Correcting scale mismatch in sustainability indicators: Spatial decomposition evidence from Vietnam's provincial indicator system

Composite sustainability indicators are central to environmental monitoring, policy formulation, and sustainable development assessment, but many remain jurisdiction-bound. They report performance within administrative units even when ecological, infrastructural, and socio-technical processes operate across borders. This creates a scale-mismatch problem: the spatial unit used for reporting may not match the spatial scale of the process being assessed. This study develops a provincial Sustainable Development Indicator (SDI) system for Vietnam's 63 provinces during 2010-2022 and applies Spatial Durbin Model (SDM) partial-derivative decomposition to distinguish direct, indirect, and total indicator associations. The SDI integrates thirteen indicators across economic, social, and environmental sub-indices, including CO₂ emissions, PM2.5 exposure, forest cover, and industrial wastewater compliance, and is validated using Principal Component Analysis (PCA), internal consistency tests, and convergent validity checks. The results indicate significant positive spatial dependence in provincial sustainability indicator performance, suggesting that purely jurisdiction-bounded interpretation is statistically incomplete. Spatial decomposition shows that digital connectivity has the largest total spatially adjusted association with SDI performance; its spillover component is equivalent to approximately 82% of its direct association and accounts for about 45% of the total. Transport indicators also show significant cross-provincial associations, whereas energy infrastructure is more spatially localised. Institutional quality and fiscal autonomy strengthen the conversion of infrastructure-related endowments into sustainability indicator performance. The study contributes to environmental and sustainability indicator research by showing that indicator validity depends not only on variable selection, weighting, and internal consistency, but also on spatial scale alignment. Spatial decomposition offers a practical method for improving ecological validity, regional comparability, and management relevance in sustainability indicator systems.