Spatial accessibility and availability measures and statistical properties in the food environment
Introduction
Spatial accessibility and availability indices are now used frequently in the analysis of various environments. Original work on these indices was carried out in the 1970s to examine traffic flows and commuter trips for urban planning (Wilson, 1971), but more recently the indices have been applied within nutritional and physical activity studies to assess access to food or exercise resources (Ball et al., 2009, Feng et al., 2010, Galvez et al., 2009, Macdonald et al., 2009, Smoyer-Tomic et al., 2008, Spence et al., 2009). The use of indices in comparative inference about different areas and their properties has increased; however, the statistical properties of such indices have never been fully evaluated. Analyses of these measures often resort to low powered non-parametric tests, which do not exploit the special nature of the indices studied.
In this paper we examine a range of measures that can be used to measure both spatial availability and accessibility. Commonly used availability measures applied in epidemiologic studies on the food environment include number of food outlets, stores, or restaurants in a given location or within a fixed distance ‘buffer’ of a location. In terms of accessibility, commonly used measures are distance-based; assuming that increased distance acts as a deterrent and reduces the frequency of use of the resource. We explore various statistical properties of these measures including correlation between indices. We derived Monte Carlo critical values to be used for statistical analyses after an extensive simulation study. These tests identify differences between accessibility and availability attributes of different study areas and can test for difference between the average value of the measure as well as the spatial correlation, Moran’s I.
Section snippets
Background to measures
In our study we have evaluated a range of measures. Our choice of measures is defined by those commonly found in the literature for studies of the food environment and the accessibility of food resources (Edmonds et al., 2001, Guy, 1983, Inagami et al., 2006, Jeffery et al., 2006, Morland et al., 2002a, Morland et al., 2002b, Morland et al., 2006, Sturm and Datar, 2005). Each measure is calculated from multiple spatial locations within a study area. We define an individual location as s, which
Simulation study design
Our aim was to provide statistical criteria for inference between various accessibility and availability measures calculated in two spatial environments. To this end we have conducted a simulation study which addresses the nature of the spatial variation of these measures. This study was motivated by and part of a larger effort on characterizing the built food environment in an eight county region in South Carolina (Liese et al., 2009). Therefore, our choice of features in the simulation design
Model assumptions
The simulation design is partially based on characteristics of the local food environment and also more general considerations of applicability to a variety of food environment scenarios. To this end we have examined food outlet densities in an eight county urban and rural area of South Carolina (Liese et al., 2009). While no very large cities are represented in that study, the average characteristics of outlet density and its variation between rural and urban areas are highlighted. In initial
Statistical description and hypothesis testing
All the measures that we evaluate are available at any s location point on the grid within a spatial domain (study area). Hence the resulting measure is in fact a surface. At any single location on the selected grid we are making a measurement on what is a continuous surface. For counts of outlets this is of course an approximation but the use of the square root transform of the counts will help to normalize the surface (Cressie, 1993).
Often geostatistical methods are used to characterize such
Simulation-based results: hypothesis testing
Using these combined simulations, we were able to identify critical values to test for significant differences between spatial measures and Moran’s I spatial autocorrelation between two areas using Monte Carlo simulation testing. Table 1 displays the Monte Carlo critical values for various alpha levels for each of these comparison tests between average spatial measures identified above. Similarly, Table 2 displays the critical values for comparison tests between Moran’s I for spatial
Simulation-based results: correlation
Another statistical property assessed during this simulation study was correlations between the various accessibility/availability spatial measures. These correlations are not meant for inference; they are simply presented to inform about some of the patterns we find between these measures. They are also not consistent between simulation scenarios of urban versus non-urban and different number of total outlets. For a specific simulation scheme, correlations were calculated for each dataset (500
Mapped results
Another result of our simulation study was to observe spatial patterns of these various availability/accessibility measures. Once again, these patterns are highly dependent on the simulation design, cluster centers, and the total number of outlets in an area. But these contour plots are informative of the variability of these measures within an individual area. Fig. 5 displays four contour plots for an individual dataset simulated for an urban environment with 15 cluster centers, a clustering
Data example
We provide a real data example of how these new statistical inference tests can be applied using previously collected data from urban and rural areas of South Carolina (Liese et al., 2009). Table 5 provides basic demographic characteristics for this study area. We decided to focus on rural Kershaw County and urban Richland County to assess differences in accessibility and availability measures between two study areas. Fig. 7 gives a graphical representation of both Kershaw and Richland counties
Discussion and conclusions
As a result of this simulation study, we have gained significantly more information regarding the statistical properties of various accessibility and availability measures commonly found in the literature. We also constructed two tests to assess differences in average values and Moran’s I for spatial autocorrelation. These tests are scale-invariant and can be applied to study areas that are not the same size. These tests are also not dependent on the spatial properties of outlets, stores, or
Acknowledgements
This project was supported by R21CA132133 from the National Cancer Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute or the National Institutes of Health.
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