Spatially continuous modelling of aggregated outcome data
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914481973493760 |
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| author | Villejo, Stephen Jun Diggle, Peter Lindgren, Finn Rue, Haavard Li, Guangquan White, Ella Wade, Matthew Blangiardo, Marta |
| author_facet | Villejo, Stephen Jun Diggle, Peter Lindgren, Finn Rue, Haavard Li, Guangquan White, Ella Wade, Matthew Blangiardo, Marta |
| contents | This work develops a block aggregation approach to spatial estimation and prediction when the response is observed at a coarse spatial scale, for example as counts of events in administrative areas, or blocks, while covariates are available at a finer spatial resolution, typically as raster images. Our approach specifies a linear predictor at the finer resolution as a combination of covariate effects and a latent, spatially continuous Gaussian process. This linear predictor then determines the distribution of the response through an inverse link function and spatial integration. We use a simulation study to evaluate the performance of the proposed approach in comparison to two industry standard approaches: a traditional geostatistical model that associates each response with the centroid of its block; and a Markov random field (MRF) approach that aggregates covariate data to block-level. As expected, the differences in performance among the three approaches are small with respect to block-level prediction. The rationale for, and advantage of, the block aggregation approach lies in its delivery of reliable inferences at whatever spatial resolution is required in a particular application. We describe two applications: a linear Gaussian sampling model of wastewater virus concentrations in England, using population density as covariate; and log-linear Poisson model of cardiovascular hospitalisations in England using socio-demographic variables at fine-scale administrative units as covariates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15452 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spatially continuous modelling of aggregated outcome data Villejo, Stephen Jun Diggle, Peter Lindgren, Finn Rue, Haavard Li, Guangquan White, Ella Wade, Matthew Blangiardo, Marta Methodology Computation This work develops a block aggregation approach to spatial estimation and prediction when the response is observed at a coarse spatial scale, for example as counts of events in administrative areas, or blocks, while covariates are available at a finer spatial resolution, typically as raster images. Our approach specifies a linear predictor at the finer resolution as a combination of covariate effects and a latent, spatially continuous Gaussian process. This linear predictor then determines the distribution of the response through an inverse link function and spatial integration. We use a simulation study to evaluate the performance of the proposed approach in comparison to two industry standard approaches: a traditional geostatistical model that associates each response with the centroid of its block; and a Markov random field (MRF) approach that aggregates covariate data to block-level. As expected, the differences in performance among the three approaches are small with respect to block-level prediction. The rationale for, and advantage of, the block aggregation approach lies in its delivery of reliable inferences at whatever spatial resolution is required in a particular application. We describe two applications: a linear Gaussian sampling model of wastewater virus concentrations in England, using population density as covariate; and log-linear Poisson model of cardiovascular hospitalisations in England using socio-demographic variables at fine-scale administrative units as covariates. |
| title | Spatially continuous modelling of aggregated outcome data |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2604.15452 |