Quantitative Methods and Applications in GIS - Chapter 5

5 GIS-Based Measures of Spatial Accessibility and Application in Examining Health Care Access Accessibility refers to the relative ease by which the locations of activities, such as work, shopping, recreation, and health care, can be reached from a given location. Accessibility is an important issue for several reasons. Resources or services are scarce, and their efficient delivery requires adequate access by people. The spatial distribution of resources or services is not uniform and needs careful planning and allocation to match demands. Disadvantaged population groups (low-income and minority residents) often suffer from poor access to certain activities or opportunities because of their lack of economic or transportation means. Access can thus become a social justice issue, which calls for careful planning and effective public policies by government agencies. Accessibility is determined by the distributions of supply and demand and how they are connected in space, and thus is a classic issue for location analysis well suited for GIS to address. This chapter focuses on how spatial accessibility is measured by GIS-based methods. Section 5.1 overviews the issues on accessibility, followed by two GIS-based methods for defining spatial accessibility: the floating catchment area method in Section 5.2 and the gravity-based method in Section 5.3. Section 5.4 illustrates how the two methods are implemented in a case study of measuring access to primary care physicians in the Chicago region. The chapter is concluded with extended discussion and a brief summary. 5.1 ISSUES ON ACCESSIBILITY Access may be classified according to two dichotomous dimensions (potential vs. revealed, and spatial vs. aspatial) into four categories, such as potential spatial access, potential aspatial access, revealed spatial access, and revealed aspatial access (Khan, 1992). Revealed accessibility focuses on actual use of a service, whereas potential accessibility signifies the probable utilization of a service. The revealed accessibility may be reflected by frequency or satisfaction level of using a service, and thus be obtained in a survey. Most studies examine potential accessi-bility, based on which planners and policy analysts evaluate the existing system of service delivery and identify strategies for improvement. Spatial access emphasizes the importance of spatial separation between supply and demand as a barrier or a 77 © 2006 by Taylor & Francis Group, LLC 78 Quantitative Methods and Applications in GIS facilitator, whereas aspatial access stresses nongeographic barriers or facilitators (Joseph and Phillips, 1984). Aspatial access is related to many demographic and socioeconomic variables. In a study on job access, Wang (2001b) examined how workers’ characteristics, such as race, sex, wages, family structure, educational attainment, and homeownership status, affect commuting time and thus job access. In the study on health care access, Wang and Luo (2005) included several categories of aspatial variables: demographics such as age, sex, and ethnicity; socioeconomic status such as population in poverty, female-headed households, homeownership, and income; environment such as residential crowdedness and housing units’ lack of basic amenities; linguistic barrier and service awareness such as population without a high school diploma and households linguistically isolated; and transpor-tation mobility such as households without vehicles. Since these variables are often correlated to each other, they may be consolidated into a few factors by using the principal components and factor analysis techniques (see Chapter 7). This chapter focuses on measuring potential spatial accessibility, an issue par-ticularly interesting to geographers and location analysts. If the capacity of supply is less a concern, one can use simple supply-oriented accessibility measures that emphasize the proximity to supply locations. For instance, Brabyn and Gower (2003) used minimum travel distance (time) to the closest service provider to measure accessibility to general medical practitioners in New Zealand. Distance or time from the nearest provider can be obtained using the techniques illustrated in Chapter 2. Hansen (1959) used a simple gravity-based potential model to measure accessibility to jobs. The model is written as n AH = Sjdij b, (5.1) j=1 where AiH is the accessibility at location i, Sj is the supply capacity at location j, dij is the distance or travel time between the demand (at location i) and a supply location j, b is the travel friction coefficient, and n is the total number of supply locations. The superscript H in AiH denotes the measure based on the Hanson model vs. F for the measure based on the two-step floating catchment area method in Equation 5.2 or G for the measure based on the gravity model in Equation 5.3. The potential model values supplies at all locations, each of which is discounted by a distance term. The model does not account for the demand side. That is to say, the amount of population competing for the supplies is not considered to affect accessibility. The model is the foundation for a more advanced gravity-based method that will be explained in Section 5.3. In most cases, accessibility measures need to account for both supply and demand because of scarcity of supply. Prior to the widespread use of GIS, the simple supply–demand ratio method computed the ratio of supply vs. demand in an area (usually an administrative unit such as township or county) to measure accessibility. For example, Cervero (1989) and Giuliano and Small (1993) measured job acces-sibility by the ratio of jobs vs. resident workers across subareas (central city and © 2006 by Taylor & Francis Group, LLC GIS-Based Measures of Spatial Accessibility and Application in Health Care 79 combined suburban townships) and used the ratio to explain intraurban variations of commuting time. In the literature on job access and commuting, the method is commonly referred to as the jobs–housing balance approach. The U.S. Department of Health and Human Services (DHHS) uses the population-to-physician ratio within a rational service area (most as large as a whole county or a portion of a county or established neighborhoods and communities) as a basic indicator for defining phy-sician shortage areas1 (GAO, 1995; Lee, 1991). In the literature on health care access and physician shortage area designation, the method is referred to as the regional availability measure (vs. the regional accessibility measure based on a gravity model) (Joseph and Phillips, 1984). The simple supply–demand ratio method has at least two shortcomings. First, it cannot reveal the detailed spatial variations within the areas (usually large). For example, the job–housing balance approach computes the jobs–resident workers ratio and uses it to explain commuting across cities, but cannot explain the variation within a city. Second, it assumes that the boundaries are impermeable; i.e., demand is met by supply only within the areas. For instance, in physician shortage area designation by the DHHS, the population-to-physician ratio is often calculated at the county level, implying that residents do not visit physicians beyond county borders. The next two sections discuss a two-step floating catchment area (2SFCA) method and a more advanced gravity-based model, respectively. Both methods consider supply and demand and overcome the shortcomings mentioned above. 5.2 THE FLOATING CATCHMENT AREA METHODS 5.2.1 EARLIER VERSIONS OF FLOATING CATCHMENT AREA METHOD Earlier versions of the floating catchment area (FCA) method are very much like the one discussed in Section 3.1 on spatial smoothing. For example, in Peng (1997), a catchment area is defined as a square around each location of residents, and the jobs–residents ratio within the catchment area measures the job accessibility for that location. The catchment area “floats” from one residential location to another across the study area, and defines the accessibility for all locations. The catchment area may also be defined as a circle (Immergluck, 1998; Wang, 2000) or a fixed travel time range (Wang and Minor, 2002), and the concept remains the same. Figure 5.1 uses an example to illustrate the method. For simplicity, assume that each demand location (e.g., tract) has only one resident at its centroid and the capacity of each supply location is also 1. Assume that a circle around the centroid of a residential location defines its catchment area. Accessibility in a tract is defined as the supply-to-demand ratio within its catchment area. For instance, within the catchment area of tract 2, total supply is 1 (i.e., only a) and total demand is 7. Therefore, accessibility at tract 2 is the supply–demand ratio, i.e., 1/7. The circle floats from one centroid to another while its radius remains the same. The catchment area of tract 11 contains a total supply of 3 (i.e., a, b, and c) and a total demand of 7, and thus the accessibility at tract 11 is 3/7. Note that the ratio is based on the floating catchment area and not confined by the boundary of an administrative unit. © 2006 by Taylor & Francis Group, LLC 80 Quantitative Methods and Applications in GIS 1 R = 1/7 a 1 3 2 4 Catchment area for demand Demand centroid and ID Supply location and ID Administrative unit boundary Demand tract boundary 5 6 7 a b 8 10 11 12 13 9 R = 3/7 c 14 15 FIGURE 5.1 An earlier version of the FCA method. The above example can also be used to explain the fallacies of this simple FCA method. It assumes that services within the catchment area are fully available to residents within that catchment area. However, the distance between a supply and a demand within the catchment area may exceed the threshold distance (e.g., in Figure 5.1, the distance between 13 and a is greater than the radius of the catchment area of tract 11). Furthermore, the supply at a is within the catchment of tract 2, but may not be fully available to serve demands within the catchment, as it is also reachable by tract 11. This points out the need to discount the availability of a supplier by the intensity of competition for its service of surrounding demands. 5.2.2 TWO-STEP FLOATING CATCHMENT AREA (2SFCA) METHOD A method developed by Radke and Mu (2000) overcomes the above fallacies. It repeats the process of floating catchment twice (once on supply locations and once on demand locations) and is therefore referred to as the two-step floating catchment area (2SFCA) method (Luo and Wang, 2003). First, for each supply location j, search all demand locations (k) that are within a threshold travel distance (d0) from location j (i.e., catchment area j) and compute the supply-to-demand ratio Rj within the catchment area: Rj = Sj k k∈{dkj£d0} © 2006 by Taylor & Francis Group, LLC GIS-Based Measures of Spatial Accessibility and Application in Health Care 81 where d is the distance between k and j, D is the demand at location k that falls within the catchment (i.e., dkj £ d0), and Sj is the capacity of supply at location j. Next, for each demand location i, search all supply locations (j) that are within the threshold distance (d0) from location i (i.e., catchment area i) and sum up the supply-to-demand ratios Rj at those locations to obtain the accessibility AiF at demand location i: AF = å Rj = å ( Sj ) (5.2) j∈{dij£d0} j∈{dij£d0} k k∈{dkj£d0} where d is the distance between i and j, and R is the supply-to-demand ratio at supply location j that falls within the catchment centered at i (i.e., dij £ d0). A larger value of AiF indicates a better accessibility at a location. The first step above assigns an initial ratio to each service area centered at a supply location as a measure of supply availability (or crowdedness). The second step sums up the initial ratios in the overlapped service areas to measure accessibility for a demand location, where residents have access to multiple supply locations. The method considers interaction between demands and supplies across areal unit borders and computes an accessibility measure that varies from one location to another. Equation 5.2 is basically the ratio of supply to demand (filtered by a threshold distance or filtering window twice). Figure 5.2 uses the same example to illustrate the 2SFCA method. Here we use travel time instead of straight-line distance to define catchment area. The catchment area for supply a has one supply and eight residents, and thus carries a supply-to-demand ratio of 1/8. Similarly, the ratio for catchment b is 1/4; and for catchment c, 1/5. The resident at tract 3 has access to a only, and the accessibility at tract 3 is equal to the supply-to-demand ratio at a (the only supply location), i.e., Ra = 0.125. Similarly, the resident at tract 5 has access to b only, and thus its accessibility is Rb = 0.25. However, the resident at 4 can reach both supplies a and b (shown in an area overlapped by catchment areas a and b), and therefore enjoys a better accessibility (i.e., Ra + Rb = 0.375). Note that supply a or b can reach tract 4 within the threshold travel time, and on the other side, tract 4 can reach both supply a and b within the same threshold. The catchment drawn in the first step is centered at a supply location, and thus the travel time between the supply and any demand within the catchment does not exceed the threshold. The catchment drawn in the second step is centered at a demand location, and all supplies within the catchment contribute to the supply–demand ratios at that demand location. The method overcomes the fallacies in the earlier FCA methods. Equation 5.2 is basically a ratio of supply to demand, with only selected supplies and demands entering the numerator and denominator, and the selections are based on a threshold distance or time within which supplies and demands interact. Travel time should be used if distance is a poor measure of travel impedance (e.g., in areas where roads are unevenly distributed and travel speeds vary to a great extent). © 2006 by Taylor & Francis Group, LLC ... - tailieumienphi.vn