Numerical Experiments with AMLET, a New Monte-Carlo Al- gorithm for Estimating Mixed Logit Models

Researchers and analysts are increasingly using mixed logit models for estimating responses to forecast demand and to determine the factors that affect individual choices. These models are interesting in that they allow for taste variations between individuals and they do not exhibit the independent of irrelevant alternatives property. 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 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 new results on the convergence of accuracy and bias estimators to considerably increase its numerical efficiency. Numerical experiments are presented for both simulated and real data. They indicate that the new algorithm is very competitive and compares favourably with existing tools, including quasi MonteCarlo techniques based on Halton sequences.

[1]  J. Halton.  On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals , 1960 .

[2]  D. McFadden,et al.  The method of simulated scores for the estimation of LDV models , 1998 .

[3]  Nicholas I. M. Gould,et al.  Convergence of quasi-Newton matrices generated by the symmetric rank one update , 1991, Math. Program..

[4]  Reuven Y. Rubinstein,et al.  Discrete Event Systems , 1993 .

[5]  David J. Thuente,et al.  Line search algorithms with guaranteed sufficient decrease , 1994, TOMS.

[6]  Nicholas I. M. Gould,et al.  Numerical experiments with the LANCELOT package (release A) for large-scale nonlinear optimization , 1996, Math. Program..

[7]  Richard H. Byrd,et al.  Analysis of a Symmetric Rank-One Trust Region Method , 1996, SIAM J. Optim..

[8]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[9]  C. Bhat.  Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model , 2001 .

[10]  Alexander Shapiro,et al.  Stochastic programming by Monte Carlo simulation methods , 2000 .

[11]  K. Train.  Halton Sequences for Mixed Logit , 2000 .

[12]  Nicholas I. M. Gould,et al.  Trust Region Methods , 2000, MOS-SIAM Series on Optimization.

[13]  K. Axhausen,et al.  Observing the rhythms of daily life: A six-week travel diary , 2002 .

[14]  Kay W. Axhausen,et al.  Mode choice of complex tours , 2002 .

[15]  David A. Hensher,et al.  The Mixed Logit Model: the State of Practice and Warnings for the Unwary , 2001 .

[16]  C. Bhat.  Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences , 2003 .

[17]  F. Koppelman,et al.  Activity-Based Modeling of Travel Demand , 2003 .

[18]  Zsolt Sándor,et al.  Quasi-random simulation of discrete choice models , 2004 .