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

Abstract

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 choice, departure time choice, activity duration, and vehicle usage). In this paper, the continuous cross-nested logit (CCNL) model is introduced. 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 outperforms the continuous logit in terms of out-of-sample prediction with these data. Theoretically, however, the CCNL allows a more flexible choice behavior to emerge. Finally, a simple welfare example is illustrated and a number of model extensions are presented

A model of bus bunching under reliability-based passenger arrival patterns

“…Choices in a continuous setting instead have been often described by models based on hazard functions; but such an approach is criticized because it lacks a proper behavioural support. Recently Lemp et al (2010) suggested a continuous cross-nested logit model, which retains the behavioural justification of the logit models and allows for correlation across alternatives.…”

Agent-Based Microsimulation Approach for Design and Evaluation of Flexible Work Schedules

“…In terms of the departure time analysis, there has been extensive research applying the theory of rational behavior, such as the bottleneck model (14) and discrete departure time choice models (25)(26)(27)(28). Under rational behavior theory, travelers have access to information about all feasible alternatives and maximize their utility (29).…”

Methodological issues in modelling time-of-travel preferences

“…These various approaches include the use of discrete (see, e.g. Small 1982) versus continuous time models (Wang 1996, van Vuren et al 1999; model structures ranging from logit to other more general models such as nested logit (Brownstone and Small 1989), ordered generalised extreme value (Small 1987), bivariate and multinomial probit (Liu andMahmassani 1998, Lemp et al 2011), error components logit (Bhat 1998, de Jong et al 2003, RAND Europe 2005, Hess et al 2007, Holyoak 2007, Kristoffersson and Engelson 2008, continuous hazard-based logit (Bhat and Steed 2002), continuous cross-nested logit (Lemp et al 2010), and the presence of schedule delay terms, generally available from stated preferences but not revealed preferences surveys (see, e.g. de Jong et al 2003).…”

“…Other papers apply only the cyclicality property (see, e.g. Lemp et al 2010). Carrier (2008) models time-of-travel choice for airline travellers by using trigonometric functions to represent time as a continuous variable.…”