The continuous cross-nested logit model: Formulation and application for departure time choice

Discrete choice models, like the multinomial logit (MNL), have long been recognized for their ability to capture a wide array of transport-related choice phenomena. However, a number of choices are continuous response variables (e.g., location, departure time, activity duration, and vehicle usage). This paper introduces the continuous cross-nested logit (CCNL) model. The CCNL model results from generalizing the discrete cross-nested logit (CNL) model for a continuous response variable, much like the continuous logit model emerges by generalizing the MNL. The model is formulated and shown to come from the generalized extreme value (GEV) class of models. In addition, the structure of utility correlations is presented. The model's parameters are estimated for a work-tour departure time context using Bayesian estimation techniques and San Francisco Bay Area data. Empirical results suggest model predictions that are very similar to the continuous logit, but it out-performs the continuous logit in terms of out-of-sample prediction with these data. The CCNL also allows a more flexible choice behavior to emerge. Finally, a simple welfare example is illustrated and a number of model extensions are presented.