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.

中文翻译：

---

网络实验的最佳块设计

我们提出了一种为网络实验构建最佳块设计的方法。给定网络干扰结构的响应模型扩展了线性网络效应模型以合并块。选择最优性标准以反映实验目标，并且当无法进行详尽搜索时，使用交换算法在设计空间中搜索以获得有效设计。我们的兴趣在于估计治疗之间的直接比较，在存在滋扰网络效应的情况下，这些网络效应源于控制实验单元的潜在网络干扰结构，或网络效应本身。通过比较治疗效果估计量的方差和偏差来检查不同模型（包括标准治疗模型）下的最佳设计的比较。我们还提出了一种定义块的方法，同时考虑到网络内实验单元组的相互关系，使用谱聚类技术实现最佳模块化。我们期望封闭形式社区内的连接单元的行为类似于外部刺激。我们提供的证据表明，我们的方法可以比传统设计（例如忽略网络结构的随机设计）提高效率，并说明其对网络实验的有用性。