Spatial Prediction Simulation with Nonlinear Multicovariate

Cokriging is a multivariate spatial method used to predict the observed value for a primary variable in an unknown location with the help of a spatially correlated secondary variable. The existence of two or more nonlinear secondary variables in predicting spatial data usually arises, especially in cokriging. Therefore, a method that can improve the model's predictive power by adding the interaction of variables is proposed. The proposed method can be effectively used, especially when the primary and secondary variables have a nonlinear relationship. By transforming the nonlinear variables, a higher correlation can be attained. This study used principal component analysis with interaction (PCAI) method among secondary variables to reduce two or more secondary variables into one dimension as a secondary variable in the cokriging technique. The proposed method was tested and verified through simulation and real data using the 2015 South Korea Air Pollution, a dataset known for its complex spatial patterns and high variability, to prove its validity and usefulness. The predicted residual error sum of squares (PRESS) statistic was used for cross-validations. Computations were done using the R Project for Statistical Computing software. PCAI as a secondary variable gives the lowest PRESS value compared to only one secondary variable or principal component analysis (PCA). Considering the criterion, the lowest value of PRESS indicates the best model. Thus, PCAI cokriging outperformed PCA cokriging. Using PCAI as a secondary variable may be a better method than PCA for cokriging with nonlinear multicovariates.