Interpretable, predictive spatio-temporal models via enhanced Pairwise Directions Estimation

This article concerns the predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. Intrinsically, we develop a novel approach based on dimension reduction for such data in order to capture nonlinear mean structures without requiring a prespecified parametric model. In addition to prediction as a common interest, this approach focuses more on the exploration of geometric information in the data. The method of Pairwise Directions Estimation (PDE) is incorporated in our approach to implement the data-driven function searching of spatial structures and temporal patterns, useful in exploring data trends. The benefit of using geometrical information from the method of PDE is highlighted. We further enhance PDE, referring to it as PDE+, by using resolution adaptive fixed rank kriging to estimate the random effects not explained in the mean structures. Our proposal can not only produce more accurate and explainable prediction, but also increase the computation efficiency for model building. Several simulation examples are conducted and comparisons are made with four existing methods. The results demonstrate that the proposed PDE+ method is very useful for exploring and interpreting the patterns of trend for spatio-temporal data. Illustrative applications to two real datasets are also presented.