On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice

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 16dimensional 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. 0191-2615/$ see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.trb.2004.10.005 * Corresponding author. Tel.: +44 0 20 7594 6105; fax: +44 0 20 7594 6102. E-mail addresses: [email protected] (S. Hess), [email protected] (K.E. Train), j.polak@ imperial.ac.uk (J.W. Polak). 1 Tel.: +1 415 291 1023; fax: +1 415 291 1020. 2 Tel.: +44 0 20 7594 6089; fax: +44 0 20 7594 6102. 148 S. Hess et al. / Transportation Research Part B 40 (2006) 147–163 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. 2005 Elsevier Ltd. All rights reserved.