Taste Heterogeneity and Substitution Patterns in Models of the Simultaneous Choice of Activity Timing and Duration

The recent growth of interest in activity-based methods has focused particular attention on travellers’ decision making regarding the timing and duration of their participation in activities. However, to date these two dimensions of activity participation have been largely treated separately. It is clear, however, that in general, the benefit that an individual derives from participating in an activity will depend inter alia both upon the time at which the activity is undertaken and the amount of time devoted to the activity. Moreover, it is also clear that this benefit will also depend on a wide range of other factors such as the quality of the activity opportunities available at particular destinations and the intensity with which activities are undertaken. Since these factors are inherently difficult or impossible to completely characterise or measure via conventional travel or time use data sources, it is likely that such decisions will also be characterised by significant unobserved heterogeneity. Based on earlier theoretical work by the authors, this paper proposes a model for the simultaneous choice of the timing and duration of activities and associated travel and uses data from a stated preference experiment to estimate the parameters of this model. The first section of the paper provides a brief review of the existing literature on activity timing and duration choice. The second section introduces the theoretical approach, which assume that the marginal utility derived from activities encompasses two distinct components; one derived from the duration of activity involvement and the other derived from activity participation at a particular time-of-day. A number of alternative additive and multiplicative specifications are introduced and their properties are explored. The third section briefly describes the stated preference data, which was collected in a survey undertaken in London in which respondents were presented with a number of scenarios in which they were asked to choose between alternative tours involving a single destination activity. The timing and duration both of the destination activity and the associated travel varied across scenarios. The fourth section discusses the empirical specification and estimation of the model and presents the estimation results. This uses an error-components formulation of the mixed multinomial logit model to account both for unobserved heterogeneity in tastes and for heteroskedascity and complex substitution patterns amongst activity alternatives. Particular attention is given to the use of advanced optimisation techniques needed to estimate the non-linear utility function expressing individuals’ timing and duration preferences.The fifth section discusses the significance of the results and their potential application to a number of practical transport planning problems including the prediction of user response to travel demand management policies and accessibility planning. The paper closes with some overall conclusions and a discussion of future research directions.