| 摘要(英) |
Connected experimental units can be characterized by a network structure, where related examples are abundant in the world. If there exists a connection between two units, then they are neighbors of each other. In this case, a treatment affects both the unit to which it applies and the neighbors of that unit, simultaneously causing a treatment effect and a network effect. Parker, Gilmour, and Schormans (2017) launched a numerical study for designing experiments on general network structures. They proposed a linear model with unstructured treatments and assumed both treatment effects and network effects were fixed effects. A relevant work is Chang, Phoa, and Huang (2020), which argued using random network effects. In this work, we adopt the model in Chang, Phoa, and Huang (2020) and extend the network structure to directed/weighted graphs. We study optimal designs on specific graphs, devote to obtaining theoretical results, and provide templates of the corresponding optimal designs.
Keywords: Treatment Effect, Network Effect, Unstructured Treatment, Bipartite/Path/Cycle Graph, D-optimality, (M.S)-optimality. |
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