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Random covariance heterogeneity in discrete choice models

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Author Info

  • Stephane Hess

    ()

  • Denis Bolduc

    ()

  • John Polak

    ()

Abstract

The area of discrete choice modelling has developed rapidly in recent years. In particular, continuing refinements of the Generalised Extreme Value (GEV) model family have permitted the representation of increasingly complex patterns of substitution and parallel advances in estimation capability have led to the increased use of model forms requiring simulation in estimation and application. One model form especially, namely the Mixed Multinomial Logit (MMNL) model, is being used ever more widely. Aside from allowing for random variations in tastes across decision-makers in a Random Coefficients Logit (RCL) framework, this model additionally allows for the representation of inter-alternative correlation as well as heteroscedasticity in an Error Components Logit (ECL) framework, enabling the model to approximate any Random Utility model arbitrarily closely. While the various developments discussed above have led to gradual gains in modelling flexibility, little effort has gone into the development of model forms allowing for a representation of heterogeneity across respondents in the correlation structure in place between alternatives. Such correlation heterogeneity is however possibly a crucial factor in the variation of choice-making behaviour across decision-makers, given the potential presence of individual-specific terms in the unobserved part of utility of multiple alternatives. To the authors' knowledge, there has so far only been one application of a model allowing for such heterogeneity, by Bhat (1997). In this Covariance NL model, the logsum parameters themselves are a function of socio-demographic attributes of the decision-makers, such that the correlation heterogeneity is explained with the help of these attributes. While the results by Bhat show the presence of statistically significant levels of covariance heterogeneity, the improvements in terms of model performance are almost negligible. While it is possible to interpret this as a lack of covariance h

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s11116-009-9255-3
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Bibliographic Info

Article provided by Springer in its journal Transportation.

Volume (Year): 37 (2010)
Issue (Month): 3 (May)
Pages: 391-411

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Handle: RePEc:kap:transp:v:37:y:2010:i:3:p:391-411

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Web page: http://www.springerlink.com/link.asp?id=103007

Related research

Keywords: Covariance heterogeneity; Discrete choice; Mixed logit; Random coefficients; Departure time choice; Stated preference;

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References

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  1. Hess, Stephane & Rose, John M., 2009. "Allowing for intra-respondent variations in coefficients estimated on repeated choice data," Transportation Research Part B: Methodological, Elsevier, vol. 43(6), pages 708-719, July.
  2. Hess, Stephane & Polak, John W., 2005. "Mixed logit modelling of airport choice in multi-airport regions," Journal of Air Transport Management, Elsevier, vol. 11(2), pages 59-68.
  3. Kenneth Train, 2003. "Discrete Choice Methods with Simulation," Online economics textbooks, SUNY-Oswego, Department of Economics, number emetr2, March Cit.
  4. Stephane Hess & John Polak & Andrew Daly & Geoffrey Hyman, 2007. "Flexible substitution patterns in models of mode and time of day choice: new evidence from the UK and the Netherlands," Transportation, Springer, vol. 34(2), pages 213-238, March.
  5. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," University of California Transportation Center, Working Papers qt1j6814b3, University of California Transportation Center.
  6. 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.
  7. Wen, Chieh-Hua & Koppelman, Frank S., 2001. "The generalized nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 627-641, August.
  8. 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.
  9. Bhat, Chandra R. & Castelar, Saul, 2002. "A unified mixed logit framework for modeling revealed and stated preferences: formulation and application to congestion pricing analysis in the San Francisco Bay area," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 593-616, August.
  10. Hess, Stephane & Daly, Andrew & Rohr, Charlene & Hyman, Geoff, 2007. "On the development of time period and mode choice models for use in large scale modelling forecasting systems," Transportation Research Part A: Policy and Practice, Elsevier, vol. 41(9), pages 802-826, November.
  11. Greene, William H. & Hensher, David A. & Rose, John, 2006. "Accounting for heterogeneity in the variance of unobserved effects in mixed logit models," Transportation Research Part B: Methodological, Elsevier, vol. 40(1), pages 75-92, January.
  12. Hess, Stephane & Train, Kenneth E. & Polak, John W., 2006. "On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 147-163, February.
  13. Small, Kenneth A, 1987. "A Discrete Choice Model for Ordered Alternatives," Econometrica, Econometric Society, vol. 55(2), pages 409-24, March.
  14. Papola, Andrea, 2004. "Some developments on the cross-nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 38(9), pages 833-851, November.
  15. Bhat, Chandra R. & Guo, Jessica, 2004. "A mixed spatially correlated logit model: formulation and application to residential choice modeling," Transportation Research Part B: Methodological, Elsevier, vol. 38(2), pages 147-168, February.
  16. Daniel McFadden, 1977. "Modelling the Choice of Residential Location," Cowles Foundation Discussion Papers 477, Cowles Foundation for Research in Economics, Yale University.
  17. 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.
  18. Swait, Joffre & Adamowicz, Wiktor L., 1996. "The Effect of Choice Environment and Task Demands on Consumer Behavior: Discriminating Between Contribution and Confusion," Staff Paper Series 24091, University of Alberta, Department of Resource Economics and Environmental Sociology.
  19. Hess, Stephane & Bierlaire, Michel & Polak, John W., 2005. "Estimation of value of travel-time savings using mixed logit models," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(2-3), pages 221-236.
  20. 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.
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Citations

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Cited by:
  1. Eric Gautier & Yuichi Kitamura, 2009. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Cowles Foundation Discussion Papers 1721, Cowles Foundation for Research in Economics, Yale University.
  2. Morten Mørkbak & Jonas Nordström, 2009. "The Impact of Information on Consumer Preferences for Different Animal Food Production Methods," Journal of Consumer Policy, Springer, vol. 32(4), pages 313-331, December.
  3. Matzkin, Rosa L., 2012. "Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 166(1), pages 106-115.

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