An empirical analysis of post-work grocery shopping activity duration using modified accelerated failure time model to differentiate time-dependent and time-independent covariates

In this paper, the accelerated failure time (AFT) model is modified to analyze post-work grocery shopping activity duration. Much previous shopping duration analysis was conducted using the proportional hazard (PH) modeling approach. Once the proportionality assumption was violated, the traditional accelerated failure time (TAFT) model was usually selected as an alternative modeling approach. However, a TAFT model only has covariates with non-proportional and time-dependent effects on the hazard overtime while a PH model only accommodates covariates with proportional and time-independent effects. Neither of them considers the possibility that some of covariates may have proportional and time-independent effects and some may have non-proportional and time-dependent effects on the hazard value in one model. To address this issue, the paper generalizes the TAFT model and develops a modified accelerated failure time (MAFT) model to accommodate both time-dependent and time-independent covariates for activity duration analysis. Checking on the proportionality assumption indicates that the assumption is not valid in the post-work grocery shopping activity data extracted from the 2017 National Household Travel Survey (NHTS) conducted by the U.S. Department of Transportation (USDOT). Both TAFT and MAFT models are developed for comparisons and analysis. The empirical and statistical results show that there do exist two different types of covariates affecting shopping activity duration, including covariates only with proportional and time-independent effects (i.e. working duration, commute travel time) and those with non-proportional and time-dependent effects. The MAFT model can capture the subtleties in various types of covariate effects and help better understand how those covariates affect activity duration overtime. This paper also shows the importance to develop a flexible duration model with both time-dependent and time-independent covariates for accurately evaluating travel demand management (TDM) policies, like flexible work hours.