Ordinal areal data represent a special type of areal data in which outcomes or categories for spatial units follow a natural order, such as social vulnerability levels (low, low–medium, medium–high, and high) for U.S. counties. Clustering, loosely defined as areas with similar outcomes located close to one another, is one of the most common spatial patterns of interest in spatial data analysis. However, clustering patterns in ordinal areal data can be complex, and existing statistical methods often lack the power to detect them or the ability to distinguish between different types of clustering. In this study, we introduce the ordinal areal proportion function and develop a multi-stage testing procedure, along with a practical workflow, to detect a broad range of clustering patterns, including homogeneous clusters and heterogeneous clusters with or without an ordered pattern. We validate the proposed procedure through carefully designed simulation studies and apply it to the 2022 Centers for Disease Control and Prevention and Agency for Toxic Substances and Disease Registry Social Vulnerability Index data to detect clustering patterns across U.S. counties. The results of this data application provide important insights into spatial distributions of social vulnerability and can inform preparedness for emergencies and disease outbreaks. • We propose a function to detect clusters at specific distances among ordinal areal data. • We use a multi-stage testing procedure to distinguish different clustering patterns. • Our method is able to detect and classify different types of clusters in ordinal data. • Heterogeneous unordered clusters are detected in US county-level social vulnerability data.
Zhao et al. (Fri,) studied this question.