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

2026-05-01

AI Summary

This study addresses the computational inefficiency and degeneracy issues of traditional spatial generalized linear mixed models (GLMMs) when applied to large-scale count data. To overcome these limitations, the authors propose CF-GLMM, the first spatial GLMM framework incorporating a coarse-to-fine learning strategy. By leveraging multi-scale modeling, CF-GLMM effectively mitigates model degeneracy and substantially enhances scalability and flexibility for non-Gaussian spatial data. The method integrates Monte Carlo simulation and is implemented as the R package spCF. Extensive simulations demonstrate its superior spatial prediction accuracy and capability in capturing multi-scale spatial features. The approach is successfully applied to real-world modeling of COVID-19 incidence data, showcasing its practical utility in epidemiological analysis.

Abstract

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/).

Problem

• spatial GLMM
• coarse-to-fine learning
• count data
• non-Gaussian responses
• scalable spatial modeling

Innovation

• coarse-to-fine
• spatial GLMM
• scalable prediction
• multiscale analysis
• count data