Optimal Designs for Network Experimentation with Unstructured Treatments

Experiments on connected units are commonly conducted in many scientific fields. An experimental unit in these applications may connect with some others, resulting in possible contamination, termed as network adjustments in this paper, on the responses of the neighboring units. Designing such experiments is rarely discussed in the literature. Parker, Gilmour, and Schormans (2017) initiated a study of 𝐴𝑠-optimal designs on connected experimental units with unstructured treatments under the framework of linear models. Our work investigates a similar design problem, but we incorporate the network adjustments into the model, which leads to the property that the responses of two units are correlated if some neighbors of one unit and those of the other receive the same treatment. Alphabetical optimality criteria are considered for selecting good designs with high efficiency of estimating treatment effects and/or high accuracy of quantifying network adjustments. We provide theoretical conditions for optimal designs and illustrate our theory with numerical examples using a real network.

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