Cohering Disaggregation and Uncertainty Quantification for Spatially Misaligned Data

Spatial misalignments arise from data aggregation or attempts to align misaligned data, leading to information loss. We propose a disaggregation framework that combines the finite element method (FEM) with a first-order Taylor approximation via integrated nested Laplace approximation (INLA). In landslide studies, landslide occurrences are often aggregated into counts based on slope units, reducing spatial detail. Our framework examines point pattern and aggregated count models under four covariate field scenarios: \textit{Raster at Full Resolution (RastFull), Raster Aggregation (RastAgg), Polygon Aggregation (PolyAgg), and Point Values (PointVal)}. The first three involve aggregation, while the latter two have incomplete fields. For these, we estimate the full covariate field using \textit{Value Plugin, Joint Uncertainty, and Uncertainty Plugin} methods, with the latter two accounting for uncertainty propagation and showing superior performance. Even under model misspecification (i.e.\ modelling a nonlinear field as linear), these methods remain more robust. Whenever possible, point pattern observations and full-resolution covariate fields should be prioritized. For incomplete fields, methods incorporating uncertainty propagation are preferred. This framework supports landslide susceptibility and other spatial mapping, integrating seamlessly with R-INLA \ extension packages.