With a focus on the multitasking behavior of public transportation users during travel, an examination is made of factors affecting activity participation along the axis of travel time. The probability of participation in an activity is represented by using a scobit (or a skewed logit) model, within which the widely used logit model is nested with the help of a skewness parameter. With this skewness parameter, it is not necessary to assume that individuals with a probability of 0.5 for performing an activity are most sensitive to changes in travel time or other influential factors. This analysis is the first attempt to apply the scobit model to transportation issues. An empirical analysis was conducted by using data (523 individuals) collected in Hiroshima City, Japan, in December 2008. Because multitasking behavior along the axis of travel time may be interrelated, the scobit model is extended to simultaneously incorporate the influences of state dependency and the remaining travel time as well as the other influential factors, by dealing with the data as panel data. As a result, a scobit-based panel model was developed. Model estimation results confirm the effectiveness of the scobit model. It was further revealed that introduction of a heterogeneous skewness parameter is more effective for representing activity participation than assumption of a homogeneous skewness parameter. Calculation results of travel time elasticity show that activity participation is sensitive to change in the travel time up to the first half of travel time and becomes less sensitive to travel time afterward.