The Effect of Spatial Heterogeneity on Statistical Model Assumptions and Estimation Efficiency

Posted: Feb 20, 2017

• Evelyn Gray
• Grace Brooks
• Hannah Turner

Abstract

Spatial heterogeneity represents one of the most fundamental yet challenging characteristics of spatial data across numerous scientific disciplines. The conventional statistical modeling paradigm often relies on assumptions of spatial homogeneity or simplified spatial structures that fail to capture the complex, multi-scale nature of real-world spatial processes. This research addresses the critical gap in understanding how spatial heterogeneity systematically influences statistical model assumptions and estimation efficiency, moving beyond traditional approaches that treat spatial effects as secondary considerations. The prevailing literature on spatial statistics has predominantly focused on developing methods to account for spatial dependence through various covariance structures, including geostatistical models, spatial autoregressive frameworks, and conditional autoregressive specifications. While these approaches represent important advances, they often implicitly assume that spatial heterogeneity can be adequately captured through mean structures or variance-covariance specifications. This assumption proves problematic when heterogeneity manifests across multiple spatial scales and domains simultaneously, creating complex interactions that conventional models cannot adequately represent. Our research questions challenge this conventional wisdom by asking: How does multi-scale spatial heterogeneity systematically violate standard statistical model assumptions? To what extent does estimation efficiency deteriorate as heterogeneity complexity increases? Can we develop diagnostic tools that effectively detect heterogeneity-induced assumption violations? These questions remain largely unexplored in the existing literature, which tends to focus on specific types of spatial models rather than the fundamental relationship between