  Ride-sourcing or transportation network companies (TNCs) provide on-demand
transportation service for compensation, connecting drivers of personal
vehicles with passengers through smartphone applications. In this study, we
consider the problem of estimating a spatiotemporally varying probability
distribution for the productivity of a TNC driver, using data on more than 1.2
million TNC trips in Austin, Texas. We propose a graph-based smoothing approach
that allows for distinct spatial and temporal dynamics, including different
degrees of smoothness, spatio-temporal interactions, and interpolation in
regions with little or no data. For such a goal, we introduce the Graph-fused
Elastic Net (GFEN) and use it in combination with a dyadic tree decomposition
for density estimation. In addition, we present an optimization-driven approach
for fast point estimates scalable to massive graphs. Bayesian inference and
uncertainty quantification with MCMC are also illustrated. The main results
demonstrate that the optimization strategy is an effective exploration tool for
selecting adequate regularization schemes using Bayesian optimization of the
cross-validation loss. Two key empirical findings made possible by our method
include: 1) the probability that a TNC driver can expect to earn a living wage
in Austin exhibits high variability in space and time, from as low as 25% to as
high as 85%; and 2) some drivers suffer considerable "tail risk", with the
bottom 10% of the earnings distribution falling below $10 per hour -- grossly
below a living wage in Austin for a single adult -- for specific times and
locations. All code and data for the paper are publicly available, as a Shiny
app for visualizing the results and a software package in Julia for
implementing the GFEN.
