Fast Spatio‐Temporally Varying Coefficient Modeling With Reluctant Interaction Selection

ABSTRACT Spatially and temporally varying coefficient (STVC) models are attracting attention as a flexible tool to explore the spatio‐temporal patterns in regression coefficients. However, these models often struggle with balancing the computational efficiency, flexibility, and interpretability of the coefficients. This study develops a fast and flexible STVC model to address this challenge. To enhance flexibility and interpretability, we assume multiple processes in each varying coefficient, including purely spatial, purely temporal, and spatio‐temporal interaction processes with or without time cyclicity. We combine a pre‐conditioning method with a model selection procedure, inspired by reluctant interaction modeling, to estimate the strength of each process in each coefficient in a computationally efficient manner, while removing redundant processes as necessary. Monte Carlo experiments demonstrate that the proposed method outperforms alternatives in terms of coefficient estimation accuracy and computational efficiency. We then apply the proposed method to a crime analysis. The result confirms that the proposed method provides reasonable estimates. The STVC model is implemented in the R package spmoran.