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

Author

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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)

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.

Suggested Citation

  • Michel Bierlaire & Tsippy Lotan & Philippe Toint, 1997. "On The Overspecification of Multinomial and Nested Logit Models Due to Alternative Specific Constants," Transportation Science, INFORMS, vol. 31(4), pages 363-371, November.
    • Handle: RePEc:inm:ortrsc:v:31:y:1997:i:4:p:363-371
    DOI: 10.1287/trsc.31.4.363
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    Citations

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    Cited by:

    1. Michel Bierlaire, 2006. "A theoretical analysis of the cross-nested logit model," Annals of Operations Research, Springer, vol. 144(1), pages 287-300, April.
    2. Halima Bensmail & Ramon P. DeGennaro, 2004. "Analyzing imputed financial data: a new approach to cluster analysis," FRB Atlanta Working Paper 2004-20, Federal Reserve Bank of Atlanta.
    3. Bunch, David S. & Rocke, David M., 2016. "Variance-component-based nested logit specifications: Improved formulation, and practical microsimulation of random disturbance terms," Journal of choice modelling, Elsevier, vol. 21(C), pages 30-35.
    4. José Luis Espinosa-Aranda & Ricardo García-Ródenas & María Luz López-García & Eusebio Angulo, 2018. "Constrained nested logit model: formulation and estimation," Transportation, Springer, vol. 45(5), pages 1523-1557, September.
    5. García-Ródenas, Ricardo & Marín, Ángel, 2009. "Simultaneous estimation of the origin-destination matrices and the parameters of a nested logit model in a combined network equilibrium model," European Journal of Operational Research, Elsevier, vol. 197(1), pages 320-331, August.
    6. Steven Miller & Eric Bradlow & Kevin Dayaratna, 2006. "Closed-form Bayesian inferences for the logit model via polynomial expansions," Quantitative Marketing and Economics (QME), Springer, vol. 4(2), pages 173-206, June.

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