A Probabilistic Approach to Address Data Uncertainty in Regionalization

Abstract

Spatial data regularly suffer from error and uncertainty, ranging from poorly georeferenced coordinate pairs to sampling error associated with American Community Survey data. Geographic information systems can amplify and propagate error and uncertainty through the abstraction and representation of spatial data, as can the manipulation, processing, and analysis of spatial data using exploratory and confirmatory statistical techniques. The purpose of this article is to explore and address uncertainty in regionalization, a fundamental spatial analytical method that aggregates spatial units (e.g., tracts) into a set of contiguous regions for strategic purposes, including school districting, habitat areas, and the like. Specifically, we develop a new regionalization method, the uncertain‐max‐p‐regions problem that explicitly incorporates attribute uncertainty and allows its impacts to be evaluated with a degree of statistical certainty. We also detail an efficient solution approach for dealing the problem. The results suggest that the developed problem can out‐perform existing regionalization approaches and that the addition of a measure of statistical confidence can help to facilitate more clarity in planning and policy decisions.