Optimal block designs for small experiments on networks
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We propose a method for constructing optimal block designs for experiments on networks. The response model for a given network interference structure extends the linear network effects model of Parker et al. (2016) to incorporate blocks. The optimality criteria are chosen to reflect the experimental objectives and an exchange algorithm is used to search across the design space for obtaining an efficient design when an exhaustive search is not possible. Our interest lies in estimating the direct comparisons among treatments, in the presence of nuisance spillover effects that stem from the underlying interference structure governing the experimental units, or in the spillover effects themselves. Comparisons of optimal designs under different models, including the standard treatment models, are examined by comparing the variance and bias of treatment effect estimators. We also suggest a way of defining blocks, while taking into account the interrelations of groups of experimental units within a network, using spectral clustering techniques to achieve optimal modularity. We expect connected units within closed-form communities to behave similarly to an external stimulus. We provide evidence that our approach can lead to efficiency gains over conventional designs such as randomized designs while ignoring the network structure and we illustrate its usefulness for experiments on networks.
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