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

Abstract

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.

Understanding the formation and influence of attitudes in patients' treatment choices for lower back pain: Testing the benefits of a hybrid choice model approach

“…In the models with random coefficients, we made use of 500 MLHS draws per respondent and per random component (cf. Hess et al, 2006). Finally, the repeated choice nature of the data was recognised in the specification of the sandwich matrix for estimating robust standard errors (cf.…”

Contrasting imputation with a latent variable approach to dealing with missing income in choice models

“…Four models were estimated in the analysis, all of them allowing for random heterogeneity in the sensitivities to the six attributes, using Lognormal distributions (with µ and σ giving means and standard deviations for the underlying Normal distributions of the logarithms of the parameters), with a linear in attributes specification 1 , and with constants for the first two alternatives (δ 1 and δ 2 ). All models were coded and estimated in Ox 6.2 (Doornik, 2001), making use of Modified Latin Hypercube Sampling (MLHS) draws (Hess et al, 2006) for the random component, with simultaneous estimation of both model components for the hybrid structure in Equation 6, and computing robust standard errors using the sandwich method.…”

The value of water quality improvements in the region Berlin–Brandenburg as a function of distance and state residency

“…Currently, i.e. in the phase 24 between 2012 and 2015, administrations are asked to operationalize programmes of measures 25 ensuring that the environmental objectives can be met. It has, however, become obvious that it is 26 very unlikely to reach the above target for all water bodies by 2015.…”

“…142 Models were estimated using the CFSQP algorithm [24] considering the repeated choice nature of 143 the data. Since the choice probabilities in equations 4 has no closed form, it is estimated by 144 maximum simulated likelihood (MSL) with 1000 quasi-random draws via Latin-hypercube sampling 145 [25]. 146…”