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Transportation

, Volume 40, Issue 5, pp 1003–1020 | Cite as

Accounting for attribute non-attendance and common-metric aggregation in a probabilistic decision process mixed multinomial logit model: a warning on potential confounding

  • David A. Hensher
  • Andrew T. Collins
  • William H. Greene
Article

Abstract

Latent class models offer an alternative perspective to the popular mixed logit form, replacing the continuous distribution with a discrete distribution in which preference heterogeneity is captured by membership of distinct classes of utility description. Within each class, preference homogeneity is usually assumed, although interactions with observed contextual effects are permissible. A natural extension of the fixed parameter latent class model is a random parameter latent class model which allows for another layer of preference heterogeneity within each class. A further extension is to overlay attribute processing rules such as attribute non-attendance (ANA) and aggregation of common-metric attributes (ACMA). This paper sets out the random parameter latent class model with ANA and ACMA, and illustrates its application using a stated choice data set in the context of car commuters and non-commuters choosing amongst alternative packages of travel times and costs pivoted around a recent trip in Australia. What we find is that for the particular data set analysed, in the presence of attribute processing together with the discrete distributions defined by latent classes, that adding an additional layer of heterogeneity through random parameters within a latent class only very marginally improves on the statistical contribution of the model. Nearly all of the additional fit over the fixed parameter latent class model is added by the account for attribute processing. This is an important finding that might suggest the role that attribute processing rules play in accommodating attribute heterogeneity, and that random parameters within class are essentially a potentially confounding effect. An interesting finding, however, is that the introduction of random parameters increases the probability of membership to full attribute attendance classes, which may suggest that some individuals assign a very low marginal disutility (but not zero) to specific attributes or that there are very small differences in the marginal disutility of common-metric attributes, and this is being accommodated by random parameters, but not observed under a fixed parameter latent class model.

Keywords

Latent class mixed multinomial logit Random parameters Preference heterogeneity Attribute non-attendance Aggregation of common-metric attributes Stated choice experiment Car commuters 

Notes

Acknowledgments

We thank the three referees for their extensive comments, which have resulted in major revisions and new models.

References

  1. Bujosa, A., Riera, A., Hicks, R.: Combining discrete and continuous representation of preference heterogeneity: a latent class approach. Environ. Resour. Econ. 47, 477–493 (2010)CrossRefGoogle Scholar
  2. Campbell, D., Hensher, D.A., Scarpa, R.: Non-attendance to attributes in environmental choice analysis: a latent class specification. J. Environ. Plan. Manag. 54(8), 1061–1076 (2011)CrossRefGoogle Scholar
  3. Campbell, D., Hutchinson, W., Scarpa, R.: Incorporating discontinuous preferences into the analysis of discrete choice experiments. Environ. Resour. Econ. 41(3), 401–417 (2008)CrossRefGoogle Scholar
  4. Carlsson, F., Kataria, M., Lampi, E.: Dealing with ignored attributes in choice experiments on valuation of Sweden. Environ. Resour. Econ. 47(1), 65–89 (2010)CrossRefGoogle Scholar
  5. Collins, A.T., Rose, J.M., and Hensher, D.A.: The random parameters attribute nonattendance model. Paper presented at The 13th International Conference on Travel Behaviour Research, Toronto, July (2012)Google Scholar
  6. Everitt, B.: A finite mixture model for the clustering of mixed-mode data. Stat. Probab. Lett. 6, 305–309 (1988)CrossRefGoogle Scholar
  7. Fiebig, D., Keane, M., Louviere, J., Wasi, N.: The generalized multinomial logit: accounting for scale and coefficient heterogeneity. Mark. Sci. 29(3), 393–421 (2010)CrossRefGoogle Scholar
  8. Greene, W.H., Hensher, D.A.: A latest class model for discrete choice analysis: contrasts with mixed logit. Transp. Res. Part B 37, 681–698 (2003)CrossRefGoogle Scholar
  9. Greene, W.H., Hensher, D.A.: Does scale heterogeneity matter? a comparative assessment of logit models. Transportation 37(3), 413–428 (2010)CrossRefGoogle Scholar
  10. Greene, W.H., Hensher, D.A.: Revealing additional dimensions of preference heterogeneity in a latent class mixed multinomial logit model. Appl. Econ. 45(14), 1897–1902 (2013)CrossRefGoogle Scholar
  11. Heckman, J., Singer, B.: A method for minimizing the impact of distributional assumptions in econometric models. Econometrica 52, 271–320 (1984)CrossRefGoogle Scholar
  12. Hensher, D.A.: How do respondents process stated choice experiments? Attribute consideration under varying information load. J. Appl. Econ. 21(6), 861–878 (2006)CrossRefGoogle Scholar
  13. Hensher, D.A., Greene, W.H.: Non-attendance and dual processing of common-metric attributes in choice analysis: a latent class specification. Empir. Econ. 39(2), 413–426 (2010)CrossRefGoogle Scholar
  14. Hensher, D.A., Rose, J.M.: Simplifying choice through attribute preservation or non-attendance: implications for willingness to pay. Transp. Res. Part E 45(4), 583–590 (2009)CrossRefGoogle Scholar
  15. Hensher, D.A., Rose, J.M., Greene, W.H.: The implications on willingness to pay of respondents ignoring specific attributes. Transportation 32, 203–222 (2005)CrossRefGoogle Scholar
  16. Hensher, D.A., Li, Z., and Rose, J.M.: Accommodating risk in the valuation of expected travel time savings. J. Adv. Transp. online 16 January 2011 (2012a). doi: 10.1002/atr.160
  17. Hensher, D.A., Rose, J.M., Greene, W.H.: Inferring attribute non-attendance from stated choice data: implications for willingness to pay estimates and a warning for stated choice experiment design. Transportation 39(2), 235–246 (2012)CrossRefGoogle Scholar
  18. Hess, S., Hensher, D.A.: Using conditioning on observed choices to retrieve individual-specific attribute processing strategies. Transp. Res. Part B 44(6), 781–790 (2010)CrossRefGoogle Scholar
  19. Hess, S., Rose, J.M.: A latent class approach to modelling heterogeneous information processing strategies in SP studies. Paper presented at the Oslo Workshop on valuation methods in transport planning, Oslo (2007)Google Scholar
  20. Hess, S., Stathopoulos, A., Campbell, D., O’Neill, V., Caussade, S.: It’s not that I don’t care, I just don’t care very much: confounding between attribute non-attendance and taste heterogeneity. Transportation (2011). doi: 10.1007/s11116-012-9438-1
  21. Hess, S., Stathopoulos, A., Daly, A.: Allowing for heterogeneous decision rules in discrete choice models: an approach and four case studies. Transportation 39(3), 565–591 (2012)CrossRefGoogle Scholar
  22. Hole, A.R.: A discrete choice model with endogenous attribute attendance. Econ. Lett. 110(3), 203–205 (2011)CrossRefGoogle Scholar
  23. Layton, D., Hensher, D.A.: Aggregation of common-metric attributes in preference revelation in choice experiments and implications for willingness to pay. Transp. Res. Part D 15, 394–404 (2010)CrossRefGoogle Scholar
  24. Li, Z., Hensher, D.A., Rose, J.M.: Willingness to pay for travel time reliability for passenger transport: a review and some new empirical evidence. Transp. Res. Part E. 46(3), 384–403 (2010)CrossRefGoogle Scholar
  25. McNair, B., Hensher, D.A., Bennett, J.: Modelling heterogeneity in response behaviour towards a sequence of discrete choice questions: a probabilistic decision process model. Environ. Resour. Econ. 51, 599–616 (2012)CrossRefGoogle Scholar
  26. Puckett, S.M., Hensher, D.A.: The role of attribute processing strategies in estimating the preferences of road freight stakeholders under variable road user charges. Transp. Res. E 44, 379–395 (2008)CrossRefGoogle Scholar
  27. Rose, J.M., Bliemer, M.C., Hensher, D.A., Collins, A.T.: Designing efficient stated choice experiments in the presence of reference alternatives. Transp. Res. B 42(4), 395–406 (2008)CrossRefGoogle Scholar
  28. Scarpa, R., Gilbride, T.J., Campbell, D., Hensher, D.A.: Modelling attribute non-attendance in choice experiments for rural landscape valuation. Eur. Rev. Agric. Econ. 36(2), 151–174 (2009)CrossRefGoogle Scholar
  29. Scarpa, R., Thiene, M., Hensher, D.A.: Monitoring choice task attribute attendance in nonmarket valuation of multiple park management services: does it matter? Land Econ. 86(4), 817–839 (2010)Google Scholar
  30. Shen, J.: Latent class model or mixed logit model? A comparison by transport mode choice data. Appl. Econ. 41, 2915–2924 (2009)CrossRefGoogle Scholar
  31. Thiene, M., Meyerhoff, J., De Salvo, M.: Scale and taste heterogeneity for forest biodiversity: models of serial nonparticipation and their effects. J. For. Econ. 18(4), 355–369 (2012)Google Scholar
  32. Train, K.: EM algorithms for nonparametric estimation of mixing distributions. J. Choice Model. 1(1), 40–69 (2008)CrossRefGoogle Scholar
  33. Train, K., Weeks, M.: Discrete choice models in preference space and willing to-pay space. In: Scarpa, R., Alberini, A. (eds.) Applications of Simulation Methods in Environmental and Resource Economics, chapter 1, pp. 1–16. Springer Publisher, Dordrecht, (2005)Google Scholar
  34. Wasi, N., Carson, R.T.: The Influence of Rebate Programs on the Demand for Water Heaters The Case of New South Wales. UC Center for Energy and Environmental Economics, Berkeley (2011)Google Scholar
  35. Vij, A., Carrel, A., Walker, J.L.: Latent modal preferences: behavioral mixture models with longitudinal data, E3 WP-025, UC Berkeley, Department of Civil and Environmental Engineering, Berkeley (2012)Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • David A. Hensher
    • 1
  • Andrew T. Collins
    • 1
  • William H. Greene
    • 2
  1. 1.Institute of Transport and Logistics Studies, The Business SchoolThe University of SydneySydneyAustralia
  2. 2.Department of Economics, Stern School of BusinessNew York UniversityNew YorkUSA

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