  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.
