Incentives, as one of the travel demand management strategies, are deployed to eliminate or temporally and spatially shift trips away from congested periods and corridors. This study analyzes the impact of incentives on departure time for seven main trip purposes in order to further provide a personalized incentive scheme to achieve an optimal manner at the system wide level. We compare two consecutive incentive schemes, each lasting for over a 1-year period, to understand how effectively these incentive scenarios influence the departure time of seven trip purposes. The data used in this research were collected by the Metropia app, one of the first reward-based travels demand management smartphone applications, and include 364,966 trips conducted by 2270 users between May 2015 and May 2018. Four accelerated failure time models are conducted to explain the time to observe a departure event and the acceleration factors for various trip purposes under two incentive scenarios. The results suggest that peak hour travelers may be open to behavioral incentives that promotes non-peak hour departure time. The incentives, however, may need to be tailored based on time of the day and the purpose of the trip. The findings highlight that traveling for recreation, errands, and work is the most sensitive trip purposes to the incentives in the morning peak hour. However, in the evening peak hour, traveling for other trips, errands, and school becomes the most sensitive trip purposes. These results can facilitate the design of incentives tailored to a specific individual and trip, to incentivize lasting and meaningful behavioral changes.