Un Estimador Máximo-Entrópico de Modelos Logit Jerárquicos
Palabras clave:
Modelos Logit, Logit Jerárquico, Multiplicadores de Lagrange, Máxima Entropía, Máxima Verosimilitud, SesgoResumen
En este trabajo presentamos un nuevo enfoque para estimar modelos de demanda agregados de tipo Logit Jerárquicos. Para ello, formulamos modelos de programación matemática no lineal con componentes entrópicas cuyas condiciones de optimalidad proporcionan modelos tipo Logit Jerárquicos, equivalentes a los modelos basados en la teoría de la utilidad aleatoria, y cuyos multiplicadores de Lagrange corresponden a los parámetros de los modelos Logit Jerárquicos; a estos parámetros les denominamos máximo entrópicos. A partir de simulaciones, concluimos que los estimadores máximo entrópicos presentan mejores propiedades estadísticas que los clásicos estimadores máximo verosímiles, específicamente en lo que a sesgo se refiere, especialmente en muestras de menor tamaño que son normalmente utilizadas para calibrar modelos Logit Jerárquicos en la práctica.Citas
Abrahamsson, T. and L. Lundqvist (1999): Formulation and Estimation of
Combined Network Equilibrium Models with Applications to Stockholm.
Transportation Science, 33, 80-100.
Anas, A, (1983). Discrete Choice Theory, Information Theory and the
Multinomial Logit and Gravity Models. Transportation Research, 17B,
-23.
Boyce, D., Le Blanc L., Chon K., Lee Y. and Lin, K. (1983).
Implementation and computational issues for combined models of
location, destination, mode and route choice. Environment and
Planning, 15A, 1219–1230.
Boyce, D. E., Leblanc, L.J. and Chon, K.S. (1988). Network equilibrium
models of urban location and travel choices: a retrospective survey,
Journal of Regional Science, 28, 159-183.
Boyce, D. and H. Bar-Gera (2003). Validation of Multiclass Urban Travel
Forecasting Models Combining Origin-Destination, Mode, and Route
Choices, Journal of Regional Science, 43, 517-540.
Brice, S. (1989). Derivation of nested transport models within a
mathematical programming framework. Transportation Research, 23B,
– 28.
De Cea, J. Fernandez, J.E., Soto, A. and Dekock, V. (2005). Solving
network equilibrium on multimodal urban transportation networks with
multiple user classes. Transport Reviews, 25, 293-317.
De Cea, J., J.E. Fernandez and L. De Grange (2008) Combined models
with hierarchical demand choices: a multi-objective entropy optimization
approach. Transport Reviews, 28, 415-438.
De Grange, L., Ibeas, A. and Gonzalez, F. (2009). A Hierarchical Gravity
Model with Spatial Correlation: Mathematical Formulation and Parameter
Estimation. Networks and Spatial Economics. (DOI: 10.1007/s11067-008-9097-0).
Fang, S. C. and S. J. Tsao (1995). Linearly-constrained entropy
maximization problem with quadratic cost and its applications to
transportation planning problems. Transportation Science, 29, 353-365.
Fotheringham, A.S. (1986). Modeling hierarchical destination choice.
Environment and Planning, 18A, 401-418.
García, R. and Marín, A. (2005). Network equilibrium with combined
modes: models and solution algorithms. Transportation Research, 39B,
-254.
Oppenheim, N. (1995). Urban Travel Demand Modeling. John Wiley &
Sons, New York.
Safwat, K. and Magnanti, T. (1988). A combined trip generation, trip
distribution, modal split and traffic assignment model. Transportation
Science, 22, 14–30.
Williams, H.C.W.L. (1977) On the formation of travel demand models
and economic evaluation measures of user benefit. Environment and
Planning, 9A, 285-344.
Wilson, A. G. (1970). Entropy in Urban and Regional Modeling. Pion,
London.
