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.

Key Words:

• Geodetector q-statistic
• head/tail breaks
• spatial stratified heterogeneity
• stratification
• structural hierarchy

Data Availability Statement

The data and codes that support the proposed approach and case studies of this article are available at figshare. com at the identifier https://doi.org/10.6084/m9.figshare.21786014. The file package includes (1) the codes in R to support the head/tail breaks-based stratification and the SSH calculation in the case studies, and the codes in MATLAB to support the power law detection for urban populations; and (2) the raw data used in the case studies. Alternatively, the geographical detector and head/tail breaks software can be found at http://www.geodetector.cn/ and https://en.wikipedia.org/wiki/head/tail_breaks, respectively. The codes to support the power law detection and the detections of other heavy-tailed distributions can be found at https://aaronclauset.github.io/. The data used in the case studies are publicly available. The data set of China’s urban populations is owned by China Population Census Yearbook 2020 (http://www.stats.gov.cn/tjsj/pcsj/rkpc/7rp/zk/indexce.htm). The annual NTL image comes from an extended time series of global NPP-VIIRS-like NTL data (https://doi.org/10.7910/dvn/ygivcd). The monthly image of NDVI and annual bamboo-forest density image are owned by the Resource and Environment Science and Data Center, Chinese Academy of Sciences (https://www.resdc.cn/).

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study was supported by the National Natural Science Foundation of China (Grant Nos. 42061075, 42071375), the Startup Fund of The Hong Kong University of Science and Technology (Guangzhou), and the City-University Joint Fund of the Science and Technology Project of Guangzhou.

Notes on contributors

Bisong Hu

BISONG HU is a Full Professor at the School of Geography and Environment, Jiangxi Normal University, Nanchang, China. E-mail: [email protected]. His research interests center on spatial statistics, spatial epidemiology, epidemic spread simulation, and spatial-temporal big data analysis.

Tingting Wu

TINGTING WU is a Master’s Candidate at the School of Geography and Environment, Jiangxi Normal University, Nanchang, China. E-mail: [email protected]. Her research interests include spatial analysis and urban systems.

Qian Yin

QIAN YIN is an Associate Professor at the State Key Laboratory of Resources and Environmental Information Systems, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China. E-mail: [email protected]. Her research interests include spatial statistics and environmental health.

Jinfeng Wang

JINFENG WANG is a Distinguished Professor at the State Key Laboratory of Resources and Environmental Information Systems, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing, China. E-mail: [email protected]. His research interests include spatial statistics and their application in geoscience and population health.

Bin Jiang

BIN JIANG is a Full Professor at Urban Governance and Design Thrust, Society Hub, The Hong Kong University of Science and Technology (Guangzhou), China. E-mail: [email protected]. His research interests center on geospatial analysis of urban structure and dynamics, or geospatial big data in general.

Jin Luo

JIN LUO is an Associate Professor and the Executive Dean of the School of Geography and Environment, Jiangxi Normal University, Nanchang, China. E-mail: [email protected]. He specializes in spatial databases and data mining.