Distributional assumptions in mixed logit models

Abstract

The characterisation of taste heterogeneity in discrete choice models has been an area of intense research activity in recent years. Although the underlying theory imposes few constraints on the structure of this heterogeneity, in practice most empirical work has adopted an approach based on the use of a relatively limited range of standard probability distributions such as the Normal and Lognormal. However, a number of recent studies have raised doubts about the adequacy of these commonly used distributional assumptions. Against this backdrop, the aim of this paper is to explore the potential of a much wider range of distributional assumptions, including a number offering substantially greater flexibility than the most commonly used forms. Using data from a recent stated preference study undertaken to estimate travellers’ valuation of travel time savings, we compare eleven different distributions for characterising travellers tastes with respect to changes in travel time and travel cost. The results demonstrate that the choice of distributional assumption can have a significant impact on estimation results, particularly and predictably, in the inferences that can potentially be drawn regarding extreme values. Overall, our results suggest that for attributes such as travel time and travel cost there are potentially significant advantages in using bounded distributions (such as the Johnson SB) and in estimating these bounds simultaneously with other model parameters.