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Extending the logit-mixed logit model for a combination of random and fixed parameters

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  • Bansal, Prateek
  • Daziano, Ricardo A.
  • Achtnicht, Martin

Abstract

The logit-mixed logit (LML) model, which allows the analyst to semi-parametrically specify the mixing distribution of preference heterogeneity, is a very recent advancement in logit-type choice models. In addition to generalize many previous semi- and non-parametric specifications, LML is computationally very efficient due to a computationally-convenient likelihood equation that does not require computation of choice probabilities in iterative optimization. However, the original LML formulation assumes all utility parameters to be random. This study extends LML to a combination of fixed and random parameters (LML-FR), and motivates such combination in random parameter choice models in general. We further show that the likelihood of the LML-FR specification loses its special properties, leading to a much higher estimation time. In an empirical application about preferences for alternative fuel vehicles in China, estimation time increased by a factor of 20–40 when introducing fixed parameters. Despite losses in computation efficiency, we show that the flexibility of LML-FR is essential for retrieving eventual multimodality of mixing distributions.

Suggested Citation

  • Bansal, Prateek & Daziano, Ricardo A. & Achtnicht, Martin, 2018. "Extending the logit-mixed logit model for a combination of random and fixed parameters," Journal of choice modelling, Elsevier, vol. 27(C), pages 88-96.
    • Handle: RePEc:eee:eejocm:v:27:y:2018:i:c:p:88-96
    DOI: 10.1016/j.jocm.2017.10.001
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    1. Fosgerau, Mogens & Mabit, Stefan L., 2013. "Easy and flexible mixture distributions," Economics Letters, Elsevier, vol. 120(2), pages 206-210.
    2. 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.
    3. 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.
    4. Bunch, David S. & Bradley, Mark & Golob, Thomas F. & Kitamura, Ryuichi & Occhiuzzo, Gareth P., 1993. "Demand for clean-fuel vehicles in California: A discrete-choice stated preference pilot project," Transportation Research Part A: Policy and Practice, Elsevier, vol. 27(3), pages 237-253, May.
    5. Jeremy T. Fox & Kyoo il Kim & Stephen P. Ryan & Patrick Bajari, 2011. "A simple estimator for the distribution of random coefficients," Quantitative Economics, Econometric Society, vol. 2(3), pages 381-418, November.
    6. 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.
    7. 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).
    8. Train, Kenneth, 2016. "Mixed logit with a flexible mixing distribution," Journal of choice modelling, Elsevier, vol. 19(C), pages 40-53.
    9. 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.
    10. 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.
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    Cited by:

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    4. 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.
    5. 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.
    6. Renato Perez Loyola & Erda Wang & Nannan Kang, 2021. "Economic valuation of recreational attributes using a choice experiment approach: An application to the Galapagos Islands," Tourism Economics, , vol. 27(1), pages 86-104, February.
    7. 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.
    8. 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.
    9. Sergio Colombo & Wiktor Budziński & Mikołaj Czajkowski & Klaus Glenk, 2020. "Ex-ante and ex-post measures to mitigate hypothetical bias. Are they alternative or complementary tools to increase the reliability and validity of DCE estimates?," Working Papers 2020-20, Faculty of Economic Sciences, University of Warsaw.
    10. Daziano, Ricardo A., 2020. "Flexible customer willingness to pay for bundled smart home energy products and services," Resource and Energy Economics, Elsevier, vol. 61(C).
    11. Riccardo Scarpa & Cristiano Franceschinis & Mara Thiene, 2021. "Logit Mixed Logit Under Asymmetry and Multimodality of WTP: A Monte Carlo Evaluation," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(2), pages 643-662, March.
    12. 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.
    13. 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.
    14. 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.
    15. Mallikarjun Patil & Bandhan Bandhu Majumdar & Prasanta Kumar Sahu & Long T. Truong, 2021. "Evaluation of Prospective Users’ Choice Decision toward Electric Two-Wheelers Using a Stated Preference Survey: An Indian Perspective," Sustainability, MDPI, vol. 13(6), pages 1-22, March.
    16. 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.

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