On The Overspecification of Multinomial and Nested Logit Models Due to Alternative Specific Constants

Michel Bierlaire, Tsippy Lotan and Philippe Toint
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Michel Bierlaire: Intelligent Transportation Systems Program, Center for Transportation Studies, Massachusetts Institute of Technology, Cambridge, Massachusetts
Tsippy Lotan: Service de Mathématique de la Gestion, Université Libre de Bruxelles, Brussels, Belgium
Philippe Toint: Transportation Research Group, Department of Mathematics, Facultés Universitaires ND de la Paix, Namur, Belgium

Transportation Science, 1997, vol. 31, issue 4, 363-371

Abstract: Discrete choice models as demand forecasting techniques have been used for transportation applications for more than thirty years. The multinomial and nested logit models are probably the most widely applied in this context. Alternative specific constants, although playing an important role in these models, have received very little attention in theoretical studies. In this paper, we try to fill this gap by providing an analysis of the overspecification caused by alternative specific constants to the log-likelihood function of multinomial and nested logit models. The theoretical results lead directly to a particular strategy of alternative specific constant specification, called here the orthogonal strategy . The analysis of the relationship between any two arbitrary strategies and the derivation of an interesting geometrical property of the orthogonal strategy provide a motivation to prefer the latter.

Date: 1997
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