Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions
Akshay Vij and
Transportation Research Part B: Methodological, 2017, vol. 106, issue C, 76-101
This study proposes a mixed logit model with multivariate nonparametric finite mixture distributions. The support of the distribution is specified as a high-dimensional grid over the coefficient space, with equal or unequal intervals between successive points along the same dimension; the location of each point on the grid and the probability mass at that point are model parameters that need to be estimated. The framework does not require the analyst to specify the shape of the distribution prior to model estimation, but can approximate any multivariate probability distribution function to any arbitrary degree of accuracy. The grid with unequal intervals, in particular, offers greater flexibility than existing multivariate nonparametric specifications, while requiring the estimation of a small number of additional parameters. An expectation maximization algorithm is developed for the estimation of these models. Multiple synthetic datasets and a case study on travel mode choice behavior are used to demonstrate the value of the model framework and estimation algorithm. Compared to extant models that incorporate random taste heterogeneity through continuous mixture distributions, the proposed model provides better out-of-sample predictive ability. Findings reveal significant differences in willingness to pay measures between the proposed model and extant specifications. The case study further demonstrates the ability of the proposed model to endogenously recover patterns of attribute non-attendance and choice set formation.
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