Designs with complex blocking structures and network effects for use in agricultural field experiments

We propose a novel model-based approach for constructing optimal designs with complex blocking structures and network effects, for application in agricultural field experiments. The potential interference among plots is viewed as a network structure, defined via the adjacency matrix, which performs two functions: capturing the spatial structure to reflect distances between neighbouring plots across space and adjusting for farmer operations. We consider a field trial run at Rothamsted Research and provide a comparison of optimal designs under various different models, including the commonly used designs in such situations. It is shown that when there is interference between treatments on neighbouring plots, due to the spatial arrangement of the plots, such designs are at least as good as, and often even more efficient than, randomised row-column designs. The advantage of network designs is that we can construct the neighbouring structure even for an irregular layout by means of a graph to address the particular characteristics of the experiment. The need for such designs arises when control of heterogeneity is required. Ignoring the neighbouring structure can lead to imprecise estimates of the treatment parameters and invalid conclusions.