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Circumventing the problem of the scale: discrete choice models with multiplicative error terms


  • Fosgerau, Mogens
  • Bierlaire, Michel


We propose a multiplicative specification of a discrete choice model that renders choice probabilities independent of the scale of the utility. The scale can thus be random with unspecified distribution. The model mostly outperforms the classical additive formulation over a range of stated choice data sets. In some cases, the improvement in likelihood is greater than that obtained from adding observed and unobserved heterogeneity to the additive specification. The multiplicative specification makes it unnecessary to capture scale heterogeneity and, consequently, yields a significant potential for reducing model complexity in the presence of heteroscedasticity. Thus the proposed multiplicative formulation should be a useful supplement to the techniques available for the analysis of discrete choices. There is however a cost to be paid in terms of increased analytical complexity relative to the additive formulations.

Suggested Citation

  • Fosgerau, Mogens & Bierlaire, Michel, 2007. "Circumventing the problem of the scale: discrete choice models with multiplicative error terms," MPRA Paper 3901, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:3901

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    References listed on IDEAS

    1. Small, Kenneth A & Rosen, Harvey S, 1981. "Applied Welfare Economics with Discrete Choice Models," Econometrica, Econometric Society, vol. 49(1), pages 105-130, January.
    2. Train, K. & Weeks, M., 2004. "Discrete Choice Models in Preference Space and Willingness-to Pay Space," Cambridge Working Papers in Economics 0443, Faculty of Economics, University of Cambridge.
    3. DeShazo, J. R. & Fermo, German, 2002. "Designing Choice Sets for Stated Preference Methods: The Effects of Complexity on Choice Consistency," Journal of Environmental Economics and Management, Elsevier, vol. 44(1), pages 123-143, July.
    4. Fosgerau, Mogens, 2007. "Using nonparametrics to specify a model to measure the value of travel time," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(9), pages 842-856, November.
    5. Swait, Joffre & Adamowicz, Wiktor, 2001. "Choice Environment, Market Complexity, and Consumer Behavior: A Theoretical and Empirical Approach for Incorporating Decision Complexity into Models of Consumer Choice," Organizational Behavior and Human Decision Processes, Elsevier, vol. 86(2), pages 141-167, November.
    6. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    7. Daniel McFadden, 1977. "Modelling the Choice of Residential Location," Cowles Foundation Discussion Papers 477, Cowles Foundation for Research in Economics, Yale University.
    8. Fosgerau, Mogens, 2006. "Investigating the distribution of the value of travel time savings," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 688-707, September.
    9. Bhat, Chandra R., 1997. "Covariance heterogeneity in nested logit models: Econometric structure and application to intercity travel," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 11-21, February.
    10. Koppelman, Frank S. & Sethi, Vaneet, 2005. "Incorporating variance and covariance heterogeneity in the Generalized Nested Logit model: an application to modeling long distance travel choice behavior," Transportation Research Part B: Methodological, Elsevier, vol. 39(9), pages 825-853, November.
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    Cited by:

    1. Hess, S. & Bierlaire, Michel & Polak, J.W., 2007. "A systematic comparison of continuous and discrete mixture models," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 37, pages 35-61.

    More about this item


    Multivariate extreme value; logsum;

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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