Spatially continuous modelling of aggregated outcome data

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.