Coarse-to-fine spatial GLMM for scalable prediction and multiscale analysis

Abstract

We develop CF-GLMM, a scalable and covariance-free framework for spatial generalized linear mixed models with exponential-family responses, by extending coarse-to-fine spatial modeling (CFSM) beyond Gaussian data. CF-GLMM reformulates coarse-to-fine refinement on the deviance scale using iteratively updated working responses and non-constant working weights, while retaining the local-model aggregation structure of CFSM. Through validation-guided refinement, CF-GLMM automatically adapts spatial complexity and reduces the risk of oversmoothing caused by an insufficient number of basis functions. Monte Carlo experiments demonstrate accurate spatial prediction, efficient computation, and effective multiscale feature extraction, while an analysis of COVID-19 cases in Tokyo illustrates its practical utility. The proposed method is implemented in an R package spCF (https://cran.r-project.org/web/packages/spCF/).