Digital quality gradient and the burden of elderly depression: A spatial multi kernel SVR analysis of socio economically vulnerable groups in England.

Digital infrastructure is increasingly understood as part of the contemporary built environment and as a policy-relevant area-level correlate of older adults' mental health. Existing studies have often relied on linear models and have paid limited attention to spatial heterogeneity, making it difficult to identify how broadband quality is associated with depression-related burden across vulnerable groups. This cross-sectional ecological study examines nonlinear and spatially varying associations between digital infrastructure and antidepressant prescribing among socio-economically vulnerable older populations in England. Using area-level data collected and processed in July 2025, the analysis focuses on older adults in areas with low social grade (DE) and high income deprivation. We used stepwise regression, multi-kernel support vector regression (SVR), and spatially weighted multi-kernel SVR to estimate the conditional contribution of digital infrastructure after accounting for built-environment covariates. The results indicate a digital quality gradient: high-speed and gigabit-capable broadband variables show stronger predictive contributions for low-social-grade areas, whereas medium-speed broadband coverage is more consistently associated with the depression-related burden of older adults in high-deprivation areas. Spatial coefficient maps identify policy-relevant priority geographies, including post-industrial communities in the Northwest and Midlands and remote or ageing communities in northern and southwestern England. The multi-kernel SVR model achieved cross-validated R