Investigating the distribution of the value of travel time savings

A link based network route choice model with unrestricted choice set

“…The estimation of the WTP for travel time is reviewed in Hensher (2001) and Gunn (2000). See Fosgerau (2006) for warnings about estimating a mean WTP from discrete data.…”

Easy and flexible mixture distributions

“…where is a scale parameter to be estimated, v it is the trade-off value of travel time implicitly presented for respondent i in choice occasion t; is a vector of parameters to be estimated, x it is a vector of explanatory variables, the same as in Fosgerau (2006), i is an individual-specific parameter with an unknown distribution to be estimated and " it are i.i.d. standard logistic.…”

“…We estimate nine different models using a standard off-the-shelf software for estimation of discrete choice models. 5 The first uses just a normal distribution for ; such that the WTP becomes lognormal, which provided the best fit to the data in Fosgerau (2006). The next four models use a polynomial in a standard uniform random variable with powers up to 1, 2, 3 and 4, respectively.…”

A new approach to specify and estimate non-normally mixed multinomial probit models

“…3 In the context of continuous mixing distributions, the normal distribution has been used quite extensively in the past. However, several studies (see, for example, Amador et al, 2005, Train and Sonnier, 2005, Hensher et al, 2005, Fosgerau, 2005, Greene et al, 2006, Balcombe et al, 2009, and Torres et al, 2011 have underscored the potentially serious misspecification consequences (in terms of theoretical considerations, data fit, as well as trade-off evaluations) of using the normal distribution. In particular, the symmetric nature of the normal distribution, when combined with mean values that may not be too far away from zero, implies that a significant fraction of individuals may have an unexpected sign on variables (such as a 3 Note here that discrete distributions may also be used for the mixing.…”

“…If the mixing vector is assumed to take M possible value states with state-specific probabilities, this leads to the familiar latent class model used in marketing (see Kamakura andRussell, 1989, Chintagunta et al, 1991) and transportation (see Bhat, 1997b, Greene and Hensher, 2003, Hess et al, 2007, and Train, 2008. On the other hand, if a discrete distribution is considered separately for each individual random coefficient, this is essentially a non-parametric distribution (see Bastin et al, 2010, Cherchi et al, 2009, Fosgerau, 2006. However, the use of a continuous distribution dominates the literature, at least in part because it offers efficiency in the number of mixing distribution parameters to be estimated.…”