Singly- and Doubly-Constrained Methods of Areal Interpolation for Vector-based GIS

Traditionally, areal interpolation has referred to techniques for transferring attribute values from one partitioning of space to a different partition of space but this is only one of several situations that create the need for estimating unknown data values for areal units. This paper presents a categorization of four areal interpolation problems that includes the "missing" data problem, the traditional "alternative geography" problem, the overlay of a choropelth and an area-class data layer, and the overlay of two choropleth data layers and demonstrates the relationship between the last three problems and general spatial interaction modelling. The "alternative geography" and overlay of choropleth and area-class data layers mirrors a singly constrained spatial interaction model while the overlay of two choropleth layers is analogous to a doubly constrained interaction model. Iterative proportional fitting techniques with and without ancillary data are developed to solve these three classes of problems.