Fast and scalable variable selection for spatial autoregressive models

Abstract In urban and regional studies, spatial autoregressive models are widely employed to capture spatial patterns and a dependence structure in data. While numerous variable selection techniques based on the likelihood principle with favorable theoretical properties have been proposed, the practical applicability is limited by the computational burden of repeatedly evaluating the logarithm of the Jacobian occurring in the quasi log-likelihood which scales poorly with the number of observations. In this article, variable selection techniques that leverage a closed-form estimator for the spatial autoregressive parameter are discussed. The closed-form estimator in combination with spatial-cross validation techniques for regularization parameter tuning enables fast and scalable variable selection utilizing the least absolute shrinkage and selection operator as well as $$L_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -boosting while preserving theoretical properties and ensuring computational efficiency. Furthermore, a dimensionality reduction approach is proposed that enables feasibility in high-dimensional settings where classical quasi-maximum likelihood or two-stage least squares estimators may fail to yield unique solutions. Monte Carlo experiments confirm proper functionality of the proposed methodology while the potential application is illustrated by investigating the drivers of life expectancy in German districts.