Estimation of latent network flows is a common problem in statistical network analysis. The typical setting is that we know the margins of the network, i.e. in- and outdegrees, but the flows are unobserved. In this paper, we develop a mixed regression model to estimate network flows in a bike-sharing network if only the hourly differences of in- and outdegrees at bike stations are known. We also include exogenous covariates such as weather conditions. Two different parameterizations of the model are considered to estimate 1) the whole network flow and 2) the network margins only. The estimation of the model parameters is proposed via an iterative penalized maximum likelihood approach. This is exemplified by modeling network flows in the Vienna Bike-Sharing Network. Furthermore, a simulation study is conducted to show the performance of the model. For practical purposes it is crucial to predict when and at which station there is a lack or an excess of bikes. For this application, our model shows to be well suited by providing quite accurate predictions.

中文翻译：

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共享单车系统中潜在网络流量的估计

潜在网络流量的估计是统计网络分析中的常见问题。典型的设置是我们知道网络的边际，即入度和出度，但未观察到流量。在本文中，我们开发了一个混合回归模型来估计共享单车网络中的网络流量，前提是仅知道自行车站的每小时进出度差异。我们还包括外生协变量，例如天气条件。模型的两种不同参数化被认为是估计 1) 整个网络流量和 2) 仅网络边际。模型参数的估计是通过迭代惩罚最大似然方法提出的。这可以通过对维也纳自行车共享网络中的网络流进行建模来说明。此外，还进行了仿真研究以显示模型的性能。出于实际目的，预测何时以及在哪个站点缺少或过多的自行车至关重要。对于此应用程序，我们的模型通过提供非常准确的预测显示非常适合。