Matrix-Variate Regression Model for Multivariate Spatio-Temporal Data

TL;DR

This paper proposes a matrix-variate regression model tailored for multivariate spatio-temporal data, effectively capturing spatial and temporal dependencies and demonstrating its utility through simulations and real-world agricultural data analysis.

Contribution

It introduces a novel matrix-variate regression framework with a separable covariance structure and maximum likelihood estimation for multivariate spatio-temporal data.

Findings

Model accurately recovers parameters in simulations

Effectively captures spatio-temporal patterns in real data

Demonstrates practical utility in agricultural studies

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.