Optimal treatment placement for on-farm experiments: pseudo-Bayesian optimal designs with a linear response plateau model

On-farm experiments are increasingly being used as their costs have decreased with technological advances in collecting, storing, and processing geospatial data. A question that has not been well addressed is what spatial experimental design is best for on-farm experiments when the goal is to estimate a spatially varying coefficients (SVC) model. The focus here is determining the optimal location of treatments to obtain a nearly D-optimal experimental design when estimating a linear plateau model. A pseudo-Bayesian approach is taken here because the field’s site-specific optimal nitrogen value is unknown. Optimal designs are generated, assuming a fixed number of replications for each treatment level. The resulting designs are more efficient than classic Latin square, strip plot, and completely randomized designs. The method consistently produces designs that have 95% efficiency or higher. Random designs had efficiencies varying from 41 to 64% with Latin squares having higher efficiencies and strip plots lower.