  The Covid-19 pandemic drastically changed urban mobility, both during the
height of the pandemic with government lockdowns, but also in the longer term
with the adoption of working-from-home policies. To understand its effects on
rail public transport ridership, we propose a dedicated Regression Mixture
Model able to perform both the clustering of public transport stations and the
segmentation of time periods, while ignoring variations due to additional
variables such as the official lockdowns or non-working days. Each cluster is
thus defined by a series of segments in which the effect of the exogenous
variables is constant. As each segment within a cluster has its own regression
coefficients to model the impact of the covariates, we analyze how these
coefficients evolve to understand the changes in the cluster. We present the
regression mixture model and the parameter estimation using the EM algorithm,
before demonstrating the benefits of the model on both simulated and real data.
Thanks to a five-year dataset of the ridership in the Paris public transport
system, we analyze the impact of the pandemic, not only in terms of the number
of travelers but also on the weekly commute. We further analyze the specific
changes that the pandemic caused inside each cluster.
