  Traditional network models encapsulate travel behavior among all
origin-destination pairs based on a simplified and generic utility function.
Typically, the utility function consists of travel time solely and its
coefficients are equated to estimates obtained from stated preference data.
While this modeling strategy is reasonable, the inherent sampling bias in
individual-level data may be further amplified over network flow aggregation,
leading to inaccurate flow estimates. This data must be collected from surveys
or travel diaries, which may be labor intensive, costly and limited to a small
time period. To address these limitations, this study extends classical
bi-level formulations to estimate travelers' utility functions with multiple
attributes using system-level data. We formulate a methodology grounded on
non-linear least squares to statistically infer travelers' utility function in
the network context using traffic counts, traffic speeds, traffic incidents and
sociodemographic information, among other attributes. The analysis of the
mathematical properties of the optimization problem and of its pseudo-convexity
motivate the use of normalized gradient descent. We also develop a hypothesis
test framework to examine statistical properties of the utility function
coefficients and to perform attributes selection. Experiments on synthetic data
show that the coefficients are consistently recovered and that hypothesis tests
are a reliable statistic to identify which attributes are determinants of
travelers' route choices. Besides, a series of Monte-Carlo experiments suggest
that statistical inference is robust to noise in the Origin-Destination matrix
and in the traffic counts, and to various levels of sensor coverage. The
methodology is also deployed at a large scale using real-world multi-source
data in Fresno, CA collected before and during the COVID-19 outbreak.
