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.

翻译：本文提出了一种矩阵变量回归模型，用于分析在空间位置和时间维度上观测的多元数据。该模型的设计包含一个将协变量与响应矩阵关联的均值结构，以及基于克罗内克积的可分离协方差结构，以高效捕捉空间和时间依赖性。我们推导了所有模型参数的最大似然估计量。模拟研究验证了该模型，展示了其在不同空间分辨率下参数恢复的有效性。最后，通过对巴西各市农业和畜牧业生产实际数据的应用，展示了该模型在揭示结构化时空变异模式及协变量效应方面的实际效用。