A Microeconomic Interpretation of the Maximum Entropy Estimator of Multinomial Logit Models and Its Equivalence to the Maximum Likelihood Estimator
Abstract
:1. Introduction
2. Formulation of Entropy Maximization Problem and its Dual
3. Microeconomic Interpretation of the Entropy Maximization Dual Problem
4. Statistical Interpretation of the Entropy Maximization Dual Problem
5. Conclusions
References and Notes
- Wilson, A.G. Entropy in Urban and Regional Modeling; Pion: London, UK, 1970. [Google Scholar]
- Fang, S.; Tsao, J. Linearly-constrained entropy maximization problem with quadratic cost and its applications to transportation planning problems. Transp. Sci. 1995, 29, 353–365. [Google Scholar] [CrossRef]
- Thorsen, I.; Gitlesen, J.P. Empirical evaluation of alternative model specifications to predict commuting flows. J. Reg. Sci. 1998, 38, 273–292. [Google Scholar] [CrossRef]
- De Grange, L.; Fernandez, J.E.; De Cea, J. A consolidated model of trip distribution. Transp. Res. 2010, 46, 61–75. [Google Scholar] [CrossRef]
- Anas, A. Discrete choice theory, information theory and the multinomial logit and gravity models. Transp. Res. 1983, 17, 13–23. [Google Scholar] [CrossRef]
- Boyce, D.; LeBlanc, L.; Chon, K.; Lee, Y; Lin, K. Implementation and computational issues for combined models of location, destination, mode and route choice. Environ. Plan. 1983, 15, 1219–1230. [Google Scholar] [CrossRef]
- Fotheringham, A. Modeling hierarchical destination choice. Environ. Plan. 1986, 18, 401–418. [Google Scholar] [CrossRef]
- Boyce, D.; LeBlanc, L.; Chon, K. Network equilibrium models of urban location and travel choices: A retrospective survey. J. Reg. Sci. 1988, 28, 159–183. [Google Scholar] [CrossRef]
- Safwat, K.; Magnanti, T. A combined trip generation, trip distribution, modal split and traffic assignment model. Transp. Sci. 1988, 22, 14–30. [Google Scholar] [CrossRef]
- Brice, S. Derivation of nested transport models within a mathematical programming framework. Transp. Res. 1989, 23, 19–28. [Google Scholar] [CrossRef]
- Fernandez, J.E.; De Cea, J.; Florian, M.; Cabrera, E. Network equilibrium models with combined modes. Transp. Sci. 1994, 28, 182–192. [Google Scholar] [CrossRef]
- Oppenheim, N. Urban Travel Demand Modeling; John Wiley & Sons: New York, NY, USA, 1995. [Google Scholar]
- Abrahamsson, T.; Lundqvist, L. Formulation and estimation of combined network equilibrium models with applications to stockholm. Transp. Sci. 1999, 33, 80–100. [Google Scholar] [CrossRef]
- Boyce, D.; Bar-Gera, H. Validation of multiclass urban travel forecasting models combining origin-destination, mode, and route choices. J. Reg. Sci. 2003, 43, 517–540. [Google Scholar] [CrossRef]
- Ham, H.; Tschangho, J.; Boyce, D. Implementation and estimation of a combined model of interregional, multimodal commodity shipments and transportation network flows. Transp. Res. 2005, 39, 65–79. [Google Scholar] [CrossRef]
- Garcia, R.; Marin, A. Network equilibrium with combined modes: models and solution algorithms. Transp. Res. 2005, 39, 223–254. [Google Scholar] [CrossRef]
- De Cea, J.; Fernandez, J.E.; De Grange, L. Combined models with hierarchical demand choices: A multi-objective entropy optimization approach. Transp. Rev. 2008, 28, 415–438. [Google Scholar] [CrossRef]
- McFadden, D. Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics; Zarembka, P., Ed.; Academic Press: New York, NY, USA, 1974. [Google Scholar]
- Ortuzar, J. de D.; Willumsen, L.G. Modeling Transport; John Wiley & Sons: Chichester, UK, 2001. [Google Scholar]
- Fang, S.; Rajasekera, J.; Tsao, J. Entropy Optimization and Mathematical Programming; Kluwer Academic Publisher: Norwell, MA, USA, 1997. [Google Scholar]
- Williams, H.C.W.L. On the formation of travel demand models and economic evaluation measures of user benefit. Environ. Plan. 1977, 9, 285–344. [Google Scholar] [CrossRef]
- Imbens, G.W.; Johnson, P.; Spady, R.H. Information theoretic approaches to inference in moment condition models. Econometrica 1998, 66, 333–357. [Google Scholar] [CrossRef]
- Golan, A. Information and entropy econometrics — Editor’s view. J. Econom. 2002, 107, 1–15. [Google Scholar] [CrossRef]
- Golan, A. Information and Entropy Econometrics: A Review and Synthesis; Now Publishers Inc.: Hanover, MA, USA, 2008. [Google Scholar]
- Bercher, J.F.; Besnerais, G.L.; Demoment, G. The maximum entropy on the mean method, noise and sensitivity. In Maximum Entropy and Bayesian Studies; Skilling, J., Sibisi, S., Eds.; Kluwer Academic Publishers: Cambridge, UK, 1996. [Google Scholar]
- Csiszar, I.; Shields, P. Information theory and statistics: A tutorial. Found. Tr. Commun. Inform. Theory 2004, 1, 417–528. [Google Scholar] [CrossRef]
- Soofi, E.S.; Retzer, J.J. Information indices: Unifications and applications. J. Econom. 2002, 107, 17–40. [Google Scholar] [CrossRef]
- Cover, T.M.; Thomas, J.A. Elements of Information Theory; John Wiley & Sons: New York, NY, USA, 2006. [Google Scholar]
© 2010 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
Share and Cite
Donoso, P.; Grange, L.d. A Microeconomic Interpretation of the Maximum Entropy Estimator of Multinomial Logit Models and Its Equivalence to the Maximum Likelihood Estimator. Entropy 2010, 12, 2077-2084. https://doi.org/10.3390/e12102077
Donoso P, Grange Ld. A Microeconomic Interpretation of the Maximum Entropy Estimator of Multinomial Logit Models and Its Equivalence to the Maximum Likelihood Estimator. Entropy. 2010; 12(10):2077-2084. https://doi.org/10.3390/e12102077
Chicago/Turabian StyleDonoso, Pedro, and Louis de Grange. 2010. "A Microeconomic Interpretation of the Maximum Entropy Estimator of Multinomial Logit Models and Its Equivalence to the Maximum Likelihood Estimator" Entropy 12, no. 10: 2077-2084. https://doi.org/10.3390/e12102077
APA StyleDonoso, P., & Grange, L. d. (2010). A Microeconomic Interpretation of the Maximum Entropy Estimator of Multinomial Logit Models and Its Equivalence to the Maximum Likelihood Estimator. Entropy, 12(10), 2077-2084. https://doi.org/10.3390/e12102077