Bayesian Multinomial Logit: Theory and Route Choice Example
Abstract
Statisticians along with other scientists have made significant computational advances that enable the estimation of formerly complex statistical models. The Bayesian inference framework combined with Markov chain Monte Carlo estimation methods such as the Gibbs sampler enable the estimation of discrete choice models such as the multinomial logit (MNL) model. MNL models are frequently applied in transportation research to model choice outcomes such as mode, destination, or route choices or to model categorical outcomes such as crash outcomes. Recent developments allow for the modification of the potentially limiting assumptions of MNL such as the independence from irrelevant alternatives (IIA) property. However, relatively little transportation-related research has focused on Bayesian MNL models, the tractability of which is of great value to researchers and practitioners alike. This paper addresses MNL model specification issues in the Bayesian framework, such as the value of including prior information on parameters, allowing for nonlinear covariate effects, and extensions to random parameter models, so changing the usual limiting IIA assumption. This paper also provides an example that demonstrates, using route-choice data, the considerable potential of the Bayesian MNL approach with many transportation applications. This paper then concludes with a discussion of the pros and cons of this Bayesian approach and identifies when its application is worthwhile.
Get full access to this article
View all access and purchase options for this article.
References
1. Anderson S., de Palma A., and Thisse J. F. A Discrete Choice Theory of Product Differentiation. MIT Press, Cambridge, Mass., 1992.
2. Bolduc D. A Practical Technique to Estimate Multinomial Probit Models in Transportation. Transportation Research Part B, Vol. 33, No. 1, 1999, pp. 272–278.
3. Bhat C. R. A Heteroscedastic Extreme Value Model of Intercity Travel Mode Choice. Transportation Research Part A, Vol. 29, No. 6, 1995, pp. 471–483.
4. Bhat C. R. Accommodating Variations in Responsiveness to Level-of-Service Measures in Travel Choice Modeling. Transportation Research Part A, Vol. 32, No. 7, 1998, pp. 495–507.
5. Caldas M. A. F., and Black I. G. Formulating a Methodology for Modeling Revealed Preference Discrete Choice Data: The Selectively Replicated Logit Estimation. Transportation Research Part B, Vol. 31, No. 6, 1997, pp. 463–472.
6. Picard G., and Gaudry M. Exploration of a Box–Cox Logit Model of Intercity Freight Mode Choice. Transportation Research Part E, Vol. 34, No. 1, 1998, pp. 1–12.
7. Hensher D. A., Louviere J. J., and Swait J. Combining Sources of Preference Data. Journal of Econometrics, Vol. 89, 1999, pp. 197–221.
8. Hensher D. A., and Ton T. T. A Comparison of the Predictive Potential of Artificial Neural Networks and Nested Logit Models for Commuter Mode Choice. Transportation Research Part E, Vol. 36, 2000, pp. 155–172.
9. Hoogendoorn S., Lanser S., and Bovy P. H. L. Modelling Interurban Multi-Modal Trips Using a Fuzzy Logic Approach. Proc. 26th PTRC European Transport Conference, London, 1998.
10. Holland R. Fuzzy Logic Model of Mode Choice. Proc. 28th PTRC European Transport Conference, Cambridge, United Kingdom, 2000.
11. Sayed T., and Razavi A. Comparison of Neural and Conventional Approaches to Mode Choice Analysis. ASCE Journal of Computing in Civil Engineering, Vol. 14, No. 1, 2000, pp. 23–30.
12. Joh C.-H., Arentze T., and Timmermans H. Pattern Recognition in Complex Activity Travel Patterns: A Comparison of Euclidean Distance, Signals Processing Theoretical, and Multidimensional Sequence Alignment Method. In Transportation Research Record: Journal of the Transportation Research Board, No. 1752, Transportation Research Board of the National Academies, Washington, D.C., 2001, pp. 16–22.
13. Kuppam A. R., and Pendyala R. M. A Structural Equation Analysis of Commuters Activity and Travel Patterns. Transportation, Vol. 28, No. 1, 2001, pp. 33–54.
14. Sakano R., and Benjamin J. A Structural Equation Analysis of Revealed and Stated Travel Mode and Activity Choices. Presented at 80th Annual Meeting of the Transportation Research Board, Washington, D.C., 2001.
15. Zellner A., and Rossi P. E. Bayesian Analysis of Dichotomous Quantal Response Models. Journal of Econometrics, Vol. 25, Issue 3, 1984, pp. 365–393.
16. Koop G., and Poirier D. J. Bayesian Analysis of Logit Models Using Natural Conjugate Priors. Journal of Econometrics, Vol. 56, Issue 3, 1993, pp. 323–340.
17. Lahiri K., and Gao J. Bayesian Analysis of Nested Logit Model by Markov Chain Monte Carlo. Journal of Econometrics, Vol. 111, Issue 1, 2002, pp. 103–133.
18. Geweke J. Using Simulation Methods for Bayesian Econometric Models: Inference, Development, and Communication. Econometric Reviews, Vol. 18, 1999, pp. 1–126.
19. Poirier D. J. A Bayesian Analysis of Nested Logit Models. Journal of Econometrics, Vol. 75, 1996, pp. 163–181.
20. Kim Y., Kim T.-Y., and Heo O. Bayesian Estimation of Multinomial Probit Models of Work Trip Choice. Kluwer Academic Publishers, Netherlands. V30, 3. 2003, pp. 351–365.
21. Nobile A., Bhat C., and Pas E. A Random Effects Multinomial Probit Model of Car Ownership Choice. In Case Studies in Bayesian Statistics: Volume 3 (Gatsonis C., Hodges J., Kass R., McCulloch R., Rossi P., and Singpurwalla N., eds.), Springer, New York, 1997, pp. 419–434.
22. McFadden D., and Train K. Mixed MNL Models for Discrete Response. Journal of Applied Econometrics, Vol. 15, 2002, pp. 447–470.
23. Spiegelhalter D., Thomas A., Best N., and Lunn D. WinBUGS User Manual: Version 1.4. MRC Biostatistics Unit, Cambridge, United Kingdom, 2003.
24. Gelman A., Carlin J., Stern H., and Rubin D. B. Bayesian Data Analysis. Chapman and Hall, New York, 1995.
25. Carlin B., and Louis T. Bayes and Empirical Bayes Methods for Data Analysis. Chapman and Hall/CRC, New York, 1996.
26. Robert C., and Casella G. Monte Carlo Statistical Methods. Springer, New York, 1997.
27. Chen M., Ibrahim J., and Shao Q. Monte Carlo Methods in Bayesian Computation. Springer-Verlag, New York, 2000.
28. Kadane J. B., and Lazar N. A. Methods and Criteria for Model Selection. Journal of the American Statistical Association, Vol. 99, 2004, pp. 279–290.
29. Chib S. Marginal Likelihood From the Gibbs Output. Journal of the American Statistical Association, Vol. 90, 1995, pp. 1313–1321.
30. Congdon P. Bayesian Statistical Modeling. Wiley, New York, 2001.
31. Meyn S. P., and Tweedie R. L. Markov Chains and Stochastic Stability. Springer-Verlag, New York, 1993.
32. Norris J. R. Markov Chains. Cambridge University Press, Cambridge, United Kingdom, 1997.
33. Reznick S. Adventures in Stochastic Process. Birkhauser, Basel, Switzerland, 1994.
34. Brooks S. P., and Gelman A. Alternative Methods for Monitoring Convergence of Iterative Simulations. Journal of Computational and Graphical Statistics, Vol. 7, 1998, pp. 434–455.
35. Spiegelhalter D. J., Best N. G., Carlin B. P., and van der Linde A. Bayesian Measures of Model Complexity and Fit (With Discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 64, Issue 4, 2002, pp. 583–640.
36. Green P. Reversible Jump Markov Chain Monte Carlo Bayesian Model Determination. Biometrika, Vol. 82, 1995, pp. 711–732.
37. Congdon P. Bayesian Predictive Model Comparison via Parallel Sampling. Computational Statistics and Data Analysis, Vol. 48, No. 4, 2005, pp. 735–753.
38. Congdon P. Applied Bayesian Statistical Models. Wiley, New York, 2003.
39. Brooks S. Markov Chain Monte Carlo Method and its Application. The Statistician, Vol. 47, 1998, pp. 69–100.
40. Brooks S., and Roberts G. O. Assessing Convergence on Markov Chain Monte Carlo Algorithms. Statistics and Computing, Vol. 8, 1998, pp. 319–335.
41. Sahu S., and Roberts G. On Convergence of the EM Algorithm and the Gibbs Sampler. Statistics and Computing, Vol. 9, 1999, pp. 55–64.
42. Hensher D., and Greene W. The Mixed Logit Model: The State of Practice. Working paper. School of Business, Institute of Transport and Logistics Studies, University of Sydney, Australia, 2002.
43. Rossi P., and Allenby G. Bayesian Statistics and Marketing. Marketing Science, Vol. 22, 2003, pp. 304–328.
44. McFadden D. Conditional Logit Analysis of Qualitative Choice Behavior. In Frontiers in Econometrics (Zarembka P., ed.), Academic Press, New York, 1974, pp. 105–142.
45. McCulloch R., and Rossi P. An Exact Likelihood Analysis of the Multinomial Probit Model. Journal of Econometrics, Vol. 64, 1994, pp. 207–240.
46. Chen Z., and Kuo L. Discrete-Choice Models Based on the Scale Mixtures of Multivariate Normal Distributions, Sankhya B, Vol. 64, 2002, pp. 192–213.
47. Hoffman S., and Duncan G. A Comparison of Choice-Based Multinomial and Nested Logit Models: The Family Structure and Welfare Use Decisions of Divorced or Separated Women. Journal of Human Resources, Vol. 23, 1988, pp. 550–562.
48. Greene W. Econometric Analysis, 4th ed. Prentice-Hall, Upper Saddle River, New Jersey, 2000.
49. Washington S., Karlaftis M., and Mannering F. Statistical and Econometric Methods for Transportation Data Analysis. Chapman & Hall/CRC, Boca Raton, Fla., 2003.
50. Glasgow G. Mixed Logit Models for Multiparty Elections. Political Analysis, Vol. 9, 2001, pp. 116–136.
Cite article
Cite article
Cite article
OR
Download to reference manager
If you have citation software installed, you can download article citation data to the citation manager of your choice
Information, rights and permissions
Information
Published In
Article first published online: January 1, 2009
Issue published: January 2009
Authors
Metrics and citations
Metrics
Journals metrics
This article was published in Transportation Research Record: Journal of the Transportation Research Board.
VIEW ALL JOURNAL METRICSArticle usage*
Total views and downloads: 189
*Article usage tracking started in December 2016
Altmetric
See the impact this article is making through the number of times it’s been read, and the Altmetric Score.
Learn more about the Altmetric Scores
Articles citing this one
Receive email alerts when this article is cited
Web of Science: 0
Crossref: 11
- The Importance of Modeling Path Choice Behavior in the Vehicle Routing...
- Sentiment Analysis Models with Bayesian Approach: A Bike Preference Ap...
- Two-vehicle driver-injury severity: A multivariate random parameters l...
- Frequentist and Bayesian Approaches for Understanding Route Choice of ...
- Socio Demographic and Travel Related Variables Affecting Tourist Route...
- Performance of US Concrete Highway Bridge Decks Characterized by Rando...
- Spatial heterogeneous impact of built environment on household auto ow...
- Impacts of Alternative Toll-Fee Structures on Highway Use
- Exploring the influence of built environment on tour-based commuter mo...
- Computational Bayesian Statistics in Transportation Modeling: From Roa...
- A comparison of different Bayesian design criteria for setting up stat...
Figures and tables
Figures & Media
Tables
View Options
Get access
Access options
If you have access to journal content via a personal subscription, university, library, employer or society, select from the options below:
loading institutional access options
Alternatively, view purchase options below:
Purchase 24 hour online access to view and download content.
Access journal content via a DeepDyve subscription or find out more about this option.
