Block aggregation modelling approach for spatial models
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This work develops a spatial modelling approach for areal data when predictors are available at finer grid‑based resolutions. The method treats area‑level response data as aggregates of an underlying latent spatial process. The aggregation involves an appropriate functional depending on the likelihood or sampling model. The proposed method provides a unified framework for understanding response-covariate relationship, doing spatial disaggregation, and predicting the latent process at arbitrary block configurations. A simulation study evaluates performance under varying sampling proportions, spatial correlation ranges, and marginal variances, and compares the proposed block‑aggregation model with two alternatives: a traditional geostatistical modelling approach and a Markov random field (MRF) approach. Results show that for Gaussian data, the proposed approach and the first model comparator perform similarly, while the MRF performs poorly when spatial range is smaller than area size. For Poisson data, the proposed method yields more accurate latent‑field predictions and reduced parameter bias. Two real‑data applications illustrate the approaches: modelling wastewater viral concentrations across England during the COVID-19 pandemic using population density raster as covariate, and modelling the number of cardiovascular hospitalisations at local authority level in England using socio-demographic variables at fine-scale administrative units as covariates.