Estimating flexible route choice models using sparse data

GPS and nomad devices are increasingly used to provide data from individuals in urban traffic networks. In many different applications, it is important to predict the continuation of an observed path, and also, given sparse data, predict where the individual (or vehicle) has been. Estimating the perceived cost functions is a difficult statistical estimation problem, for different reasons. First, the choice set is typically very large. Second, it may be important to take into account the correlation between the (generalized) costs of different routes, and thus allow for realistic substitution patterns. Third, due to technical or privacy considerations, the data may be temporally and spatially sparse, with only partially observed paths. Finally, the position of vehicles may have measurement errors. We address all these problems using a indirect inference approach. We demonstrate the feasibility of the proposed estimator in a model with random link costs, allowing for a natural correlation structure across paths, where the full choice set is considered.