KGR-SKATER: Spatially clustered kernel graph regression for counting processes

This paper proposes a procedure for fitting a spatiotemporal model with an interpretable and parsimonious dependence structure to high-dimensional non-Gaussian data. A graph is estimated to represent spatial dependence, and a locally periodic kernel is estimated to represent temporal dependence. These two components are then combined via a Kronecker product, producing a separable spatiotemporal covariance matrix that can account for multiple relevant variables and their dependencies at different time scales. Spatial clustering is used to reduce the dimensionality and estimation is carried out via the integrated nested Laplace approximation. The proposed model, which relies on all of these preceding steps, is introduced along with some alternative spatiotemporal reference models for comparison. The utility of this novel multi-step procedure is demonstrated by modeling monthly time series of respiratory-related deaths across California. Social deprivation indices are used to learn a graph structure, and surrogate variables constructed from exposure adjusted measures of air quality are used to learn time series regression relationships encoded by a kernel. The modeling results indicate that KGR-SKATER models fit the data in and out of sample as well as the reference models and have better coverage properties. A synthetic case study is also presented to demonstrate how the proposed procedure makes better forecasts than the reference model in settings where time series exhibit less stationary amplitudes and periods. Data and code available at: https://doi.org/10.5061/dryad.j3tx95xtt.