Linear regression and its inference on noisy network‐linked data
Linear regression and its inference on noisy network‐linked data
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DOI：
10.1111/rssb.12554
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
Can M. Le;Tianxi Li
中科院分区：
文献类型：
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作者：
Can M. Le;Tianxi Li
网络链接观测值的线性回归一直是模拟响应和协变量之间关系的重要工具。以前的方法要么缺乏推理工具，要么依赖于对社会效应的限制性假设，并且通常假设网络被观察到没有错误。本文提出了一个非参数网络效应的回归模型。该模型不假设关系数据或网络结构被精确观察，并且可以证明对网络扰动具有鲁棒性。在网络观测误差的一般要求下，建立了渐近推理框架，并在特定的环境下，研究了误差来源于随机网络模型时，该方法的鲁棒性。当没有网络模型的先验知识时，我们发现了关于网络密度的推理有效性的相变现象，同时也显示出通过知道网络模型而实现的显着改善。仿真研究进行了验证这些理论结果，并证明了所提出的方法在不同的数据生成模型下的精度和计算效率方面优于现有的工作。然后，将该方法应用于中学生的网络数据，研究教育研讨会在减少学校冲突的有效性。
Linear regression on network‐linked observations has been an essential tool in modelling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive assumptions on social effects and usually assume that networks are observed without errors. This paper proposes a regression model with non‐parametric network effects. The model does not assume that the relational data or network structure is exactly observed and can be provably robust to network perturbations. Asymptotic inference framework is established under a general requirement of the network observational errors, and the robustness of this method is studied in the specific setting when the errors come from random network models. We discover a phase‐transition phenomenon of the inference validity concerning the network density when no prior knowledge of the network model is available while also showing a significant improvement achieved by knowing the network model. Simulation studies are conducted to verify these theoretical results and demonstrate the advantage of the proposed method over existing work in terms of accuracy and computational efficiency under different data‐generating models. The method is then applied to middle school students' network data to study the effectiveness of educational workshops in reducing school conflicts.