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Discrete choice models with multiplicative error terms

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  • Fosgerau, M.
  • Bierlaire, M.

Abstract

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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Bibliographic Info

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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Keywords: Discrete choice Multiplicative specification Multivariate extreme value Random scale Heteroscedasticity;

References

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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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Citations

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Cited by:
  1. Li, Baibing, 2011. "The multinomial logit model revisited: A semi-parametric approach in discrete choice analysis," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 461-473, March.
  2. Stephane Hess & John Rose, 2012. "Can scale and coefficient heterogeneity be separated in random coefficients models?," Transportation, Springer, vol. 39(6), pages 1225-1239, November.
  3. Mattsson, Lars-Göran & Weibull, Jörgen W. & Lindberg, Per Olov, 2014. "Extreme values, invariance and choice probabilities," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 81-95.
  4. Hoyos, David, 2010. "The state of the art of environmental valuation with discrete choice experiments," Ecological Economics, Elsevier, vol. 69(8), pages 1595-1603, June.
  5. Paul Koster & Eric Kroes & Erik T. Verhoef, 2010. "Travel Time Variability and Airport Accessibility," Tinbergen Institute Discussion Papers 10-061/3, Tinbergen Institute.
  6. Swait, Joffre, 2009. "Choice models based on mixed discrete/continuous PDFs," Transportation Research Part B: Methodological, Elsevier, vol. 43(7), pages 766-783, August.
  7. Kitthamkesorn, Songyot & Chen, Anthony, 2013. "A path-size weibit stochastic user equilibrium model," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 378-397.
  8. Kitthamkesorn, Songyot & Chen, Anthony, 2014. "Unconstrained weibit stochastic user equilibrium model with extensions," Transportation Research Part B: Methodological, Elsevier, vol. 59(C), pages 1-21.

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