Multivariate Spatio-Temporal Modeling for Regional GIS Data: A Statistical Framework for Analyzing Multidimensional Spatial Interactions

Abstract. Open geospatial datasets increasingly contain multiple regional indicators that evolve jointly across space and time, but applied workflows often fit separate regressions for each indicator and communicate results through static choropleth maps. We present an open-source, reproducible workflow for comparing multivariate spatio-temporal regression models that allow for cross-equation dependence against separate single-equation spatial regressions using interactive map-based diagnostics. The statistical core is a multivariate generalized nesting spatio-temporal (MGNST) framework that represents spatial-lag dependence, spatial-error dependence, temporal autoregression, and cross-equation dependence; independent spatial error models (SEMs) and ordinary regressions are obtained as nested restrictions. Eleven specifications are estimated by maximum likelihood and evaluated using AIC and BIC. A Shiny–leaflet web application loads precomputed model outputs and allows users to inspect observed, fitted, residual, and residual-difference choropleths for municipalities in the Kansai region of Japan. In a synthetic benchmark generated from the full MGNST model, AIC selects the true multivariate specification for all lattice sizes and ranks it above all separate regressions. In the Kansai case study, the independent SEM is marginally preferred by AIC and BIC, while the multivariate SEM estimates statistically significant cross-equation spatial-error dependence. The application makes this near-tie interpretable beyond numerical values by showing where residuals from the two models differ across municipalities. The released data, spatial weights, source code, model outputs, and application provide a reusable FOSS4G workflow for moving from choropleth visualization to spatial model diagnosis.