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A new mixed MNP model accommodating a variety of dependent non-normal coefficient distributions

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  • Chandra R. Bhat

    (The University of Texas at Austin
    The Hong Kong Polytechnic University)

  • Patrícia S. Lavieri

    (The University of Texas at Austin)

Abstract

In this paper, we propose a general copula approach to accommodate non-normal continuous mixing distributions in multinomial probit models. In particular, we specify a multivariate mixing distribution that allows different marginal continuous parametric distributions for different coefficients. A new hybrid estimation technique is proposed to estimate the model, which combines the advantageous features of each of the maximum simulated likelihood inference technique and Bhat’s maximum approximate composite marginal likelihood inference approach. The effectiveness of our formulation and inference approach is demonstrated through simulation exercises and an empirical application.

Suggested Citation

  • Chandra R. Bhat & Patrícia S. Lavieri, 2018. "A new mixed MNP model accommodating a variety of dependent non-normal coefficient distributions," Theory and Decision, Springer, vol. 84(2), pages 239-275, March.
    • Handle: RePEc:kap:theord:v:84:y:2018:i:2:d:10.1007_s11238-017-9638-4
    DOI: 10.1007/s11238-017-9638-4
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    as
    1. Robert Bartels & Denzil Fiebig & Arthur Soest, 2006. "Consumers and experts: an econometric analysis of the demand for water heaters," Empirical Economics, Springer, vol. 31(2), pages 369-391, June.
    2. Torres, Cati & Hanley, Nick & Riera, Antoni, 2011. "How wrong can you be? Implications of incorrect utility function specification for welfare measurement in choice experiments," Journal of Environmental Economics and Management, Elsevier, vol. 62(1), pages 111-121, July.
    3. Ho, Chinh & Mulley, Corinne, 2015. "Intra-household Interactions in tour-based mode choice: The role of social, temporal, spatial and resource constraints," Transport Policy, Elsevier, vol. 38(C), pages 52-63.
    4. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
    5. Bhat, Chandra R. & Guo, Jessica Y., 2007. "A comprehensive analysis of built environment characteristics on household residential choice and auto ownership levels," Transportation Research Part B: Methodological, Elsevier, vol. 41(5), pages 506-526, June.
    6. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    7. 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.
    8. Cristiano Varin & Paolo Vidoni, 2005. "A note on composite likelihood inference and model selection," Biometrika, Biometrika Trust, vol. 92(3), pages 519-528, September.
    9. David Revelt & Kenneth Train, 1998. "Mixed Logit With Repeated Choices: Households' Choices Of Appliance Efficiency Level," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 647-657, November.
    10. 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.
    11. Bhat, Chandra R. & Dubey, Subodh K. & Nagel, Kai, 2015. "Introducing non-normality of latent psychological constructs in choice modeling with an application to bicyclist route choice," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 341-363.
    12. 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.
    13. Mittelhammer, Ron C. & Judge, George, 2011. "A family of empirical likelihood functions and estimators for the binary response model," Journal of Econometrics, Elsevier, vol. 164(2), pages 207-217, October.
    14. Francisco Amador & Rosa González & Juan Ortúzar, 2005. "Preference Heterogeneity and Willingness to Pay for Travel Time Savings," Transportation, Springer, vol. 32(6), pages 627-647, November.
    15. Bhat, Chandra R., 2014. "The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models," Foundations and Trends(R) in Econometrics, now publishers, vol. 7(1), pages 1-117, July.
    16. Balcombe, Kelvin & Chalak, Ali & Fraser, Iain, 2009. "Model selection for the mixed logit with Bayesian estimation," Journal of Environmental Economics and Management, Elsevier, vol. 57(2), pages 226-237, March.
    17. Bhat, Chandra R. & Sener, Ipek N. & Eluru, Naveen, 2010. "A flexible spatially dependent discrete choice model: Formulation and application to teenagers' weekday recreational activity participation," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 903-921, September.
    18. Small, Kenneth A., 2012. "Valuation of travel time," Economics of Transportation, Elsevier, vol. 1(1), pages 2-14.
    19. Bhat, Chandra R. & Eluru, Naveen, 2009. "A copula-based approach to accommodate residential self-selection effects in travel behavior modeling," Transportation Research Part B: Methodological, Elsevier, vol. 43(7), pages 749-765, August.
    20. Kyoo il Kim, 2014. "Identification of the Distribution of Random Coefficients in Static and Dynamic Discrete Choice Models," Korean Economic Review, Korean Economic Association, vol. 30, pages 191-216.
    21. Wang, Rui, 2015. "The stops made by commuters: evidence from the 2009 US National Household Travel Survey," Journal of Transport Geography, Elsevier, vol. 47(C), pages 109-118.
    22. 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.
    23. McFadden, Daniel, 1974. "The measurement of urban travel demand," Journal of Public Economics, Elsevier, vol. 3(4), pages 303-328, November.
    24. Bhat, Chandra R., 1997. "Work travel mode choice and number of non-work commute stops," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 41-54, February.
    25. 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.
    26. Paleti, Rajesh & Bhat, Chandra R., 2013. "The composite marginal likelihood (CML) estimation of panel ordered-response models," Journal of choice modelling, Elsevier, vol. 7(C), pages 24-43.
    27. Antonella Capitanio, 2010. "On the approximation of the tail probability of the scalar skew-normal distribution," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-308.
    28. Bhat, Chandra R. & Sardesai, Rupali, 2006. "The impact of stop-making and travel time reliability on commute mode choice," Transportation Research Part B: Methodological, Elsevier, vol. 40(9), pages 709-730, November.
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    Cited by:

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    2. 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.
    3. Bhat, Chandra R. & Mondal, Aupal, 2022. "A New Flexible Generalized Heterogeneous Data Model (GHDM) with an Application to Examine the Effect of High Density Neighborhood Living on Bicycling Frequency," Transportation Research Part B: Methodological, Elsevier, vol. 164(C), pages 244-266.
    4. 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.
    5. Saxena, Shobhit & Bhat, Chandra R. & Pinjari, Abdul Rawoof, 2023. "Separation-based parameterization strategies for estimation of restricted covariance matrices in multivariate model systems," Journal of choice modelling, Elsevier, vol. 47(C).
    6. 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.
    7. I. G. Ukpong & K. G. Balcombe & I. M. Fraser & F. J. Areal, 2019. "Preferences for Mitigation of the Negative Impacts of the Oil and Gas Industry in the Niger Delta Region of Nigeria," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 74(2), pages 811-843, October.
    8. Prateek Bansal & Rico Krueger & Michel Bierlaire & Ricardo A. Daziano & Taha H. Rashidi, 2019. "Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluations," Papers 1904.03647, arXiv.org, revised Dec 2019.

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