Specification of the cross nested logit model with sampling of alternatives for route choice models

A novel approach is proposed to use the Cross Nested Logit (CNL) model in route choice when sampling of paths is considered. It adopts the Metropolis-Hasting algorithm to sample the choice sets for the model. A new expansion factor and an approximation method are put forward to calculate the sampled probabilities of alternatives. We build on state-of-the-art results for the Multivariate Extreme Value models and extend then to the route choice context. Case studies on both synthetic data and a real network demonstrate that the new method is valid and practical. This paper thus provides an operational solution to use the CNL model in the route choice context, where the number of alternatives is particularly large.