A cross-nested recursive logit model for route choice analysis

Abstract

This paper presents a general and operational representation of the recursive models for route choice analysis. We extend the nested recursive logit model (NRL) (Mai et al., 2015) by allowing the choice at each stage to be a network multivariate extreme value (MEV) model (Daly and Bierlaire, 2006) instead of the multinomial logit (MNL) model. Similar to the NRL model, the choice of path is modeled as a sequence of state choices and the model does not require any sampling of choice sets. Furthermore, the model can be consistently estimated and efficiently used for prediction The main challenge is on the computation of the value functions which are solutions to a complex non-linear system. We present a novel approach where a new network is created by integrating the networks of correlation structures given by the network MEV models into the transport network. We show similarities between the RNMEV model and the NRL model on the integrated network. This allows us to use the methods proposed in Mai et al. (2015) to quickly estimate the RNMEV model on a real network. We propose a recursive cross-nested logit (RCNL) model, a member of the RNMEV model, where the choice model at each stage is a cross-nested logit. We show that the RCNL allows to exhibit a more general correlation structure at each choice stage. We report estimation results and a prediction study for a network comprising more than 3000 nodes and 7000 links. The results show that the RCNL model yields sensible parameter estimates and the in-sample and out-of-sample fit are significantly better than the NRL model.