Groupe d’études et de recherche en analyse des décisions

G-2010-64

Estimation of the Mixed Logit Likelihood Function by Randomized Quasi-Monte Carlo

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Advanced discrete choice models, such as parametric/non-parametric mixed logit and hybrid choice models, are heavily used in travel behavior research. The complexity of model formulation nevertheless remains limited by the associated estimation difficulties, even if important progress has been made these last years. In this piece of work, we examine the effectiveness of randomized quasi-Monte Carlo (RQMC) techniques to estimate the integrals that express the discrete choice probabilities in a mixed logit model, for which no closed form formula is available. We review some popular RQMC constructions, discuss the choice of their parameters as a function of the considered class of integrands, and compare their effectiveness to reduce both variance and bias, in comparison with standard Monte Carlo (MC), when estimating the log-likelihood function at a given parameter value. In our numerical experiments, randomized rank-1 lattice rules (with carefully selected parameters) and digital nets in base 2 outperform randomized Halton sequences and standard MC. Interestingly, they also reduce the bias as much as the variance.

, 52 pages