Combining Areal and Point Data in Geostatistical Interpolation: Applications to Soil Science and Medical Geography |
| |
| Authors: | Pierre Goovaerts |
| |
| Institution: | (1) BioMedware, Inc., Ann Arbor, MI, USA |
| |
| Abstract: | 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. |
| |
| Keywords: | |
| 本文献已被 PubMed SpringerLink 等数据库收录！ |
|
