On the Performance of the Shuffled Halton Sequence in the Estimation of Discrete Choice Models

The area of travel demand analysis has in recent years been greatly enriched by the development of new model forms that can accommodate complex patterns of substitution and taste variation. However, this added flexibility comes at a cost of greater complexity in estimation, to the degree that these models need to be estimated through simulation. While basic Monte-Carlo integration can lead to acceptable results, the cost of the simulation process can be decreased significantly by using quasi-Monte-Carlo integration, where the simulation process is based on quasi-random number draws rather than pseudo-random number draws. A popular type of quasi-random sequence in this context is the Halton sequence, in its different forms. In this paper, we compare the performance of standard, scrambled and shuffled Halton sequences in the estimation of various Mixed Logit models. The analysis shows that, while the scrambled Halton sequence offers some improvements over the standard Halton sequence, it is generally outperformed by the shuffled Halton sequence. The fact that the shuffled Halton sequence has further advantages in terms of implementation and generalisation makes it an appealing alternative to the scrambled Halton sequence in the simulationbased estimation of high-dimensional models.