Statistical Modeling of Spatially Stratified Heterogeneous Data

Spatial statistics is an important methodology for geospatial data analysis. It has evolved to handle spatially autocorrelated data and spatially (locally) heterogeneous data, which aim to capture the first and second laws of geography, respectively. Examples of spatially stratified heterogeneity (SSH) include climatic zones and land-use types. Methods for such data are relatively underdeveloped compared to the first two properties. The presence of SSH is evidence that nature is lawful and structured rather than purely random. This induces another “layer” of causality underlying variations observed in geographical data. In this article, we go beyond traditional cluster-based approaches and propose a unified approach for SSH in which we provide an equation for SSH, display how SSH is a source of bias in spatial sampling and confounding in spatial modeling, detect nonlinear stochastic causality inherited in SSH distribution, quantify general interaction identified by overlaying two SSH distributions, perform spatial prediction based on SSH, develop a new measure for spatial goodness of fit, and enhance global modeling by integrating them with an SSH q statistic. The research advances statistical theory and methods for dealing with SSH data, thereby offering a new toolbox for spatial data analysis.