Combining Areal and Point Data in Geostatistical Interpolation: Applications to Soil Science and Medical Geography
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’ residence) and aggregated data (e.g. socio-demographic and economic attributes recorded at the census track 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. This paper presents a general formulation of kriging that allows the combination of both point and areal data through the use of area-to-area, area-to-point, and point-to-point covariances in the kriging system. The procedure is illustrated using two data sets: (1) geological map and heavy metal concentrations recorded in the topsoil of the Swiss Jura, and (2) incidence rates of late-stage breast cancer diagnosis per census tract and location of patient residences for three counties in Michigan. In the second case, the kriging system includes an error variance term derived according to the binomial distribution to account for varying degree of reliability of incidence rates depending on the total number of cases recorded in those tracts. Except under the binomial kriging framework, area-and-point (AAP) kriging ensures the coherence of the prediction so that the average of interpolated values within each mapping unit is equal to the original areal datum. The relationships between binomial kriging, Poisson kriging, and indicator kriging are discussed under different scenarios for the population size and spatial support. Sensitivity analysis demonstrates the smaller smoothing and greater prediction accuracy of the new procedure over ordinary and traditional residual kriging based on the assumption that the local mean is constant within each mapping unit.
KeywordsSoil map Cancer Disaggregation Change of support Indicator Binomial
Unable to display preview. Download preview PDF.
- Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York Google Scholar
- Goovaerts P (2007) Spatial uncertainty in medical geography: a geostatistical perspective. In: Shekhar S, Xiong H (eds) Encyclopedia of GIS. Springer, Berlin, pp 1106–1112 Google Scholar
- Goovaerts P (2010) A coherent geostatistical framework for combining choropleth map and field data in the spatial interpolation of soil properties. Eur J Soil Sci (accepted) Google Scholar
- Gotway CA, Young LJ (2005) Change of support: an interdisciplinary challenge. In: Renard Ph, Demougeot-Renard H, Froidevaux R (eds) geoENV V—Geostatistics for environmental applications. Springer, Berlin, pp 1–13 Google Scholar
- Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic Press, London Google Scholar
- Kerry R, Rawlins BG, Goovaerts P (2010b) Area-to-point kriging of organic carbon and soil texture: an efficient use of legacy soil data from polygon maps for regional or national scale digital soil mapping. In: Proceedings of 4th global workshop on digital soil mapping, Rome, Italy, May 24–26, 2010 Google Scholar
- Wackernagel H (1998) Multivariate geostatistics. Springer, Berlin. 2nd completely revised edition Google Scholar
- Walker E, Monestiez P, Renard D, Bez N (2008) Kriging of the latent probability of a binomial variable: application to fish statistics. In: Ortiz J, Emery X (eds) Geostatistics 2008. GECAMIN, Santiago, pp 981–990 Google Scholar
- Webster R, Oliver MA, Muir KR, Mann JR (1994a) Kriging the local risk of a rare disease from a register of diagnoses. Geogr Anal 26:168–185 Google Scholar
- Young JL Jr, Roffers SD, Ries LAG, Fritz AG, Hurlbut AA (eds) (2001) SEER summary staging manual—2000: codes and coding instructions, National Cancer Institute. National Institutes of Health Pub # 01-4969, Bethesda, MD Google Scholar