A generalized multiple durations proportional hazard model with an application to activity behavior during the evening work-to-home commute

The model developed in this paper generalizes (in the context of multiple exit states from a duration spell) extant competing risk methods which tie the exit state of duration very tightly with the length of duration. In the current formulation, the exit state is modeled explicitly and jointly with duration models for each potential exit state. The model developed here, however, is much broader in its applicability than only to the competing risk situation; it is applicable to multiple durations arising from multiple entrance states, multiple exit states, or a combination of entrance and exit states. Multiple entrance states occur frequently in many situations, but have received little attention in the literature. Explicit consideration of the entrance state is important, even in single or multiple competing risk models in order to accommodate the sample selection in duration based on the no-entry/entry (to the duration spell) outcome. The generalized multiple durations model developed in the paper is applied to an empirical analysis of activity behavior during the return home from work.