The Edges of Areal Units: A Case Study in the Heterogeneous Effects of Assessment District Edges

Abstract

Areal units are used in a broad range of demographic and physical description and analysis related to surveying, reporting, navigation, and modeling. In The Modifiable Areal Unit Problem, Openshaw (1983) described how the arbitrariness of an areal unit’s boundaries means that any measurement aggregated to it is to some extent arbitrary as well. Therefore, those who survey, model, and report information based on these units must be aware of their shortcomings as models for describing phenomena that they aggregate. Here we propose to test an aspect of the Modifiable Areal Unit Problem, namely that the boundaries used by an application of modeling with areal units are not homogeneous in their relationship to the phenomena that they model. That is, here we focus on the general problem that the boundaries of a set of areal units aren’t entirely arbitrary. Boundaries for these areal units specifically—and many others generally—are along physical and social features of the environment, which may have an internal effect on the phenomena that they describe as homogenous in the aggregate. In this thesis, we use real estate sales data and assessor’s neighborhood boundaries to develop a method for describing differences in the effect of the boundaries of areal units. It is hoped that the methods developed here could be applied to the analysis of other urban phenomena that are restricted, afforded, described, and modeled by boundaries.