Coarse-to-fine spatial GLMM for scalable prediction and multiscale analysis
Abstract
We develop a coarse-to-fine generalized linear mixed model (CF-GLMM) for scalable spatial prediction of exponential-family responses. CF-GLMM extends coarse-to-fine spatial modeling (CFSM) beyond Gaussian data by sequentially increasing spatial resolution while validation deviance improves, so the terminal resolution need not be specified in advance. The latent spatial process is constructed by aggregating local models, avoiding costly operations on large spatial covariance matrices. An idealized convolution representation links the covariance of our assumed spatial process to a sum of Matern covariances with different ranges. Monte Carlo experiments show that CF-GLMM achieves predictive accuracy comparable to widely used scalable spatial GLMMs while requiring less computation and memory. Its scale-specific components also support exploratory multiscale analysis. An application to COVID-19 infection data in Tokyo illustrates fine-resolution spatial prediction and multiscale characterization of geographical variation. The proposed method is implemented in an R package spCF (https://cran.r-project.org/web/packages/spCF/).
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BibTeX
@misc{murakami2026coarsetofine,
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},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.01157},
eprint = {2605.01157},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.01157},
}
RIS
TY - UNPB
TI - Coarse-to-fine spatial GLMM for scalable prediction and multiscale analysis
AU - Daisuke Murakami
AU - Alexis Comber
AU - Takahiro Yoshida
AU - Narumasa Tsutsumida
AU - Chris Brunsdon
AU - Tomoki Nakaya
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2605.01157
UR - https://arxiv.org/abs/2605.01157
AB - We develop a coarse-to-fine generalized linear mixed model (CF-GLMM) for scalable spatial prediction of exponential-family responses. CF-GLMM extends coarse-to-fine spatial modeling (CFSM) beyond Gaussian data by sequentially increasing spatial resolution while validation deviance improves, so the terminal resolution need not be specified in advance. The latent spatial process is constructed by aggregating local models, avoiding costly operations on large spatial covariance matrices. An idealized convolution representation links the covariance of our assumed spatial process to a sum of Matern covariances with different ranges. Monte Carlo experiments show that CF-GLMM achieves predictive accuracy comparable to widely used scalable spatial GLMMs while requiring less computation and memory. Its scale-specific components also support exploratory multiscale analysis. An application to COVID-19 infection data in Tokyo illustrates fine-resolution spatial prediction and multiscale characterization of geographical variation. The proposed method is implemented in an R package spCF (https://cran.r-project.org/web/packages/spCF/).
ER -