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Discrete choice models with multiplicative error terms

  • Fosgerau, M.
  • Bierlaire, M.

The conditional indirect utility of many random utility maximization (RUM) discrete choice models is specified as a sum of an index V depending on observables and an independent random term [epsilon]. In general, the universe of RUM consistent models is much larger, even fixing some specification of V due to theoretical and practical considerations. In this paper, we explore an alternative RUM model where the summation of V and [epsilon] is replaced by multiplication. This is consistent with the notion that choice makers may sometimes evaluate relative differences in V between alternatives rather than absolute differences. We develop some properties of this type of model and show that in several cases the change from an additive to a multiplicative formulation, maintaining a specification of V, may lead to a large improvement in fit, sometimes larger than that gained from introducing random coefficients in V.

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Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

Volume (Year): 43 (2009)
Issue (Month): 5 (June)
Pages: 494-505

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Handle: RePEc:eee:transb:v:43:y:2009:i:5:p:494-505
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  1. Daly, Andrew & Bierlaire, Michel, 2006. "A general and operational representation of Generalised Extreme Value models," Transportation Research Part B: Methodological, Elsevier, vol. 40(4), pages 285-305, May.
  2. 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.
  3. Caussade, Sebastián & Ortúzar, Juan de Dios & Rizzi, Luis I. & Hensher, David A., 2005. "Assessing the influence of design dimensions on stated choice experiment estimates," Transportation Research Part B: Methodological, Elsevier, vol. 39(7), pages 621-640, August.
  4. 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.
  5. 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.
  6. 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.
  7. Matzkin, Rosa L., 2007. "Nonparametric identification," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 73 Elsevier.
  8. Swait, Joffre & Adamowicz, Wiktor L., 1999. "Choice Environment, Market Complexity and Consumer Behavior: A Theoretical and Empirical Approach for Incorporating Decision Complexity into Models of Consumer Choice," Staff Paper Series 24093, University of Alberta, Department of Resource Economics and Environmental Sociology.
  9. John K. Dagsvik & Anders Karlstr�m, 2005. "Compensating Variation and Hicksian Choice Probabilities in Random Utility Models that are Nonlinear in Income," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 57-76.
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