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In modern spatial statistics, the structure of data that is collected hasbecome more heterogeneous. Depending on the type of spatial data, differentmodeling strategies for spatial data are used. For example, a kriging approachfor geostatistical data; a Gaussian Markov random field model for lattice data;or a log Gaussian Cox process for point-pattern data. Despite these differentmodeling choices, the nature of underlying scientific data-generating (latent)processes is often the same, which can be represented by some continuousspatial surfaces. In this paper, we introduce a unifying framework forprocess-based multivariate spatial fusion models. The framework can jointlyanalyze all three aforementioned types of spatial data (or any combinationsthereof). Moreover, the framework accommodates different conditionaldistributions for geostatistical and lattice data. We show that someestablished approaches, such as linear models of coregionalization, can beviewed as special cases of our proposed framework. We offer flexible andscalable implementations in R using Stan and INLA. Simulation studies confirmthat the predictive performance of latent processes improves as we move fromunivariate spatial models to multivariate spatial fusion models. The introducedframework is illustrated using a cross-sectional study linked with a nationalcohort dataset in Switzerland, we examine differences in underlying spatialrisk patterns between respiratory disease and lung cancer.

Combining Heterogeneous Spatial Datasets with Process-based Spatial Fusion Models: A Unifying Framework