Nearly Ds-optimal assigned location design for a linear model with spatially varying coefficients

Abstract

Spatially varying coefficient (SVC) models are an increasingly popular approach for modeling spatial heterogeneity. One topic that has not been well addressed is how best to design experiments when the data are to be used to estimate a SVC model. The applied problem that motivated this study is that agronomists have begun conducting whole-field experiments on farmers’ fields as an alternative to small-scale experiments on experiment stations. The goal is to guide the precision application of nutrients, such as nitrogen fertilizer. The research reported here seeks to optimally allocate treatments to the farm’s plots by leveraging information from model designs. Nearly Ds-Optimal allocation designs are obtained for an experiment that provides data for estimating the parameters of a linear SVC model. This nearly optimal design is far more informative than standard designs such as Latin square, simple random allocation, and randomized strip-plot designs; all of which could also be used to generate data for SVC models. Furthermore, the suggested method does not need a regular plot shape for the experimental design, which is necessary for Latin square or strip plot designs.