When experimental subjects can interact with each other, the outcome of one individual may be affected by the treatment status of others. In many social science experiments, such spillover effects may occur through multiple networks, for example, through both online and offline face-to-face networks in a Twitter experiment. Thus, to understand how people use different networks, it is essential to estimate the spillover effect in each specific network separately. However, the unbiased estimation of these network-specific spillover effects requires an often-violated assumption that researchers observe all relevant networks. We show that, unlike conventional omitted variable bias, bias due to unobserved networks remains even when treatment assignment is randomized and when unobserved networks and a network of interest are independently generated. We then develop parametric and nonparametric sensitivity analysis methods, with which researchers can assess the potential influence of unobserved networks on causal findings. We illustrate the proposed methods with a simulation study based on a real-world Twitter network and an empirical application based on a network field experiment in China.

翻译：当实验对象能够相互交流时,一个人的结果可能受到他人待遇状况的影响。在许多社会科学实验中,这种外溢效应可能通过多种网络发生,例如,在Twitter实验中,通过在线和离线面对面网络产生。因此,为了了解人们如何使用不同网络,必须分别估计每个具体网络的外溢效应。然而,对这些网络特有外溢效应的不偏袒性估计要求人们经常作出这样的假设,即研究人员观察所有相关网络。我们表明,与传统省略的可变偏见不同,在治疗任务随机化和未观测的网络和利益网络独立产生时,未经观测的网络造成的未观测网络的偏见仍然存在。我们随后制定了参数和非对称敏感度分析方法,研究人员可据此评估未观测到的网络对因果关系结果的潜在影响。我们用基于现实世界的Twitter网络的模拟研究以及基于在中国的网络实地实验的经验应用来说明拟议的方法。