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Accounting For Spatial Correlation Using Radial Smoothers In Statistical Models Used For Developing Variable-rate Treatment Prescriptions
1K. S. McCarter, 1E. Burris
1. Louisiana State University
2. Louisiana State University AgCenter

Variable-rate treatment prescriptions for use on commercial farms can be developed from embedded field trials on those farms. Such embedded trials typically involve non-random, high-density sampling schemes that result in large datasets and response variables exhibiting spatial correlation. In order to accurately evaluate the significance of the effects of the applied treatments and the measured field characteristics on the response of interest, this spatial correlation must be accounted for in the statistical analysis of the data. One approach is to use a fully parametric model that accounts for the treatment and design structures of the experiment as well as any residual spatial correlation. For example, the MIXED procedure in SAS® includes a variety of parametric spatial covariance structures that can presumably be used for this purpose. However, we have found that because of the large size of the datasets that result from precision agriculture experiments, MIXED is often unable to fit models that include one of these parametric spatial structures. Another approach is to use a model that incorporates a non-parametric smoother to account for any residual spatial correlation, in addition to a parametric component that accounts for the treatment and design structures of the experiment Such semi-parametric models utilize fewer computing resources and can be used with large datasets. The GLIMMIX procedure in version 9.2 of SAS® includes a radial smoother that can be used for this purpose. We demonstrate the use of radial smoothers in GLIMMIX to fit semi-parametric models that account for spatial correlation. We compare inferences from models that account for spatial correlation using radial smoothers to those from models that do not account for spatial correlation. In addition, we discuss several important issues that arise when fitting models utilizing radial smoothers, such as selecting the number of knots to use in the radial smoother.

Keyword: semi-parametric model, radial smoother, linear mixed model, spatial correlation, precision agriculture