ABSTRACT Spatial heterogeneity refers to spatial variation in relationships between dependent and independent variables across geographic locations, conceptualized differently depending on the analytical perspective, each highlighting distinct patterns of variation. Spatially varying coefficient (SVC) models are commonly employed to explore spatial heterogeneity. Because each SVC model utilizes a fundamentally distinct estimation approach, performance is anticipated to vary across patterns. However, prior comparative evaluations have remained fragmented within single structural perspectives. This study systematically evaluates SVC model performance across diverse structural patterns of spatial heterogeneity, conceptualized through continuity, directionality, and scale. Using a controlled simulation framework, 12 patterns are generated and evaluated for multiscale geographically weighted regression (MGWR), spatial generalized additive models (SGAM), geographical Gaussian process GAM (GGP‐GAM), and Moran eigenvector spatial filter‐based SVC (MESF‐SVC). The findings demonstrate that GAM‐based models consistently excel in capturing smooth, continuous spatial gradients at the global scale. In contrast, MESF‐SVC proves robust in resolving localized and discontinuous spatial fragmentation. Meanwhile, MGWR exhibits instability under high frequency local variations, frequently over‐smoothing abrupt boundaries due to its localized kernel weighting. An empirical analysis of Seoul metropolitan election data shows these distinctions persist under multivariate conditions. Based on these outcomes, this study provides practical guidelines for SVC model selection.
ABSTRACT Spatial synthetic populations are increasingly used in agent‐based models, spatial microsimulation, and other forms of place‐based analysis. Their usefulness, however, depends not only on reproducing aggregate patterns but also on maintaining plausible local distributions. This creates a difficult validation problem when independent benchmarks are limited and validation cannot proceed beyond checking the technical implementation of model constraints. We develop a moment‐based validation framework for detecting and interpreting local irregularities in spatial synthetic data. Local distributions are characterized through their first four moments and we combine hierarchical clustering with SHapley Additive exPlanations to identify and explain areas whose modeled distributions depart from expected local patterns and contextual variables. The framework is demonstrated using modeled salary distributions from the Synthetic Population Catalyst in West Yorkshire, a setting in which fine‐scale synthetic populations are assembled from sources observed at coarser spatial and substantive resolutions. The application identifies locally unusual areas, shows how these can be interpreted against contextual characteristics and local knowledge, and illustrates how the framework can support judgments about whether synthetic data are fit for intended use. More broadly, the article argues that local coherence should be treated as a central criterion in the validation of spatial synthetic populations.
ABSTRACT This paper develops a statistical framework for inference on recently developed spatial polarization indices and clarifies their relationship to spatial inequality and dependence. The framework builds on a graph‐theoretic decomposition of polarization into global, meso, and local components and accommodates an asymmetry common in regional economic data: low‐income areas often form cohesive clusters, whereas high‐income areas are more spatially fragmented. The principal contributions are a graph‐preserving randomization procedure and asymptotic results for the spatial polarization index. These methods permit assessment of the significance and robustness of observed polarization patterns while connecting spatial statistics, inequality decomposition, and graph theory. A series of Monte Carlo experiments examines the properties of the inferential methods. Two case studies focusing on polarization in Mexico and the United States provide empirical illustrations.
ABSTRACT Regional inequality is conventionally assessed based on the distribution of economic outcomes across regions. However, regional disparities are spatially structured because regional economic outcomes are interdependent across space. Existing approaches generally capture either the spatial dimension of inequality at an aggregate level or unit‐specific disadvantage without incorporating spatial relevance. This study proposes a Spatially Weighted Relative Deprivation (SWRD) index that combines the one‐sided upward‐gap rule of relative deprivation (RD) with an empirically calibrated spatial weighting structure. Using real gross regional domestic product (GRDP) for 229 Korean districts from 2015 to 2021, the study estimates the distance decay of spatial dependence and constructs annual SWRD values. The empirical comparison shows that SWRD produces spatial patterns and regional rankings that differ from conventional RD. Spatial permutation tests indicate that high SWRD values are unlikely under random spatial reassignment. Monte Carlo simulations on a uniform lattice further show that the divergence between RD and SWRD increases with stronger spatial dependence, steeper distance decay, and greater dispersion and right skewness. These findings show that incorporating spatial structure can change assessments of regional disadvantage under varying spatial and distributional conditions.
The Moran effect traditionally refers to the synchronization of population dynamics driven by shared environmental forcing rather than direct interactions among populations. Although extensively studied in ecology, the Moran effect has received limited attention in geography, and its applicability has yet to be fully explored. In this study, we build upon the classical Moran effect in population ecology as a conceptual foundation, developing a more comprehensive conceptual framework in a geographic context. We introduce the new concept Geographic Moran Effect (GME), defined as temporally coherent and synchronized variation across geographic entities induced by common external forcing, with the magnitude and potentially the direction of local responses varying according to a spatially varying sensitivity field. A two-step spatiotemporal factor framework is developed to identify and interpret the GME. The framework first tests for the possible presence of GME-type synchrony in spatiotemporal data and then examines the GME and its spatiotemporal evolution by investigating its structure through spatial and temporal dimensions separately. A synthetic experiment validates the framework's reliability, while an application to U.S. county-level presidential election data (2008-2024) demonstrates its ability to identify the GME and its spatial and temporal components. By redefining the Moran effect as a geographic theory and a distinct object of inference, this work provides a mechanism-oriented perspective on spatiotemporal analysis with broad applicability in geography, ecology, and public health, where explicitly identifying and interpreting GME-type synchrony is essential for understanding system-level dynamics.
