In geostatistics, a spatial support refers to the size and shape of the area or volume over which a variable of interest is measured or observed. Examples of spatial support include the volume of a soil core analyzed to measure pH, the pixel size in satellite imagery, or the geographic extent and shape of a county for which cancer mortality rate is available. Let’s take a closer look at the importance and types of change of spatial support.
Importance of spatial support
Spatial support is an important concept in geostatistics because it determines the scale at which spatial variability can be analyzed and the size of the spatial objects for which geostatistical predictions can be made.
Too often, spatial support is overlooked for computational convenience. For example, In the early applications of geostatistics to medical data, disease rates were simply assigned to the geographic centroids of the administrative units, which enabled the implementation of traditional interpolation techniques. This implementation assumed that all the unit’s habitants live at the same location, and the measured rate thus refers to this specific location. This simplistic assumption becomes inappropriate when the administrative units are ZIP codes or states with very diverse and complex shapes, which calls for specific methods to incorporate the shape and size of those units in the analysis.
Change of spatial support
One of the most challenging tasks in environmental epidemiology is analyzing and synthesizing spatial data collected at different spatial scales and over different spatial supports. For example, if you want to explore relationships between health outcomes aggregated to the ZIP code level, census-tract demographic covariates, and exposure data measured at a few point locations. To do so, you must estimate or predict all the different variables over the same spatial support.
Such a challenge is illustrated in the example below, where original datasets have incompatible spatial supports that prevent their linkage:
- Arsenic concentrations measured at private wells
- Prostate cancer incidence recorded at the township level
- Block-group population density that served as proxy for urbanization and use of regulated public water supply versus use of potentially contaminated private wells in rural areas.
Change of spatial support refers to moving from one type of spatial support to another during the spatial prediction. Using the terminology introduced by Gotway and Long (2002), geostatistics allows one to tackle three different types of change of support: upscaling (e.g., aggregating point data into an area), downscaling (e.g., disaggregating an area data into points), and side-scaling (e.g., two sets of overlapping areas, like going from ZIP codes to census tracts).
For example, geostatistics was used to estimate groundwater arsenic concentration and population density at the township level using private well arsenic concentrations (upscaling) and block-group census data (side-scaling). This change of support allowed analysis of the relationship between drinking groundwater with high levels of arsenic and the incidence of prostate cancer (Goovaerts, 2014).
BioMedware software, SpaceStat, was the first commercial software to implement the different types of geostatistical changes of spatial support. Change of support is also implemented in BioMedware’s Vesta software.
Combining different spatial supports
A common issue in spatial interpolation is the combination of data measured over different spatial supports. For example, information available for mapping disease risk typically includes point data (e.g. patients and controls’ residences) and areal data (e.g. socio-demographic and economic attributes recorded at the census tract level).
Similarly, soil measurements at discrete locations in the field are often supplemented with choropleth maps (e.g. soil or geological maps) that model the spatial distribution of soil attributes as the juxtaposition of polygons (areas) with constant values. Once again geostatistics offers the tool to integrate all types of data into spatial prediction (Goovaerts, 2010), and is available in the Vesta software.
Sources:
Goovaerts, P. 2010. Combining areal and point data in geostatistical interpolation: Applications to soil science and medical geography. Mathematical Geosciences, vol. 42, no. 5, pp. 535-554.
Goovaerts, P. 2012. Geostatistical analysis of health data with different levels of spatial aggregation. Spatial and Spatio-temporal Epidemiology, vol. 3, no. 1, pp. 83-92.
Goovaerts, P. 2014. Geostatistics – A common link between medical geography, mathematical geology and medical geology. Danie Krige Commemorative Volume of the Journal of the Southern African Institute of Mining and Metallurgy, 114, 605-613.
Gotway, C.A., and Young, L.J. 2002. Combining incompatible spatial data. Journal of the American Statistical Association, vol. 97, no. 459, pp. 632-648