A closed-form bounded route choice model accounting for heteroscedasticity, overlap, and choice set formation

Abstract

The Multinomial Logit (MNL) model is popular in route choice modelling for its simple choice probability function. Still, it has limitations: it assumes homoscedastic error terms, ignores route overlap correlations, and assigns non-zero probabilities to all routes. We address these by developing the Bounded q-Product Logit (BgPL) model, which introduces heteroscedastic errors with bounded support. The parameter q scales error variance with trip cost, and routes exceeding a cost threshold are assigned zero probability, thus implicitly defining the choice set. We extend BqPL to capture route overlap correlations with a path size correction term, yielding the Bounded Path Size q-Product Logit (BPSqPL) model. After demonstrating the model properties on a small-scale example, it is benchmarked in a large-scale case study. The BPSqPL showed great improvements in fit and predictive ability while providing valuable insights on the non-considered routes and on how cyclists compare the different routes from a choice set.