Calibrating Spatial Stratified Heterogeneity for Heavy-Tailed Distributed Data

Abstract

The phenomena with within-strata characteristics that are more similar than between-strata characteristics are ubiquitous (e.g., land-use types and image classifications). It can be summarized as spatial stratified heterogeneity (SSH), which is measured and attributed using the geographical detector (Geodetector) q-statistic. SSH is typically calibrated by stratification and hundreds of algorithms have been developed. Little is discussed about the conditions of the methods. In this work, a novel stratification method based on head/tail breaks is introduced for the purpose of better capturing the SSH of geographical variables with a heavy-tailed distribution. Compared to conventional sample-based stratifications, the presented approach is a population-based optimized stratification that indicates an underlying scaling property in geographical spaces. It requires no prior knowledge or auxiliary variables and supports a naturally determined number of strata instead of being subjectively preset. In addition, our approach reveals the inherent hierarchical structure of geographical variables, characterizes its dominant components across all scales, and provides the potential to make the stratification meaningful and interpretable. The advantages were illustrated by several case studies in natural and social sciences. The proposed approach is versatile and flexible so that it can be applied for the stratification of both geographical and nongeographical variables and is conducive to advancing SSH-related studies as well. This study provides a new way of thinking for advocating spatial heterogeneity or scaling law and advances our understanding of geographical phenomena.