2 The Procedure for Using the Conditional Nearest- Neighbor Distance Method.........................................................133 9.3.3 The Cross K Function Method....................................................135 9.4 Conclusion ..................................................................................................136 Acknowledgments..............................................................................................137 References.............................................................................................................137 9.1 Introduction In the real world, there are many events that occur at specific locations. These are called spatial events, and they include the location of facilities in particular places. Spatial events are in part affected by their constraining geography, in particular by influencing elements that persist over a long time period. These durable controls are called infrastructural features. Examples of these that have attracted research in the humanities and social sciences are as follows: · Transport stations attract crime in Los Angeles (Loukaitou-Sideris et al., 2002). 127 Copyright © 2006 Taylor & Francis Group, LLC 128 GIS-based Studies in the Humanities and Social Sciences · Mosques are usually located on hilltops in Istanbul (Kitagawa et al., 2004). · Steel mills are distant from their supportive mines when consider-ing the period from 1974 to 1991 in the United States (Beeson and Giarratani, 1998). · Asthma sufferers reside 200–500 meters from major highways in Erie County, New York (Lin et al., 2002). · Serial thieves in Baltimore have a tendency to migrate south along the major roads (Harries, 1999). · Early ceramic sites, especially those yielding fiber-temper pottery, had been found along the coast or close to mangrove stands in Ecuador (Marcos, 2003). · Luxury apartment buildings are preferentially located around big parks in Setagaya, Tokyo (Okabe et al., 1988). This chapter introduces a user-friendly toolbox, called SAINF (Okabe and Yoshikawa, 2003), which may be used in the statistical analysis of these spatial relationships. SAINF is the abbreviated name for Spatial Analysis of the Effect of Infrastructural Features. 9.2 General Setting We consider a region where spatial events occur, and within which infra-structural features are placed. Such infrastructural features have various geometrical forms that can be classified into three types: point-like, such as railway stations; line-like, seen as roads; and polygon-like, exemplified by city parks. It should be noted that this classification is relative, in the sense that a station may be a polygon on a large-scale map but a point at small scale. In the Geographical Information Systems (GIS) environment to which SAINF is applied, geographical features and spatial events are represented by geometrical objects that are points, line segments, and polygons. Spatial events are points on a plane. The number m, of infrastructural features, for example, railway stations, is denoted by o ,… ,o and the number of spatial events n, such as crime locations is given by p ,… ,p . We assume that the spatial events do not occur on the infrastructural sites; that is, points p ,… ,p are placed on the complement of the area O, occupied by o ,… ,o with respect to a study region S, that is, S\O . SAINF statistically tests the following hypothesis, H , to examine the effect of the configuration of infrastructural features o ,… ,o on the distribution of spatial events p ,… ,p , Ho: Spatial events p1 ,… ,pn occur uniformly and randomly over the region. Copyright © 2006 Taylor & Francis Group, LLC A Toolbox for Examining the Effect of Infrastructural Features 129 FIGURE 9.1 Railway stations (white circles), streets, big parks, and luxury apartment buildings (black circles) in Kohtoh, Tokyo. In geometrical terms, points p ,… ,p are uniformly and randomly distrib-uted over the region S\ . When related to H “uniformly and randomly” implies that spatial events are distributed independently of the configuration of infrastructural features. If this hypothesis is rejected, the infrastructure may have an effect. 9.3 Procedure for Examining the Effect We consider an example of how to use SAINF by examining the influence of three infrastructural elements on the location of luxury apartment build-ings in Kohtoh, Tokyo. These are seen as black circles in Figure 9.1. The three factors are railway stations, arterial streets, and big parks, given by white circles, line segments, and polygons, respectively, in Figure 9.1. Data concerning stations, streets, parks, and apartment buildings may be available in the form of digital or paper maps. If the latter, we digitize the geographical features. GIS software varies, but SAINF adopts ArcView as one of the most popular GIS viewers. This system employs the “shapefile” format specific to ArcView. To use SAINF, we install the software package ArcView together with that of SAINF. The latter may be downloaded without charge for nonprofit- making uses from the Web site: ua.t.u-tokyo.ac.jp/okabelab/atsu/sainf/. ArcView software is available at cost from Environmental Systems Research Institute, Inc. (ESRI). Once SAINF, ArcView and the datasets are installed, we are ready to start the analysis. Clicking on “SAINF-Tools” on the ArcView menu bar reveals Copyright © 2006 Taylor & Francis Group, LLC 130 GIS-based Studies in the Humanities and Social Sciences a menu showing the available tools. SAINF provides three tools, which are the goodness-of-fit test, conditional nearest-neighbor distance, and the cross K function methods. The goodness-of-fit test method is first considered. 9.3.1 The Procedure for Using the Goodness-of-Fit Test Method The goodness-of-fit test method of SAINF generally tests the hypothesis H by comparing the observed number of point spatial events for each subregion with the expected point numbers that would be realized under a condition in which spatial events are uniformly and randomly distributed, as envis-aged by hypothesis H . Subregions are considered to be “buffer rings” for the infrastructural fea-tures. Abuffer ring, R(d ,d ) is the region in which the distance to its nearest infrastructural feature is between d and d ( d < d ). The boundaries of buffer rings are equidistant contour lines around infrastructure elements, examples of which are shown in Figures 9.2a, 9.2b, and 9.2c. We use one of the functions of ArcView to generate buffer rings. In the dialog box of “Buffer Wizard,” a set of infrastructural features is chosen in the pull-down menu “The features of a layer,” for example, railway stations, and the number k of buffer rings and the width of a ring d − d are entered. We also enter the name of an output file for the result. After a few seconds of computation, the buffer-contour rings appear, as shown in Figure 9.3. The buffer rings cover the study region, which is the polygon in Figure 9.3. To trim them outside of the study region, we use the “Geoprocessing Wizard.” Appropriate names or items are chosen in “Clip one layer based on another,” “Select the input layer to clip,” “Specify a polygon clip layer,” and “Specify the output shapefile or feature class.” Trimmed buffer rings are achieved, as seen in Figure 9.2a. Since the goodness-of-fit test method tests the hypothesis H and, while recalling that spatial events are uniformly and randomly distributed over a region, we notice that the number of events occurring in a subregion is proportional to the area of the subregion. The hypothesis H can therefore be restated as follows: H’ : The number of spatial events occurring in a buffer ring R(d ,d ) is proportional to the area of R (d, d ). In geometrical terms, the number of points that are placed in R(d ,d ) is proportional to the area of R(d ,d . To test this hypothesis, we have to measure the area of R(d ,d ). Clicking on “Areas of buffer rings” in the “SAINF-Tools” menu, the dialog box appears, where we enter the names of the buffer layer, an input file showing ring intervals, and an output file for the results. After a few seconds of computation, SAINF produces a display, such as the one shown in Table 9.1. From this result, we obtain the ratio P for the area of each buffer ring R(d ,d ) to the total area. Since the total number of points is n, the expected number of points that would be placed in a buffer ring R(d ,d ) under the null hypothesis Ho is n P. Copyright © 2006 Taylor & Francis Group, LLC A Toolbox for Examining the Effect of Infrastructural Features 131 (a) (b) (c) FIGURE 9.2 The buffer rings of (a) railway stations, (b) arterial streets, and (c) big parks. Copyright © 2006 Taylor & Francis Group, LLC ... - tailieumienphi.vn