Whole farm experimentation: Making it profitable

Abstract

The first essay considers Bayesian Kriging (BK), which provides a way to estimate spatially varying coefficient regression models where the parameters are smoothed across space. The problem is that previous methods are too computationally intensive when estimating a nonlinear production function. The first essay sought to increase the computational speed by imposing restrictions on the spatial covariance matrix. Two correlation matrices that are sparse in the precision matrix: conditional autocorrelation (CAR) and simultaneous autocorrelation (SAR), were considered. In addition, a new analytical solution is provided for finding the optimal nitrogen value with a stochastic linear plateau model. A comparison among models in the accuracy and computational burden shows that the restrictions reduced the computational burden by 90% (CAR) or 89% (SAR) and led to models that better predicted the missing values.

The second essay starts to deal with the experimentation problem for on-farm experimentation when we know that spatial heterogeneity exists. Nearly Ds-Optimal allocation designs are obtained for an experiment that provides data from estimating the parameters of a linear SVC model in the second essay. This nearly optimal design is far more informative than standard designs such as Latin square (36%), simple random allocation (32%), and randomized strip-plot designs (69%).

The third essay aims to determine the optimal location of treatments when the yield response function is an SVC linear plateau model. The optimal locations are found when the researcher decides to experiment on a portion of the field in addition to when using the whole field. A pseudo-Bayesian approach is taken here because the field's site-specific optimal nitrogen value is unknown and local optimality is impossible. The resulting designs are more efficient than classic Latin square (29%), strip plot (63%), or completely randomized designs (59%) when the underlying yield response directly models field heterogeneity.

In the second and third essays, treatment levels and their corresponding replications are considered predetermined. In the fourth essay, we consider the farmers' net present value over eight years of experimentation and find the optimal levels of treatments, their corresponding replications, the number of experimenting plots, and the quit year for experimenting. Optimal on-farm experimentation is addressed using fully Bayesian decision theory. Of the designs considered, experimenting on 15 plots of a field with treatment levels of 35, 130, 165, and 230 with 2, 3, 5, and 5 replications maximized the farmers' profit over several years. The third year was the best time to quit experimenting.