Accounting for heterogeneity in the variance of unobserved effects in mixed logit models

The growing popularity of mixed logit to obtain estimates of willingness to pay (WTP) has focussed on the distribution of the random parameters and the possibility of estimating deep parameters to account for heterogeneity around the mean of the distribution. However the possibility exists to add further behavioural information associated with the variance of the random parameter distribution, through parameterisation of its heterogeneity (or heteroskedasticity). In this paper we extend the mixed logit model to account for this heterogeneity and illustrate the implications this has on the moments of the willingness to pay for travel time savings in the context of commuter choice of mode. The empirical study highlights the statistical and behavioural gains but warns of the potential downside of exposing the distribution of the parameterised numerator and/or denominator of the more complex WTP function to a sign change and extreme values over the range of the distribution.