Using a range of nonparametric methods, the paper examines the specification of a model to evaluate the willingness-to-pay (WTP) for travel time changes from binomial choice data from a simple time-cost trading experiment. The analysis favours a model with random WTP as the only source of randomness over a model with fixed WTP which is linear in time and cost and has an additive random error term. Results further indicate that the distribution of log WTP can be described as a sum of a linear index fixing the location of the log WTP distribution and an independent random variable representing unobserved heterogeneity. This formulation is useful for parametric modelling. The index indicates that the WTP varies systematically with income and other individual characteristics. The WTP varies also with the time difference presented in the experiment which is in contradiction of standard utility theory.