Multivariate Areal Interpolation for Continuous and Count Data

Abstract

Geographic information system (GIS) users often need to disaggregate and reaggregate data collected in polygons, but classical kriging models only allow for data collected in points. We discuss our implementation of areal interpolation, a kriging-based disaggregation technique, in the Geostatistical Analyst extension of ArcGIS 10.1 for Gaussian, binomial, and overdispersed Poisson data. All methods allow for surfaces of prediction standard errors. We also allow for the use of a secondary cokriging variable, which can be any of the three above-mentioned distributions. Our areal interpolation model overcomes several computational problems, such as how to handle polygons of vastly different sizes and how to analyze polygons that are overlapping or disjoint.For Gaussian data averaged over polygons, the output is a surface predicting the value at each individual location. Gaussian polygonal data may arise when continuous point measurements are averaged to polygons in order to protect privacy or reduce overhead, and the original point data is discarded. For polygons containing Poisson counts, the output is a surface predicting the density of counts at each location in the data domain. Our model allows for overdispersed counts and for different observation times between polygons. The output for binomial data is a surface predicting the underlying risk at each location of seeing an individual with a certain trait. Each polygon of the input data must contain a count and a population value. The latter indicates the number of individuals sampled, and the former indicates the number of sampled individuals with a certain trait.Once a prediction surface has been created, predictions can be aggregated back to a new set of polygons. This allows for the collection of data over one set of polygons and the prediction for a different set of polygons. We discuss diagnostic options for determining how well the data fits a model, and we demonstrate areal interpolation with three case studies.