Combining heterogeneous spatial datasets with process-based spatial fusion models: A unifying framework

In modern spatial statistics, the structure of data has become more heterogeneous. Depending on the types of spatial data, different modeling strategies are used. For example, kriging approaches for geostatistical data; Gaussian Markov random field models for lattice data; or log Gaussian Cox process models for point-pattern data. Despite these different modeling choices, the nature of underlying data-generating (latent) processes is often the same, which can be represented by some continuous spatial surfaces. A unifying framework is introduced for process-based multivariate spatial fusion models. The framework can jointly analyze all three aforementioned types of spatial data or any combinations thereof. Moreover, the framework accommodates different likelihoods for geostatistical and lattice data. It is shown that some established approaches, such as linear models of coregionalization, can be viewed as special cases of the proposed framework. A flexible and scalable implementation using R-INLA is provided. Simulation studies confirm that the prediction of latent processes improves as one moves from univariate spatial models to multivariate spatial fusion models. The framework is illustrated via a case study using datasets from a cross-sectional study linked with a national cohort in Switzerland. The differences in underlying spatial risks between respiratory disease and lung cancer are examined in the case study.