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Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models

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  • Tinessa, Fiore

Abstract

This paper investigates the class of random utility models (RUM) derived under the assumption of random utilities or disutilities following mixture distributions. We introduce a general framework embedding the models of Mattsson et al. (2014) and the q-product GEV model of Chikaraishi and Nakayama, (2016) while extending the investigations of Papola (2016). New closed-form models are obtained, with mixtures of covariance matrices, mathematical forms of utility (additive, multiplicative or in-between), variances of utilities (heteroscedasticity) and marginal distributions. The models are compared in two cross-validation exercises, based on a real dataset of travel mode preferences, outperforming existing heteroscedastic and homoscedastic closed-form models in terms of both in-sample and out-of-sample goodness of fit. The behavioural implications of the models are also discussed.

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  • Tinessa, Fiore, 2021. "Closed-form random utility models with mixture distributions of random utilities: Exploring finite mixtures of qGEV models," Transportation Research Part B: Methodological, Elsevier, vol. 146(C), pages 262-288.
    • Handle: RePEc:eee:transb:v:146:y:2021:i:c:p:262-288
    DOI: 10.1016/j.trb.2021.02.004
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    1. Castillo, Enrique & Menéndez, José María & Jiménez, Pilar & Rivas, Ana, 2008. "Closed form expressions for choice probabilities in the Weibull case," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 373-380, May.
    2. Papola, Andrea & Tinessa, Fiore & Marzano, Vittorio, 2018. "Application of the Combination of Random Utility Models (CoRUM) to route choice," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 304-326.
    3. 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.
    4. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    5. 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.
    6. Yao, Jia & Chen, Anthony, 2014. "An analysis of logit and weibit route choices in stochastic assignment paradox," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 31-49.
    7. Small, Kenneth A, 1987. "A Discrete Choice Model for Ordered Alternatives," Econometrica, Econometric Society, vol. 55(2), pages 409-424, March.
    8. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, September.
    9. Abbe, E. & Bierlaire, M. & Toledo, T., 2007. "Normalization and correlation of cross-nested logit models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 795-808, August.
    10. Kitthamkesorn, Songyot & Chen, Anthony, 2017. "Alternate weibit-based model for assessing green transport systems with combined mode and route travel choices," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 291-310.
    11. 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.
    12. Hess, Stephane & Train, Kenneth, 2017. "Correlation and scale in mixed logit models," Journal of choice modelling, Elsevier, vol. 23(C), pages 1-8.
    13. Bhat, Chandra R., 1995. "A heteroscedastic extreme value model of intercity travel mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 471-483, December.
    14. Ennio Cascetta, 2009. "Transportation Systems Analysis," Springer Optimization and Its Applications, Springer, number 978-0-387-75857-2, June.
    15. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    16. Koppelman, Frank S. & Wen, Chieh-Hua, 2000. "The paired combinatorial logit model: properties, estimation and application," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 75-89, February.
    17. Keane, Michael P, 1992. "A Note on Identification in the Multinomial Probit Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 193-200, April.
    18. Steckel, Joel H & Vanhonacker, Wilfried R, 1988. "A Heterogeneous Conditional Logit Model of Choice," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 391-398, July.
    19. Papola, Andrea, 2016. "A new random utility model with flexible correlation pattern and closed-form covariance expression: The CoRUM," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 80-96.
    20. Xu, Xiangdong & Chen, Anthony & Kitthamkesorn, Songyot & Yang, Hai & Lo, Hong K., 2015. "Modeling absolute and relative cost differences in stochastic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 686-703.
    21. Joan L. Walker & Moshe Ben-Akiva & Denis Bolduc, 2007. "Identification of parameters in normal error component logit-mixture (NECLM) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1095-1125.
    22. Swait, Joffre, 2003. "Flexible Covariance Structures for Categorical Dependent Variables through Finite Mixtures of Generalized Extreme Value Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 80-87, January.
    23. 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.
    24. 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.
    25. 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.
    26. Papola, Andrea, 2004. "Some developments on the cross-nested logit model," Transportation Research Part B: Methodological, Elsevier, vol. 38(9), pages 833-851, November.
    27. Stephane Hess & Amanda Stathopoulos & Andrew Daly, 2012. "Allowing for heterogeneous decision rules in discrete choice models: an approach and four case studies," Transportation, Springer, vol. 39(3), pages 565-591, May.
    28. 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.
    29. Brathwaite, Timothy & Walker, Joan L., 2018. "Asymmetric, closed-form, finite-parameter models of multinomial choice," Journal of choice modelling, Elsevier, vol. 29(C), pages 78-112.
    30. Patil, Priyadarshan N. & Dubey, Subodh K. & Pinjari, Abdul R. & Cherchi, Elisabetta & Daziano, Ricardo & Bhat, Chandra R., 2017. "Simulation evaluation of emerging estimation techniques for multinomial probit models," Journal of choice modelling, Elsevier, vol. 23(C), pages 9-20.
    31. Swait, Joffre & Adamowicz, Wiktor, 2001. "Choice Environment, Market Complexity, and Consumer Behavior: A Theoretical and Empirical Approach for Incorporating Decision Complexity into Models of Consumer Choice," Organizational Behavior and Human Decision Processes, Elsevier, vol. 86(2), pages 141-167, November.
    32. Marzano, Vittorio & Papola, Andrea & Simonelli, Fulvio & Vitillo, Roberta, 2013. "A practically tractable expression of the covariances of the Cross-Nested Logit model," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 1-11.
    33. Borges, Ernesto P., 2004. "A possible deformed algebra and calculus inspired in nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 95-101.
    34. Jordan J. Louviere & Towhidul Islam & Nada Wasi & Deborah Street & Leonie Burgess, 2008. "Designing Discrete Choice Experiments: Do Optimal Designs Come at a Price?," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 35(2), pages 360-375, March.
    35. Nakayama, Shoichiro & Chikaraishi, Makoto, 2015. "Unified closed-form expression of logit and weibit and its extension to a transportation network equilibrium assignment," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 672-685.
    36. 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.
    37. 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.
    38. Recker, W. W., 1995. "Discrete choice with an oddball alternative," Transportation Research Part B: Methodological, Elsevier, vol. 29(3), pages 201-211, June.
    39. Marzano, Vittorio & Papola, Andrea, 2008. "On the covariance structure of the Cross-Nested Logit model," Transportation Research Part B: Methodological, Elsevier, vol. 42(2), pages 83-98, February.
    40. Munizaga, Marcela A. & Heydecker, Benjamin G. & Ortúzar, Juan de Dios, 2000. "Representation of heteroskedasticity in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 34(3), pages 219-240, April.
    41. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    42. Michel Bierlaire, 2006. "A theoretical analysis of the cross-nested logit model," Annals of Operations Research, Springer, vol. 144(1), pages 287-300, April.
    43. Marzano, Vittorio, 2014. "A simple procedure for the calculation of the covariances of any Generalized Extreme Value model," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 151-162.
    44. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    45. 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.
    46. 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.
    47. 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.
    48. Robert Ishaq & Shlomo Bekhor & Yoram Shiftan, 2013. "A flexible model structure approach for discrete choice models," Transportation, Springer, vol. 40(3), pages 609-624, May.
    49. Wen, Chieh-Hua & Wang, Wei-Chung & Fu, Chiang, 2012. "Latent class nested logit model for analyzing high-speed rail access mode choice," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 545-554.
    50. 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.
    51. Yai, Tetsuo & Iwakura, Seiji & Morichi, Shigeru, 1997. "Multinomial probit with structured covariance for route choice behavior," Transportation Research Part B: Methodological, Elsevier, vol. 31(3), pages 195-207, June.
    52. Fosgerau, M. & Bierlaire, M., 2009. "Discrete choice models with multiplicative error terms," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 494-505, June.
    53. del Castillo, J.M., 2016. "A class of RUM choice models that includes the model in which the utility has logistic distributed errors," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 1-20.
    54. 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.
    55. Wagner A. Kamakura & Byung-Do Kim & Jonathan Lee, 1996. "Modeling Preference and Structural Heterogeneity in Consumer Choice," Marketing Science, INFORMS, vol. 15(2), pages 152-172.
    56. Bunch, David S., 1991. "Estimability in the Multinomial Probit Model," University of California Transportation Center, Working Papers qt1gf1t128, University of California Transportation Center.
    57. Bunch, David S., 1991. "Estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 25(1), pages 1-12, February.
    58. Chikaraishi, Makoto & Nakayama, Shoichiro, 2016. "Discrete choice models with q-product random utilities," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 576-595.
    59. Newman, Jeffrey P., 2008. "Normalization of network generalized extreme value models," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 958-969, December.
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