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Quasi-random number sequences have been used extensively for many years in the simulation of integrals that do not have a closed-form expression, such as Mixed Logit and Multinomial Probit choice probabilities. Halton sequences are one example of such quasi-random number sequences, and various types of Halton sequences, including standard, scrambled, and shuffled versions, have been proposed and tested in the context of travel demand modeling. In this paper, we propose an alternative to Halton sequences, based on an adapted version of Latin Hypercube Sampling. These alternative sequences, like scrambled and shuffled Halton sequences, avoid the undesirable correlation patterns that arise in standard Halton sequences. However, they are easier to create than scrambled or shuffled Halton sequences. They also provide more uniform coverage in each dimension than any of the Halton sequences. A detailed analysis, using a sixteendimensional Mixed Logit model for choice between alternative-fuelled vehicles in California, was conducted to compare the performance of the different types of draws. The analysis shows that, in this application, the Modified Latin Hypercube Sampling (MLHS) outperforms each type of Halton sequence. This greater accuracy combined with the greater simplicity make the MLHS method an appealing approach for simulation of travel demand models and simulation-based models in general.

Article AbstractIn this paper, we discuss some of the issues that arise with the computation of the implied value of travel-time savings in the case of discrete choice models allowing for random taste heterogeneity. We specifically look at the case of models producing a non-zero probability of positive travel-time coefficients, and discuss the consistency of such estimates with theories of rational economic behaviour. We then describe how the presence of unobserved travel-experience attributes or conjoint activities can bias the estimation of the travel-time coefficient, and can lead to false conclusions with regards to the existence of negative valuations of travel-time savings. We note that while it is important not to interpret such estimates as travel-time coefficients per se, it is nevertheless similarly important to allow such effects to manifest themselves; as such, the use of distributions with fixed bounds is inappropriate. On the other hand, the use of unbounded distributions can lead to further problems, as their shape (especially in the case of symmetrical distributions) can falsely imply the presence of positive estimates. We note that a preferable solution is to use bounded distributions where the bounds are estimated from the data during model calibration. This allows for the effects of data impurities or model misspecifications to manifest themselves, while reducing the risk of bias as a result of the shape of the distribution. To conclude, a brief application is conducted to support the theoretical claims made in the paper.