Unraveling Incommensurate Spatial Partitions: A Bipartite Graph Approach to School-Neighborhood Interactions and Their Impacts

Abstract

This paper investigates the challenges and opportunities arising from incommensurate spatial partitions (ISPs) in regional science and spatial econometrics, focusing on how processes with overlapping yet distinct boundaries, interact and influence each other. ISPs are prevalent in various domains, including housing markets, employment centers, voting districts, and educational institutions, often complicating spatial econometric modeling and analysis. Using the intersection of school catchment areas and neighborhoods as a primary case study, the paper introduces a novel methodological framework utilizing bipartite graphs. This approach reframes the relationship between different spatial units, allowing for the analysis of multi-process spatial contexts without needing harmonization of spatial supports. The paper also develops new spatial weights derived from the bipartite graph, facilitating both exploratory spatial data analysis and confirmatory spatial econometric modeling. These methods are illustrated through a case study of San Diego, California analyzing 198 neighborhoods and 370 public elementary school catchments.