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Entropy 2011, 13(8), 1425-1445; doi:10.3390/e13081425

A Maximum Entropy Estimator for the Aggregate Hierarchical Logit Model

1
Laboratorio de Modelamiento del Transporte y Uso del Suelo (LABTUS), Departamento de Ingeniería Civil, Universidad de Chile, Santiago PO Box 10-D, Chile
2
Escuela de Ingeniería Civil Industrial, Universidad Diego Portales, Santiago, 8370179, Chile
*
Author to whom correspondence should be addressed.
Received: 20 June 2011 / Revised: 15 July 2011 / Accepted: 20 July 2011 / Published: 2 August 2011
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Abstract

A new approach for estimating the aggregate hierarchical logit model is presented. Though usually derived from random utility theory assuming correlated stochastic errors, the model can also be derived as a solution to a maximum entropy problem. Under the latter approach, the Lagrange multipliers of the optimization problem can be understood as parameter estimators of the model. Based on theoretical analysis and Monte Carlo simulations of a transportation demand model, it is demonstrated that the maximum entropy estimators have statistical properties that are superior to classical maximum likelihood estimators, particularly for small or medium-size samples. The simulations also generated reduced bias in the estimates of the subjective value of time and consumer surplus.
Keywords: hierarchical logit model; lagrange multipliers; maximum entropy; maximum likelihood hierarchical logit model; lagrange multipliers; maximum entropy; maximum likelihood
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Donoso, P.; De Grange, L.; González, F. A Maximum Entropy Estimator for the Aggregate Hierarchical Logit Model. Entropy 2011, 13, 1425-1445.

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