Designing experiments on networks

Abstract

Designing experiments on networks challenges an assumption common in classical experimental designs, which is that the response observed on a unit is unaffected by treatments applied to other units. This assumption is referred to as 'non-interference'. This thesis aims at improving the design efficiency and validity of networked experiments by relaxing the non-interference assumption, where efficiency stands for low variance of the estimated quantities (precision) and validity for unbiased quantities (accuracy). We develop flexible and effective methods for designing experiments on networks (with a special focus on social networks) by combining the well-established methodology of optimal design theory with the most relevant features of network theory. We provide evidence that conventional designs such as randomised designs are inefficient compared to a systematic approach that accounts for the connectivity structure that underlies the experimental units.

We investigate the impact of the network structure on the efficiency and validity of the experimental design. There is evidence that the experimental design is determined by the small-scale properties of networks. We also develop an algorithmic approach for finding efficient designs by utilising the network symmetry as defined by the automorphism group of the underlying graph. This approach reduces considerably the search time for finding a good design in moderate-sized networks. It works by decomposing the network into symmetric and asymmetric subgraphs and consequently decomposing the design problem into simpler problems on these subgraphs. Moreover, we suggest a framework for finding optimal block designs, while taking into account the interrelations of groups of units within a network. In doing so, the units are initially divided into blocks, using spectral clustering techniques and the concept of modularity, prior to assigning the treatments. We study how the structural properties of the network communities affect the optimal experimental design and its properties. We also make a transition from experiments on social networks to experiments in agriculture showing the diversity of applications this research can address. In particular, we obtain optimal designs with two blocking factors while handling different definitions of neighbour structures related to either the distance among plots or the farmer operations. Throughout this thesis, several optimal designs on networks are obtained using a simple exchange algorithm, which is implemented in the R programming language.

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Identifiers

ORCID for Peter W.F. Smith: orcid.org/0000-0003-4423-5410

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