  This work concerns the estimation of recursive route choice models in the
situation that the trip observations are incomplete, i.e., there are
unconnected links (or nodes) in the observations. A direct approach to handle
this issue would be intractable because enumerating all paths between
unconnected links (or nodes) in a real network is typically not possible. We
exploit an expectation-maximization (EM) method that allows to deal with the
missing-data issue by alternatively performing two steps of sampling the
missing segments in the observations and solving maximum likelihood estimation
problems. Moreover, observing that the EM method would be expensive, we propose
a new estimation method based on the idea that the choice probabilities of
unconnected link observations can be exactly computed by solving systems of
linear equations. We further design a new algorithm, called as
decomposition-composition (DC), that helps reduce the number of systems of
linear equations to be solved and speed up the estimation. We compare our
proposed algorithms with some standard baselines using a dataset from a real
network and show that the DC algorithm outperforms the other approaches in
recovering missing information in the observations. Our methods work with most
of the recursive route choice models proposed in the literature, including the
recursive logit, nested recursive logit, or discounted recursive models.
