A joint hazard-based model for the analysis of simultaneous (mutually interdependent) duration processes is proposed. The proposed model generalizes independent hazard-based models by accounting for correlations between simultaneous duration processes. Furthermore, the model also permits the use of flexible and variable hazard function parameters to capture realistic features observed empirically in activity duration data (e.g., bimodal peaks). To account for correlated processes (duration processes) that underlie observed stop and trip durations, the proposed model relies on an implicit component of error structure that combines a baseline hazard function (log-logistic distribution) with a mixing (log-normal) distribution. This model is estimated by the simulated maximum-likelihood technique and is used to analyze activity and trip duration for shopping activities. The results highlight the need to account for duration dependence effects in activity-travel durations. Furthermore, hazard-based models that disregard correlation across joint duration processes can provide biased estimates and inaccurate forecasts. Empirical results from San Francisco, California (1996), activity diary data imply that stop and trip durations for shopping activities are positively correlated. The hazard rate profile (shape and intensity) also varies significantly across individuals, suggesting the need for targeted demand management measures. At a substantive level, the results indicate the role of personal, household, and situational attributes on activity and trip duration decisions. These findings and models have important applications in the analysis of activity-travel dimensions of duration and timing and the evaluation of alternate travel demand management measures.
Abstract