Abstract
Abstract 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 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 network effects that stem from the underlying network interference structure governing the experimental units, or in the network 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 randomised designs that ignore the network structure and we illustrate its usefulness for experiments on networks.
Highlights
Designing experiments on networks is a growing area of research mainly due to the rise and popularity of online social networks and viral marketing
The work presented here is motivated by the need to develop a practical methodology for obtaining efficient designs which control for variation among the experimental units from two sources: blocks and network interference, so that the true effects of the treatments can be detected
With our interest in the case of treatment interference, we focus on the model of Pearce (1957) presented by Besag and Kempton (1986), which jointly takes into account ‘local’ and ‘remote’ effects in the model
Summary
Designing experiments on networks is a growing area of research mainly due to the rise and popularity of online social networks and viral marketing. We might expect subjects in the same block to have similar responses and subjects in different (non-overlapping) blocks to have dissimilar responses, irrespective of the presence or absence of viral effects of specific advertisements. By allowing for this in the design, we ensure more precise comparisons of the effects of advertisements. The LNM is similar to the model of Kunert and Martin (2000) It differs by relaxing the assumption of neighbour effects existing in only one direction and allows for a network setting in which units can be linked in a way that does not form a regular layout. We discuss some practical concerns emerging from the suggested methodology and further issues of interest (Section 7)
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