Semiparametric regression models for spatial prediction and uncertainty quantification of soil attributes

In many studies, the distribution of soil attributes depends on both spatial location and environmental factors, and prediction and process identification are performed using existing methods such as kriging. However, it is often too restrictive to model soil attributes as dependent on a known, parametric function of environmental factors, which kriging typically assumes. This paper investigates a semiparametric approach for identifying and modeling the nonlinear relationships of spatially dependent soil constituent levels with environmental variables and obtaining point and interval predictions over a spatial region. Frequentist and Bayesian versions of the proposed method are applied to measured soil nitrogen levels throughout Florida, USA and are compared to competing models, including frequentist and Bayesian kriging, based an array of point and interval measures of out-of-sample forecast quality. The semiparametric models outperformed competing models in all cases. Bayesian semiparametric models yielded the best predictive results and provided empirical coverage probability nearly equal to nominal.