Using Semi-Parametric Models to Account for Spatial Variability in Developing Variable-Rate Treatment Prescriptions for Applications in Precision Agriculture.

Variable-rate agronomic treatment prescriptions are developed from the statistical analysis of data obtained from precision agriculture field trials.  Such field trials utilize high-density sampling schemes that result in large datasets exhibiting spatial correlation.  In order to properly evaluate the significance of the applied treatments being considered, and to identify field zones within which the response is to be optimized and across which prescribed treatments can vary, spatial correlation must be accounted for in the statistical analysis of the field trial data. Because of inherent limitations in the implementations of many existing statistical software packages, however, the sizes of these datasets often preclude a fully-parametric approach to modeling spatial correlation. The GLIMMIX procedure in version 9.2 of SAS^® now provides the ability to fit semi-parametric models that include a radial smoother, a type of penalized nonparametric smoothing spline. Semi-parametric models using radial smoothers utilize fewer computing resources and can therefore be used with the large datasets produced by precision agriculture experiments.  In this presentation we demonstrate the use of GLIMMIX with its radial smoother to fit semi-parametric models that account for spatial variation and reduce spatial correlation.  We compare the inferences that result from models that account for spatial variation using radial smoothers to those that do not.  In addition, we discuss some important issues that arise when fitting models utilizing radial smoothers.