A hypothesis test for detecting spatial patterns in categorical areal data

The vast growth of spatial datasets in recent decades has fueled the development of many statistical methods for detecting spatial patterns. Two of the most commonly studied spatial patterns are clustering, loosely defined as datapoints with similar attributes existing close together, and dispersion, loosely defined as the semi-regular placement of datapoints with similar attributes. In this work, we develop a hypothesis test to detect spatial clustering or dispersion at specific distances in categorical areal data. Such data consists of a set of spatial regions whose boundaries are fixed and known (e.g., counties) associated with a categorical random variable (e.g. whether the county is rural, micropolitan, or metropolitan). We propose a method to extend the positive area proportion function (developed for detecting spatial clustering in binary areal data) to the categorical case. This proposal, referred to as the categorical positive areal proportion function test, can detect various spatial patterns, including homogeneous clusters, heterogeneous clusters, and dispersion. Our approach is the first method capable of distinguishing between different types of clustering in categorical areal data. After validating our method using an extensive simulation study, we use the categorical positive area proportion function test to detect spatial patterns in Boulder County, Colorado USA biological, agricultural, built and open conservation easements.