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Estimation of a constrained multinomial logit model


  • Marisol Castro


  • Francisco Martínez


  • Marcela Munizaga



Identifying the set of available alternatives in a choice process after considering an individual’s bounds or thresholds is a complex process that, in practice, is commonly simplified by assuming exogenous rules in the choice set formation. The Constrained Multinomial Logit (CMNL) model incorporates thresholds in several attributes as a key endogenous process to define the alternatives choice/rejection mechanism. The model allows for the inclusion of multiple constraints and has a closed form. In this paper, we study the estimation of the CMNL model using the maximum likelihood function, develop a methodology to estimate the model overcoming identification problems by an endogenous partition of the sample, and test the model estimation with both synthetic and real data. The CMNL model appears to be suitable for general applications as it presents a significantly better fit than the MNL model under constrained behaviour and replicates the MNL estimates in the unconstrained case. Using mode choice real data, we found significant differences in the values of times and elasticities between compensatory MNL and semi-compensatory CMNL models, which increase as the thresholds on attributes become active. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Marisol Castro & Francisco Martínez & Marcela Munizaga, 2013. "Estimation of a constrained multinomial logit model," Transportation, Springer, vol. 40(3), pages 563-581, May.
  • Handle: RePEc:kap:transp:v:40:y:2013:i:3:p:563-581
    DOI: 10.1007/s11116-012-9435-4

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    References listed on IDEAS

    1. Swait, Joffre, 2009. "Choice models based on mixed discrete/continuous PDFs," Transportation Research Part B: Methodological, Elsevier, vol. 43(7), pages 766-783, August.
    2. Francisco Martínez & Ricardo Hurtubia, 2006. "Dynamic Model for the Simulation of Equilibrium Status in the Land Use Market," Networks and Spatial Economics, Springer, vol. 6(1), pages 55-73, March.
    3. Swait, Joffre, 2001. "A non-compensatory choice model incorporating attribute cutoffs," Transportation Research Part B: Methodological, Elsevier, vol. 35(10), pages 903-928, November.
    4. Munizaga, Marcela A. & Heydecker, Benjamin G. & Ortúzar, Juan de Dios, 2000. "Representation of heteroskedasticity in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 34(3), pages 219-240, April.
    5. Kaplan, Sigal & Shiftan, Yoram & Bekhor, Shlomo, 2012. "Development and estimation of a semi-compensatory model with a flexible error structure," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 291-304.
    6. Swait, Joffre & Ben-Akiva, Moshe, 1987. "Incorporating random constraints in discrete models of choice set generation," Transportation Research Part B: Methodological, Elsevier, vol. 21(2), pages 91-102, April.
    7. Martínez, Francisco & Aguila, Felipe & Hurtubia, Ricardo, 2009. "The constrained multinomial logit: A semi-compensatory choice model," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 365-377, March.
    8. Huber, Joel & Klein, Noreen M, 1991. " Adapting Cutoffs to the Choice Environment: The Effects of Attribute Correlation and Reliability," Journal of Consumer Research, Oxford University Press, vol. 18(3), pages 346-357, December.
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    Cited by:

    1. Paleti, Rajesh, 2015. "Implicit choice set generation in discrete choice models: Application to household auto ownership decisions," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 132-149.
    2. Siyu Li & Der-Horng Lee, 2017. "Learning daily activity patterns with probabilistic grammars," Transportation, Springer, vol. 44(1), pages 49-68, January.


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