Next Article in Journal
Information Driven Ecohydrologic Self-Organization
Previous Article in Journal
Superstatistics and Gravitation
Previous Article in Special Issue
Estimation of Seismic Wavelets Based on the Multivariate Scale Mixture of Gaussians Model
Entropy 2010, 12(10), 2077-2084; doi:10.3390/e12102077
Article

A Microeconomic Interpretation of the Maximum Entropy Estimator of Multinomial Logit Models and Its Equivalence to the Maximum Likelihood Estimator

1
 and 2,*
Received: 21 August 2010; Accepted: 8 September 2010 / Published: 29 September 2010
(This article belongs to the Special Issue Maximum Entropy 2010)
Download PDF [64 KB, uploaded 29 September 2010]
Abstract: Maximum entropy models are often used to describe supply and demand behavior in urban transportation and land use systems. However, they have been criticized for not representing behavioral rules of system agents and because their parameters seems to adjust only to modeler-imposed constraints. In response, it is demonstrated that the solution to the entropy maximization problem with linear constraints is a multinomial logit model whose parameters solve the likelihood maximization problem of this probabilistic model. But this result neither provides a microeconomic interpretation of the entropy maximization problem nor explains the equivalence of these two optimization problems. This work demonstrates that an analysis of the dual of the entropy maximization problem yields two useful alternative explanations of its solution. The first shows that the maximum entropy estimators of the multinomial logit model parameters reproduce rational user behavior, while the second shows that the likelihood maximization problem for multinomial logit models is the dual of the entropy maximization problem.
Keywords: logit multinomial; maximum entropy; maximum likelihood; duality logit multinomial; maximum entropy; maximum likelihood; duality
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Export to BibTeX |
EndNote


MDPI and ACS Style

Donoso, P.; Grange, L. 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.

AMA Style

Donoso P, Grange L. 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.

Chicago/Turabian Style

Donoso, Pedro; Grange, Louis de. 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.


Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert