The inclusion of the geographic information into regression models is becoming increasingly popular due to the increased availability of corresponding geo-referenced data. In this paper, a novel framework for combining spatio-temporal regression techniques and artificial neural network (ANN) regression models is presented. The key idea is to use the universal approximation property of the ANN function to account for an arbitrary spatial pattern in the dependent variable by including geographic coordinate variables as regressors. Moreover, the implicit location-specific effects are allowed to exhibit arbitrary interaction effects with other regressors such as a time variable. In contrast to other machine learning approaches for spatio-temporal data, the likelihood framework of the classic (linear) spatio-temporal regression model is preserved. This allows, inter alia, for inference regarding marginal effects and associated confidence. The framework also allows for non-normal conditional distributions, conditional spatial correlation, arbitrary trend and seasonality. These features are demonstrated in a simulation section and two data examples, using linear spatio-temporal models as a reference.

由于相应地理参考数据的可用性不断增加，将地理信息纳入回归模型变得越来越流行。本文提出了一种结合时空回归技术和人工神经网络（ANN）回归模型的新颖框架。关键思想是通过将地理坐标变量作为回归量，使用 ANN 函数的万能逼近属性来解释因变量中的任意空间模式。此外，隐式位置特定效应可以表现出与其他回归量（例如时间变量）的任意交互效应。与时空数据的其他机器学习方法相比，保留了经典（线性）时空回归模型的似然框架。除其他外，这允许对边际效应和相关置信度进行推断。该框架还允许非正态条件分布、条件空间相关性、任意趋势和季节性。这些功能在模拟部分和两个数据示例中进行了演示，并使用线性时空模型作为参考。