Checking our assumptions in value-of-travel-time modelling: Recovering taste distributions

Abstract

In this paper, we discuss the issue of the choice of distribution in MMNL models in the absence of a priori information about the true shape of the distribution for a given coefficient, such as the marginal utility of travel-time. To illustrate the ability of different distributions to approximate a hypothetical true distribution, several experiments were conducted, using a combination of graphical and analytical analyses. The results show that while the SB distribution performs very well in terms of approximating the true cumulative distribution function, its use can lead to seriously biased estimates of the population mean and standard deviation. Overall, the best performance is obtained by the Beta distribution. The results further show that the performance of some of the distributions, such as the SB, is heavily dependent on the shape of the true distribution, while other distributions, such as the Triangular and Lognormal distributions, are relatively insensitive to changes in shape for the true distribution.