In this work we propose a novel approach for modeling spatio-temporal data characterized by group structures. In particular, we extend classical mixed effect regression models by introducing a space-time nonparametric component, regularized through a partial differential equation, to embed the physical dynamics of the underlying process, while random effects capture latent variability associated with the group structure present in the data. We propose a two-step procedure to estimate the fixed and random components of the model, relying on a functional version of the Iterative Reweighted Least Squares algorithm. We investigate the asymptotic properties of both fixed and random components, and we assess the performance of the proposed model through a simulation study, comparing it with state-of-the-art alternatives from the literature. The proposed methodology is finally applied to the study of hourly nitrogen dioxide concentration data in Lombardy (Italy), using random effects to account for measurement heterogeneity across monitoring stations equipped with different sensor technologies.

翻译：本文提出了一种新颖的方法，用于建模具有组结构的时空数据。具体而言，我们扩展了经典的混合效应回归模型，引入了一个通过偏微分方程正则化的时空非参数分量，以嵌入底层过程的物理动力学，同时利用随机效应捕捉数据中存在的组结构相关的潜在变异性。我们提出了一种两步程序来估计模型的固定和随机分量，该方法依赖于迭代重加权最小二乘算法的函数版本。我们研究了固定和随机分量的渐近性质，并通过模拟研究评估了所提出模型的性能，与文献中的先进替代方法进行了比较。最后，所提出的方法被应用于研究伦巴第（意大利）小时级二氧化氮浓度数据，利用随机效应来解释配备不同传感器技术的监测站之间的测量异质性。