Kriging and Semivariogram Deconvolution in the Presence of Irregular Geographical Units
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This paper presents a methodology to conduct geostatistical variography and interpolation on areal data measured over geographical units (or blocks) with different sizes and shapes, while accounting for heterogeneous weight or kernel functions within those units. The deconvolution method is iterative and seeks the point-support model that minimizes the difference between the theoretically regularized semivariogram model and the model fitted to areal data. This model is then used in area-to-point (ATP) kriging to map the spatial distribution of the attribute of interest within each geographical unit. The coherence constraint ensures that the weighted average of kriged estimates equals the areal datum.
This approach is illustrated using health data (cancer rates aggregated at the county level) and population density surface as a kernel function. Simulations are conducted over two regions with contrasting county geographies: the state of Indiana and four states in the Western United States. In both regions, the deconvolution approach yields a point support semivariogram model that is reasonably close to the semivariogram of simulated point values. The use of this model in ATP kriging yields a more accurate prediction than a naïve point kriging of areal data that simply collapses each county into its geographic centroid. ATP kriging reduces the smoothing effect and is robust with respect to small differences in the point support semivariogram model. Important features of the point-support semivariogram, such as the nugget effect, can never be fully validated from areal data. The user may want to narrow down the set of solutions based on his knowledge of the phenomenon (e.g., set the nugget effect to zero). The approach presented avoids the visual bias associated with the interpretation of choropleth maps and should facilitate the analysis of relationships between variables measured over different spatial supports.
KeywordsSimulation Change of support Choropleth map Disaggregation
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- Armstrong M (1998) Basic linear geostatistics. Springer, Berlin, 172 p Google Scholar
- Avruskin GA, Jacquez GM, Meliker JR, Slotnick MJ, Kaufmann AM, Nriagu JO (2004) Visualization and exploratory analysis of epidemiologic data using a novel space time information system. Int J Health Geogr 3(26). doi: 10.1186/1476-072X-3-26
- Berke O (2004) Exploratory disease mapping: kriging the spatial risk function from regional count data. Int J Health Geogr 3(18). doi: 10.1186/1476-072X-3-18
- Chiles JP, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. Wiley, New York, 720 p Google Scholar
- Collins JB, Woodcock CE (1996) Explicit consideration of multiple landscape scales while selecting spatial resolutions. In: Mowrer HT, Czaplewski RL, Hamre RH (eds) Spatial accuracy assessment in natural resources and environmental sciences: second international symposium. Technical report RM-GTR-277, United States department of Agriculture, Fort Collins, Colorado, pp 121–128 Google Scholar
- Collins JB, Woodcock CE (1999) Geostatistical estimation of resolution-dependent variance in remotely sensed images. Photogramm Eng Remote Sensing 65(1):41–50 Google Scholar
- Cressie N (1993) Statistics for spatial data. Wiley, New York, 900 p Google Scholar
- Croner CM, De Cola L (2001) Visualization of disease surveillance data with geostatistics. Presented at UNECE (United Nations Economic Commission for Europe) work session on methodological issues involving integration of statistics and geography, Sept 2001, Tallinn. http://www.unece.org/stats/documents/2001/09/gis/25.e.pdf
- Curran PJ, Atkinson PM (1999) Issues of scale and optimal pixel size. In: Stein A, van der Meer F, Gorte B (eds) Spatial statistics for remote sensing. Kluwer Academic, Dordrecht, pp 115–133 Google Scholar
- Deutsch CV, Journel AG (1998) GSLIB: Geostatistical software library and user’s guide, 2nd edn. Oxford University Press, New York, 369 p Google Scholar
- Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York, 483 p Google Scholar
- Goovaerts P (2005) Geostatistical analysis of disease data: estimation of cancer mortality risk from empirical frequencies using Poisson kriging. Int J Health Geogr 4(31). doi: 10.1186/1476-072X-4-31
- Goovaerts P (2006) Geostatistical analysis of disease data: accounting for spatial support and population density in the isopleth mapping of cancer mortality risk using area-to-point Poisson kriging. Int J Health Geogr 5(52). doi: 10.1186/1476-072X-5-52
- Gotway CA, Young LJ (2004) A geostatistical approach to linking geographically-aggregated data from different sources. Technical report # 2004-012, Department of Statistics, University of Florida Google Scholar
- Isaaks EH, Srivastava RM (1989) An introduction to applied geostatistics. Oxford University Press, New York, 561 p Google Scholar
- Journel AG, Huijbregts CJ (1978) Mining geostatistics. Academic Press, London, 600 p Google Scholar