An adaptive Monte Carlo algorithm for computing mixed logit estimators

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Abstract

Researchers and analysts are increasingly using mixed logit models for estimating responses to forecast demand and to determine the factors that affect individual choices. However the numerical cost associated to their evaluation can be prohibitive, the inherent probability choices being represented by multidimensional integrals. This cost remains high even if Monte Carlo or quasi-Monte Carlo techniques are used to estimate those integrals. This paper describes a new algorithm that uses Monte Carlo approximations in the context of modern trust-region techniques, but also exploits accuracy and bias estimators to considerably increase its computational efficiency. Numerical experiments underline the importance of the choice of an appropriate optimisation technique and indicate that the proposed algorithm allows substantial gains in time while delivering more information to the practitioner.
Original languageEnglish
Pages (from-to)55-79
Number of pages25
JournalComputational Management Science
Volume3
Issue number1
DOIs
Publication statusPublished - 1 Jan 2006

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Computational efficiency
Costs
Experiments
Mixed logit
Integral
Estimator
Mixed logit model
Quasi-Monte Carlo
Demand forecast
Numerical experiment
Approximation
Factors
Optimization techniques
Evaluation
Analysts

Cite this

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abstract = "Researchers and analysts are increasingly using mixed logit models for estimating responses to forecast demand and to determine the factors that affect individual choices. However the numerical cost associated to their evaluation can be prohibitive, the inherent probability choices being represented by multidimensional integrals. This cost remains high even if Monte Carlo or quasi-Monte Carlo techniques are used to estimate those integrals. This paper describes a new algorithm that uses Monte Carlo approximations in the context of modern trust-region techniques, but also exploits accuracy and bias estimators to considerably increase its computational efficiency. Numerical experiments underline the importance of the choice of an appropriate optimisation technique and indicate that the proposed algorithm allows substantial gains in time while delivering more information to the practitioner.",
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