An additive risk based multistate model for activity chaining behavior analysis

The time-use pattern has been recognized for its correlation with socio-demographic characteristics, spatial settings and the institutional contexts. Although the correlation between the duration of single activity participation and explicative covariates has been well studied, the interdependency structure between travel/activities conducted in different episodes of an activity chain is still a relatively unexplored subject. We consider that activity pattern is resulted from a semi-Markov stochastic process, assuming that the activity-specific transition probability depends on its state type, sojourn times since entering occupied state and related covariates. Conditionally on the sequence of states visited previously, the semi-Markov property admits the estimation of state transition probability separately with cause-specific covariates. The multistate model provides a relevant framework to investigate the activity chaining behavior and related state transition probability estimates. To investigate the time-dependent effects of covariates on travel/activity duration, an Aalen's additive hazard model with competing risk is applied for model estimate. Different from usual Cox proportional hazard models (Cox 1972), the additive risk model incorporates the effects of covariates in an additive way relaxing the proportionality assumption of Cox proportional hazard models and provides a more flexible way to investigate the effect of temporal constraints on the activity chaining behavior. The estimation results of additive model are compared with Cox model and provide practical knowledge for model specification.