Analysis of Trip And Stop Duration for Shopping Activities: A Simultaneous Hazard Duration Model System

In this paper, a joint hazard-based model is proposed to analyze simultaneous (mutually interdependent) duration processes. The proposed model generalizes independent hazard based models by accounting for correlations between simultaneous duration processes. Further, the model also permits flexible and variable hazard function parameters to capture realistic features observed empirically in activity duration data (e.g. bi-modal peaks etc.). To account for correlated duration processes, the proposed model relies on an implicit component of error structure that combines a baseline hazard function (log-logistic distribution) with a mixing (lognormal) distribution. This model is estimated using simulated maximum likelihood technique and is used to analyze activity and trip duration for shopping activities in this study. 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 SF (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 evaluation of alternate Travel Demand Management (TDM) measures.