  Crowding valuation of subway riders is an important input to various
supply-side decisions of transit operators. The crowding cost perceived by a
transit rider is generally estimated by capturing the trade-off that the rider
makes between crowding and travel time while choosing a route. However,
existing studies rely on static compensatory choice models and fail to account
for inertia and the learning behaviour of riders. To address these challenges,
we propose a new dynamic latent class model (DLCM) which (i) assigns riders to
latent compensatory and inertia/habit classes based on different decision
rules, (ii) enables transitions between these classes over time, and (iii)
adopts instance-based learning theory to account for the learning behaviour of
riders. We use the expectation-maximisation algorithm to estimate DLCM, and the
most probable sequence of latent classes for each rider is retrieved using the
Viterbi algorithm. The proposed DLCM can be applied in any choice context to
capture the dynamics of decision rules used by a decision-maker. We demonstrate
its practical advantages in estimating the crowding valuation of an Asian
metro's riders. To calibrate the model, we recover the daily route preferences
and in-vehicle crowding experiences of regular metro riders using a
two-month-long smart card and vehicle location data. The results indicate that
the average rider follows the compensatory rule on only 25.5% of route choice
occasions. DLCM estimates also show an increase of 47% in metro riders'
valuation of travel time under extremely crowded conditions relative to that
under uncrowded conditions.
