Capturing positive utilities during the estimation of recursive logit models: A prism-based approach

Although the recursive logit (RL) model has been recently popular and has led to many applications and extensions, an important numerical issue with respect to the evaluation of value functions remains unsolved. This issue is particularly significant for model estimation, during which the parameters are updated every iteration and may violate the model feasible condition. To solve this numerical issue, this paper proposes a prism-constrained RL (Prism-RL) model that implicitly restricts the path set by the prism constraint defined based upon a state-extended network representation. Providing a set of numerical experiments, we show that the Prism-RL model succeeds in the stable estimation regardless of the initial and true parameter values and is able to capture positive utilities. In the real application to a pedestrian network, we found the positive effect of street green presence on pedestrians. Moreover, the Prism-RL model achieved higher goodness of fit than the RL model, implying that the Prism-RL model can also describe more realistic route choice behavior.