论文标题

同时和时间自回归网络模型

Simultaneous and Temporal Autoregressive Network Models

论文作者

Sewell, Daniel K.

论文摘要

虽然研究人员很容易访问逻辑回归模型,但是当应用于网络数据时,存在对数据依赖性结构的不现实假设。对于在离散时间测得的时间网络,最近的工作使良好的进步\ citep {almquist2014Logistic},但仍然存在假设二元组在边缘历史上是有条件独立的。这个假设可能很强,有时很难证明是合理的。如果时间步骤相当大,通常人们不仅会期望二元组之间存在时间点之间的时间依赖性,而且还会期望同时影响网络二元组共聚的同时依赖关系。我们为动态网络提出了一个通用观察驱动的模型,该模型通过使用灵活的自动回归方法将平均值和协方差结构同时建模为边缘历史的函数来克服此问题。可以证明这种方法适合通用的线性混合模型框架。我们提出了一种可视化方法,该方法提供了有关同时依赖的存在的证据。我们描述了一项模拟研究,以在同时依赖的存在和不存在的情况下确定该方法的性能,并分析了会议与会者的接近网络和世界贸易网络。我们还使用最后一个数据集来说明随着时间间隔变得更加粗糙,同时依赖性如何变得更加突出。

While logistic regression models are easily accessible to researchers, when applied to network data there are unrealistic assumptions made about the dependence structure of the data. For temporal networks measured in discrete time, recent work has made good advances \citep{almquist2014logistic}, but there is still the assumption that the dyads are conditionally independent given the edge histories. This assumption can be quite strong and is sometimes difficult to justify. If time steps are rather large, one would typically expect not only the existence of temporal dependencies among the dyads across observed time points but also the existence of simultaneous dependencies affecting how the dyads of the network co-evolve. We propose a general observation driven model for dynamic networks which overcomes this problem by modeling both the mean and the covariance structures as functions of the edge histories using a flexible autoregressive approach. This approach can be shown to fit into a generalized linear mixed model framework. We propose a visualization method which provides evidence concerning the existence of simultaneous dependence. We describe a simulation study to determine the method's performance in the presence and absence of simultaneous dependence, and we analyze both a proximity network from conference attendees and a world trade network. We also use this last data set to illustrate how simultaneous dependencies become more prominent as the time intervals become coarser.

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