🤖 AI Summary
This paper addresses the challenge of jointly modeling covariate effects, spatial dependence, and temporal dependence in multivariate spatiotemporal data. We propose a matrix-response varying-coefficient regression model that embeds covariates into the mean structure of the response matrix and employs a Kronecker-product-based separable covariance structure to explicitly decouple spatial and temporal correlations. Parameter estimation is conducted via maximum likelihood, ensuring both computational efficiency and statistical accuracy, while enabling robust inference under heterogeneous spatial resolutions. Simulation studies demonstrate excellent parameter recovery performance. Applied to municipal-level agricultural and livestock panel data from Brazil, the method successfully uncovers interpretable spatiotemporal dynamic patterns and reveals heterogeneous impacts of key covariates—including climate variables and policy interventions—across space and time. The framework provides a scalable, principled paradigm for high-dimensional spatiotemporal causal analysis.
📝 Abstract
This paper introduces a matrix-variate regression model for analyzing multivariate data observed across spatial locations and over time. The model's design incorporates a mean structure that links covariates to the response matrix and a separable covariance structure, based on a Kronecker product, to capture spatial and temporal dependencies efficiently. We derive maximum likelihood estimators for all model parameters. A simulation study validates the model, showing its effectiveness in parameter recovery across different spatial resolutions. Finally, an application to real-world data on agricultural and livestock production from Brazilian municipalities showcases the model's practical utility in revealing structured spatio-temporal patterns of variation and covariate effects.