IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v106y2017icp76-101.html
   My bibliography  Save this article

Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions

Author

Listed:
  • Vij, Akshay
  • Krueger, Rico

Abstract

This study proposes a mixed logit model with multivariate nonparametric finite mixture distributions. The support of the distribution is specified as a high-dimensional grid over the coefficient space, with equal or unequal intervals between successive points along the same dimension; the location of each point on the grid and the probability mass at that point are model parameters that need to be estimated. The framework does not require the analyst to specify the shape of the distribution prior to model estimation, but can approximate any multivariate probability distribution function to any arbitrary degree of accuracy. The grid with unequal intervals, in particular, offers greater flexibility than existing multivariate nonparametric specifications, while requiring the estimation of a small number of additional parameters. An expectation maximization algorithm is developed for the estimation of these models. Multiple synthetic datasets and a case study on travel mode choice behavior are used to demonstrate the value of the model framework and estimation algorithm. Compared to extant models that incorporate random taste heterogeneity through continuous mixture distributions, the proposed model provides better out-of-sample predictive ability. Findings reveal significant differences in willingness to pay measures between the proposed model and extant specifications. The case study further demonstrates the ability of the proposed model to endogenously recover patterns of attribute non-attendance and choice set formation.

Suggested Citation

  • Vij, Akshay & Krueger, Rico, 2017. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 76-101.
  • Handle: RePEc:eee:transb:v:106:y:2017:i:c:p:76-101
    DOI: 10.1016/j.trb.2017.10.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261516301138
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.trb.2017.10.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lewandowski, Daniel & Kurowicka, Dorota & Joe, Harry, 2009. "Generating random correlation matrices based on vines and extended onion method," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1989-2001, October.
    2. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
    3. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    4. Hess, Stephane & Train, Kenneth, 2017. "Correlation and scale in mixed logit models," Journal of choice modelling, Elsevier, vol. 23(C), pages 1-8.
    5. Fosgerau, Mogens & Bierlaire, Michel, 2007. "A practical test for the choice of mixing distribution in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 784-794, August.
    6. Fosgerau, Mogens & Mabit, Stefan L., 2013. "Easy and flexible mixture distributions," Economics Letters, Elsevier, vol. 120(2), pages 206-210.
    7. Williams, H. C. W. L. & Ortuzar, J. D., 1982. "Behavioural theories of dispersion and the mis-specification of travel demand models," Transportation Research Part B: Methodological, Elsevier, vol. 16(3), pages 167-219, June.
    8. 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.
    9. Scarpa, R. & Thiene, M. & Train, K., 2008. "Appendix to Utility in WTP space: a tool to address confounding random scale effects in destination choice to the Alps," American Journal of Agricultural Economics APPENDICES, Agricultural and Applied Economics Association, vol. 90(4), pages 1-9, January.
    10. William H. Greene & David A. Hensher, 2013. "Revealing additional dimensions of preference heterogeneity in a latent class mixed multinomial logit model," Applied Economics, Taylor & Francis Journals, vol. 45(14), pages 1897-1902, May.
    11. Ory, David T. & Mokhtarian, Patricia L., 2005. "When is getting there half the fun? Modeling the liking for travel," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(2-3), pages 97-123.
    12. 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.
    13. Moshe Ben-Akiva & André Palma & Daniel McFadden & Maya Abou-Zeid & Pierre-André Chiappori & Matthieu Lapparent & Steven Durlauf & Mogens Fosgerau & Daisuke Fukuda & Stephane Hess & Charles Manski & Ar, 2012. "Process and context in choice models," Marketing Letters, Springer, vol. 23(2), pages 439-456, June.
    14. Fosgerau, Mogens & Hess, Stephane, 2009. "A comparison of methods for representing random taste heterogeneity in discrete choice models," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 42, pages 1-25.
    15. Harris, Katherine M. & Keane, Michael P., 1998. "A model of health plan choice:: Inferring preferences and perceptions from a combination of revealed preference and attitudinal data," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 131-157, November.
    16. Fabian Bastin & Cinzia Cirillo & Philippe L. Toint, 2010. "Estimating Nonparametric Random Utility Models with an Application to the Value of Time in Heterogeneous Populations," Transportation Science, INFORMS, vol. 44(4), pages 537-549, November.
    17. Danny Campbell & David A. Hensher & Riccardo Scarpa, 2011. "Non-attendance to attributes in environmental choice analysis: a latent class specification," Journal of Environmental Planning and Management, Taylor & Francis Journals, vol. 54(8), pages 1061-1076, December.
    18. 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.
    19. Denzil G. Fiebig & Michael P. Keane & Jordan Louviere & Nada Wasi, 2010. "The Generalized Multinomial Logit Model: Accounting for Scale and Coefficient Heterogeneity," Marketing Science, INFORMS, vol. 29(3), pages 393-421, 05-06.
    20. Stephane Hess & Amanda Stathopoulos & Danny Campbell & Vikki O’Neill & Sebastian Caussade, 2013. "It’s not that I don’t care, I just don’t care very much: confounding between attribute non-attendance and taste heterogeneity," Transportation, Springer, vol. 40(3), pages 583-607, May.
    21. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
    22. Yuan, Yuan & You, Wen & Boyle, Kevin J., 2015. "A guide to heterogeneity features captured by parametric and nonparametric mixing distributions for the mixed logit model," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205733, Agricultural and Applied Economics Association.
    23. Greene, William H. & Hensher, David A., 2003. "A latent class model for discrete choice analysis: contrasts with mixed logit," Transportation Research Part B: Methodological, Elsevier, vol. 37(8), pages 681-698, September.
    24. Daniel McFadden, 1986. "The Choice Theory Approach to Market Research," Marketing Science, INFORMS, vol. 5(4), pages 275-297.
    25. 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.
    26. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.
    27. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 225-238.
    28. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    29. Train, Kenneth, 2016. "Mixed logit with a flexible mixing distribution," Journal of choice modelling, Elsevier, vol. 19(C), pages 40-53.
    30. Patrick Bajari & Jeremy T. Fox & Stephen P. Ryan, 2007. "Linear Regression Estimation of Discrete Choice Models with Nonparametric Distributions of Random Coefficients," American Economic Review, American Economic Association, vol. 97(2), pages 459-463, May.
    31. Cirillo, C. & Axhausen, K.W., 2006. "Evidence on the distribution of values of travel time savings from a six-week diary," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(5), pages 444-457, June.
    32. Ben-Akiva, M. & Bolduc, D. & Bradley, M., 1993. "Estimation of Travel Choice Models with Randomly Distributed Values of Time," Papers 9303, Laval - Recherche en Energie.
    33. Braun, Michael & McAuliffe, Jon, 2010. "Variational Inference for Large-Scale Models of Discrete Choice," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 324-335.
    34. Chandra R. Bhat, 2000. "Incorporating Observed and Unobserved Heterogeneity in Urban Work Travel Mode Choice Modeling," Transportation Science, INFORMS, vol. 34(2), pages 228-238, May.
    35. Cherchi, Elisabetta & Guevara, Cristian Angelo, 2012. "A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance–covariance matrix," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 321-332.
    36. 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.
    37. Swait, Joffre & Bernardino, Adriana, 2000. "Distinguishing taste variation from error structure in discrete choice data," Transportation Research Part B: Methodological, Elsevier, vol. 34(1), pages 1-15, January.
    38. Angel Bujosa & Antoni Riera & Robert Hicks, 2010. "Combining Discrete and Continuous Representations of Preference Heterogeneity: A Latent Class Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 47(4), pages 477-493, December.
    39. William Greene & David Hensher, 2010. "Does scale heterogeneity across individuals matter? An empirical assessment of alternative logit models," Transportation, Springer, vol. 37(3), pages 413-428, May.
    40. Chandra R. Bhat, 1997. "An Endogenous Segmentation Mode Choice Model with an Application to Intercity Travel," Transportation Science, INFORMS, vol. 31(1), pages 34-48, February.
    41. Michael Keane & Nada Wasi, 2013. "Comparing Alternative Models Of Heterogeneity In Consumer Choice Behavior," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 1018-1045, September.
    42. Riccardo Scarpa & Mara Thiene & Kenneth Train, 2008. "Utility in Willingness to Pay Space: A Tool to Address Confounding Random Scale Effects in Destination Choice to the Alps," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 90(4), pages 994-1010.
    43. Allenby, Greg M. & Rossi, Peter E., 1998. "Marketing models of consumer heterogeneity," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 57-78, November.
    44. Riccardo Scarpa & Timothy J. Gilbride & Danny Campbell & David A. Hensher, 2009. "Modelling attribute non-attendance in choice experiments for rural landscape valuation," European Review of Agricultural Economics, Foundation for the European Review of Agricultural Economics, vol. 36(2), pages 151-174, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Dubey, Subodh & Bansal, Prateek & Daziano, Ricardo A. & Guerra, Erick, 2020. "A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 114-141.
    2. Melvin Wong & Bilal Farooq, 2019. "Information processing constraints in travel behaviour modelling: A generative learning approach," Papers 1907.07036, arXiv.org, revised Jul 2019.
    3. Krueger, Rico & Rashidi, Taha H. & Vij, Akshay, 2020. "A Dirichlet process mixture model of discrete choice: Comparisons and a case study on preferences for shared automated vehicles," Journal of choice modelling, Elsevier, vol. 36(C).
    4. Vanaja, Shiuli, 2021. "Are People Making Correct Choices? Drivers of Water Source Choices in Rural Jharkhand, India," 2021 Conference, August 17-31, 2021, Virtual 315156, International Association of Agricultural Economists.
    5. Tinessa, Fiore & Marzano, Vittorio & Papola, Andrea, 2020. "Mixing distributions of tastes with a Combination of Nested Logit (CoNL) kernel: Formulation and performance analysis," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 1-23.
    6. Youssef M Aboutaleb & Mazen Danaf & Yifei Xie & Moshe Ben-Akiva, 2020. "Sparse Covariance Estimation in Logit Mixture Models," Papers 2001.05034, arXiv.org.
    7. Kim, Sung Hoo & Mokhtarian, Patricia L., 2023. "Finite mixture (or latent class) modeling in transportation: Trends, usage, potential, and future directions," Transportation Research Part B: Methodological, Elsevier, vol. 172(C), pages 134-173.
    8. Bansal, Prateek & Hurtubia, Ricardo & Tirachini, Alejandro & Daziano, Ricardo A., 2019. "Flexible estimates of heterogeneity in crowding valuation in the New York City subway," Journal of choice modelling, Elsevier, vol. 31(C), pages 124-140.
    9. Bansal, Prateek & Krueger, Rico & Bierlaire, Michel & Daziano, Ricardo A. & Rashidi, Taha H., 2020. "Bayesian estimation of mixed multinomial logit models: Advances and simulation-based evaluations," Transportation Research Part B: Methodological, Elsevier, vol. 131(C), pages 124-142.
    10. Beeramoole, Prithvi Bhat & Arteaga, Cristian & Pinz, Alban & Haque, Md Mazharul & Paz, Alexander, 2023. "Extensive hypothesis testing for estimation of mixed-Logit models," Journal of choice modelling, Elsevier, vol. 47(C).
    11. Rico Krueger & Taha H. Rashidi & Akshay Vij, 2019. "Semi-Parametric Hierarchical Bayes Estimates of New Yorkers' Willingness to Pay for Features of Shared Automated Vehicle Services," Papers 1907.09639, arXiv.org.
    12. Jourdain, Damien & Lairez, Juliette & Striffler, Bruno & Lundhede, Thomas, 2022. "A choice experiment approach to evaluate maize farmers’ decision-making processes in Lao PDR," Journal of choice modelling, Elsevier, vol. 44(C).
    13. Bansal, Prateek & Daziano, Ricardo A & Guerra, Erick, 2018. "Minorization-Maximization (MM) algorithms for semiparametric logit models: Bottlenecks, extensions, and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 17-40.
    14. Danaf, Mazen & Atasoy, Bilge & Ben-Akiva, Moshe, 2020. "Logit mixture with inter and intra-consumer heterogeneity and flexible mixing distributions," Journal of choice modelling, Elsevier, vol. 35(C).
    15. Ke Wang & Chandra R. Bhat & Xin Ye, 2023. "A multinomial probit analysis of shanghai commute mode choice," Transportation, Springer, vol. 50(4), pages 1471-1495, August.
    16. Rico Krueger & Akshay Vij & Taha H. Rashidi, 2018. "A Dirichlet Process Mixture Model of Discrete Choice," Papers 1801.06296, arXiv.org.
    17. Hynes, S. & Ankamah-Yeboah, I. & O’Neill, S. & Needham, K. & Bich Xuan, B. & Armstrong, C., 2020. "Entropy balancing for causal effects in discrete choice analysis: The Blue Planet II effect," Working Papers 309500, National University of Ireland, Galway, Socio-Economic Marine Research Unit.
    18. S. Van Cranenburgh & S. Wang & A. Vij & F. Pereira & J. Walker, 2021. "Choice modelling in the age of machine learning -- discussion paper," Papers 2101.11948, arXiv.org, revised Nov 2021.
    19. Sfeir, Georges & Abou-Zeid, Maya & Rodrigues, Filipe & Pereira, Francisco Camara & Kaysi, Isam, 2021. "Latent class choice model with a flexible class membership component: A mixture model approach," Journal of choice modelling, Elsevier, vol. 41(C).
    20. Subodh Dubey & Prateek Bansal & Ricardo A. Daziano & Erick Guerra, 2019. "A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel," Papers 1904.08332, arXiv.org, revised Jan 2020.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akshay Vij & Rico Krueger, 2018. "Random taste heterogeneity in discrete choice models: Flexible nonparametric finite mixture distributions," Papers 1802.02299, arXiv.org.
    2. Rico Krueger & Akshay Vij & Taha H. Rashidi, 2018. "A Dirichlet Process Mixture Model of Discrete Choice," Papers 1801.06296, arXiv.org.
    3. Krueger, Rico & Rashidi, Taha H. & Vij, Akshay, 2020. "A Dirichlet process mixture model of discrete choice: Comparisons and a case study on preferences for shared automated vehicles," Journal of choice modelling, Elsevier, vol. 36(C).
    4. Rico Krueger & Taha H. Rashidi & Akshay Vij, 2019. "Semi-Parametric Hierarchical Bayes Estimates of New Yorkers' Willingness to Pay for Features of Shared Automated Vehicle Services," Papers 1907.09639, arXiv.org.
    5. Tinessa, Fiore & Marzano, Vittorio & Papola, Andrea, 2020. "Mixing distributions of tastes with a Combination of Nested Logit (CoNL) kernel: Formulation and performance analysis," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 1-23.
    6. Stephane Hess, 2014. "Latent class structures: taste heterogeneity and beyond," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 14, pages 311-330, Edward Elgar Publishing.
    7. Bansal, Prateek & Daziano, Ricardo A. & Achtnicht, Martin, 2018. "Comparison of parametric and semiparametric representations of unobserved preference heterogeneity in logit models," Journal of choice modelling, Elsevier, vol. 27(C), pages 97-113.
    8. Bansal, Prateek & Daziano, Ricardo A & Guerra, Erick, 2018. "Minorization-Maximization (MM) algorithms for semiparametric logit models: Bottlenecks, extensions, and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 17-40.
    9. Doherty, Edel & Campbell, Danny & Hynes, Stephen, 2012. "Exploring cost heterogeneity in recreational demand," Working Papers 148832, National University of Ireland, Galway, Socio-Economic Marine Research Unit.
    10. Sfeir, Georges & Abou-Zeid, Maya & Rodrigues, Filipe & Pereira, Francisco Camara & Kaysi, Isam, 2021. "Latent class choice model with a flexible class membership component: A mixture model approach," Journal of choice modelling, Elsevier, vol. 41(C).
    11. Riccardo Scarpa & Cristiano Franceschinis & Mara Thiene, 2017. "A Monte Carlo Evaluation of the Logit-Mixed Logit under Asymmetry and Multimodality," Working Papers in Economics 17/23, University of Waikato.
    12. Beeramoole, Prithvi Bhat & Arteaga, Cristian & Pinz, Alban & Haque, Md Mazharul & Paz, Alexander, 2023. "Extensive hypothesis testing for estimation of mixed-Logit models," Journal of choice modelling, Elsevier, vol. 47(C).
    13. Youssef M Aboutaleb & Mazen Danaf & Yifei Xie & Moshe Ben-Akiva, 2020. "Sparse Covariance Estimation in Logit Mixture Models," Papers 2001.05034, arXiv.org.
    14. Edel Doherty & Danny Campbell & Stephen Hynes, 2013. "Models of Site-choice for Walks in Rural Ireland: Exploring Cost Heterogeneity," Journal of Agricultural Economics, Wiley Blackwell, vol. 64(2), pages 446-466, June.
    15. Robert J. Johnston & Kevin J. Boyle & Wiktor (Vic) Adamowicz & Jeff Bennett & Roy Brouwer & Trudy Ann Cameron & W. Michael Hanemann & Nick Hanley & Mandy Ryan & Riccardo Scarpa & Roger Tourangeau & Ch, 2017. "Contemporary Guidance for Stated Preference Studies," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 4(2), pages 319-405.
    16. Mara Thiene & Riccardo Scarpa & Jordan Louviere, 2015. "Addressing Preference Heterogeneity, Multiple Scales and Attribute Attendance with a Correlated Finite Mixing Model of Tap Water Choice," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 62(3), pages 637-656, November.
    17. Sarrias, Mauricio & Daziano, Ricardo, 2017. "Multinomial Logit Models with Continuous and Discrete Individual Heterogeneity in R: The gmnl Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i02).
    18. Danaf, Mazen & Atasoy, Bilge & Ben-Akiva, Moshe, 2020. "Logit mixture with inter and intra-consumer heterogeneity and flexible mixing distributions," Journal of choice modelling, Elsevier, vol. 35(C).
    19. Caputo, Vincenzina & Scarpa, Riccardo & Nayga, Rodolfo M. & Ortega, David L., 2018. "Are preferences for food quality attributes really normally distributed? An analysis using flexible mixing distributions," Journal of choice modelling, Elsevier, vol. 28(C), pages 10-27.
    20. David Throsby & Anita Zednik & Jorge E. Araña, 2021. "Public preferences for heritage conservation strategies: a choice modelling approach," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 45(3), pages 333-358, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:106:y:2017:i:c:p:76-101. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.