Gradient Boosting for Spatial Regression Models with Autoregressive Disturbances

Abstract Researchers in urban and regional studies increasingly work with high-dimensional spatial data that captures spatial patterns and spatial dependencies between observations. To address the unique characteristics of spatial data, various spatial regression models have been developed. In this article, a novel model-based gradient boosting algorithm tailored for spatial regression models with autoregressive disturbances is proposed. Due to its modular nature, the approach offers an alternative estimation procedure with interpretable results that remains feasible even in high-dimensional settings where traditional quasi-maximum likelihood or generalized method of moments estimators may fail to yield unique solutions. The approach also enables data-driven variable and model selection in both low- and high-dimensional settings. Since the bias-variance trade-off is additionally controlled for within the algorithm, it imposes implicit regularization which enhances predictive accuracy on out-of-sample spatial data. Detailed simulation studies regarding the performance of estimation, prediction and variable selection in low- and high-dimensional settings support proper functionality of the proposed methodology. To illustrate the applicability of the model-based gradient boosting algorithm, a case study is presented where the life expectancy in German districts is modeled, incorporating a potential spatial dependence structure.