Anisotropic matérn correlation and spatial prediction using REML

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Journal of Agricultural, Biological, and Environmental Statistics, ISSN: 1085-7117, Vol: 12, Issue: 2, Page: 147-160

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Kathryn A. Haskard; Brian R. Cullis; Arũnas P. Verbyla
Springer Nature
Mathematics; Environmental Science; Agricultural and Biological Sciences; Decision Sciences; anisotropic; correlation; reml; spatial; prediction; matern; Physical Sciences and Mathematics
article description
The Matérn correlation function provides great flexibility for modeling spatially correlated random processes in two dimensions, in particular via a smoothness parameter, whose estimation allows data to determine the degree of smoothness of a spatial process. The extension to include anisotropy provides a very general and flexible class of spatial covariance functions that can be used in a model-based approach to geostatistics, in which parameter estimation is achieved via REML and prediction is within the E-BLUP framework. In this article we develop a general class of linear mixed models using an anisotropic Matérn class with an extended metric. The approach is illustrated by application to soil salinity data in a rice-growing field in Australia, and to fine-scale soil pH data. It is found that anisotropy is an important aspect of both datasets, emphasizing the value of a straightforward and accessible approach to modeling anisotropy. © 2007 American Statistical Association and the International Biometric Society.