Although a recent study suggested that coarse-to-fine learning provides a fast and flexible framework for large-scale spatial process modeling, the method was originally developed for Gaussian responses, limiting its applicability. To address this limitation, we extended the coarse-to-fine spatial modeling (CFSM) framework to accommodate spatial generalized linear mixed models (GLMMs), with a particular focus on count data. The resulting model, referred to as CF-GLMM efficiently addresses the degeneracy problem often encountered in conventional spatial GLMMs. The performance of the proposed CF-GLMMs was evaluated in terms of spatial prediction and multiscale feature extraction via Monte Carlo experiments. Finally, we applied the proposed method to the analysis of coronavirus disease 2019 (COVID-19). The proposed method is implemented in an R package spCF (https://cran.r-project.org/web/packages/spCF/).
@article{arxiv.2605.01157,
title = {Coarse-to-fine spatial GLMM for scalable prediction and multiscale analysis},
author = {Daisuke Murakami and Alexis Comber and Takahiro Yoshida and Narumasa Tsutsumida and Chris Brunsdon and Tomoki Nakaya},
journal= {arXiv preprint arXiv:2605.01157},
year = {2026}
}