Gradient Boosting for Spatial Regression Models with Autoregressive Disturbances

TL;DR

This paper introduces a novel gradient boosting algorithm tailored for spatial regression models with autoregressive disturbances, enhancing estimation, variable selection, and prediction accuracy in high-dimensional spatial data.

Contribution

It presents a new model-based gradient boosting approach for spatial regression with autoregressive disturbances, suitable for high-dimensional data and enabling data-driven variable selection.

Findings

Algorithm performs well in simulation studies for estimation and prediction.

Method improves out-of-sample prediction accuracy through implicit regularization.

Case study demonstrates practical application to modeling life expectancy in German districts.

Abstract

Researchers in urban and regional studies increasingly deal with spatial data that reflects geographic location and spatial relationships. As a framework for dealing with the unique nature of spatial data, various spatial regression models have been introduced. In this article, a novel model-based gradient boosting algorithm for spatial regression models with autoregressive disturbances is proposed. Due to the modular nature, the approach provides an alternative estimation procedure which is feasible even in high-dimensional settings where established quasi-maximum likelihood or generalized method of moments estimators do not yield unique solutions. The approach additionally enables data-driven variable and model selection in low- as well as high-dimensional settings. Since the bias-variance trade-off is also controlled in the algorithm, implicit regularization is imposed which improves prediction 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 confirm proper functionality of the proposed methodology. To illustrative the functionality 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.