IDEAS home Printed from https://ideas.repec.org/a/eee/eejocm/v23y2017icp9-20.html
   My bibliography  Save this article

Simulation evaluation of emerging estimation techniques for multinomial probit models

Author

Listed:
  • Patil, Priyadarshan N.
  • Dubey, Subodh K.
  • Pinjari, Abdul R.
  • Cherchi, Elisabetta
  • Daziano, Ricardo
  • Bhat, Chandra R.

Abstract

A simulation evaluation is presented to compare alternative estimation techniques for a five-alternative multinomial probit (MNP) model with random parameters, including cross-sectional and panel datasets and for scenarios with and without correlation among random parameters. The different estimation techniques assessed are: (1) The maximum approximate composite marginal likelihood (MACML) approach; (2) The Geweke-Hajivassiliou-Keane (GHK) simulator with Halton sequences, implemented in conjunction with the composite marginal likelihood (CML) estimation approach; (3) The GHK approach with sparse grid nodes and weights, implemented in conjunction with the composite marginal likelihood (CML) estimation approach; and (4) a Bayesian Markov Chain Monte Carlo (MCMC) approach. In addition, for comparison purposes, the GHK simulator with Halton sequences was implemented in conjunction with the traditional, full information maximum likelihood approach as well. The results indicate that the MACML approach provided the best performance in terms of the accuracy and precision of parameter recovery and estimation time for all data generation settings considered in this study. For panel data settings, the GHK approach with Halton sequences, when combined with the CML approach, provided better performance than when implemented with the full information maximum likelihood approach, albeit not better than the MACML approach. The sparse grid approach did not perform well in recovering the parameters as the dimension of integration increased, particularly so with the panel datasets. The Bayesian MCMC approach performed well in datasets without correlations among random parameters, but exhibited limitations in datasets with correlated parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:eejocm:v:23:y:2017:i:c:p:9-20
    DOI: 10.1016/j.jocm.2017.01.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1755534515300890
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jocm.2017.01.007?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. Bhat, Chandra R., 1998. "Accommodating variations in responsiveness to level-of-service measures in travel mode choice modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(7), pages 495-507, September.
    2. Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    3. McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
    4. Bhat, Chandra R. & Sidharthan, Raghuprasad, 2011. "A simulation evaluation of the maximum approximate composite marginal likelihood (MACML) estimator for mixed multinomial probit models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 940-953, August.
    5. Brownstone, David & Train, Kenneth, 1998. "Forecasting new product penetration with flexible substitution patterns," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 109-129, November.
    6. Yiyi Wang & Kara Kockelman & Paul Damien, 2014. "A spatial autoregressive multinomial probit model for anticipating land-use change in Austin, Texas," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(1), pages 251-278, January.
    7. Imai, Kosuke & van Dyk, David A., 2005. "A Bayesian analysis of the multinomial probit model using marginal data augmentation," Journal of Econometrics, Elsevier, vol. 124(2), pages 311-334, February.
    8. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," University of California Transportation Center, Working Papers qt3tb6j874, University of California Transportation Center.
    9. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Paper 321, Department of Economics, University of Pittsburgh, revised Jan 2007.
    10. 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.
    11. Chandra Bhat, 2015. "A new spatial (social) interaction discrete choice model accommodating for unobserved effects due to endogenous network formation," Transportation, Springer, vol. 42(5), pages 879-914, September.
    12. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
    13. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    14. Abay, Kibrom A., 2015. "Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariate binary probit models," Economics Letters, Elsevier, vol. 126(C), pages 51-56.
    15. 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.
    16. 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.
    17. Siddhartha Chib & Edward Greenberg & Yuxin Chen, 1998. "MCMC Methods for Fitting and Comparing Multinomial Response Models," Econometrics 9802001, University Library of Munich, Germany, revised 06 May 1998.
    18. Bhat, Chandra R., 2003. "Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 837-855, November.
    19. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    20. 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.
    21. Zhang, Xiao & Boscardin, W. John & Belin, Thomas R., 2008. "Bayesian analysis of multivariate nominal measures using multivariate multinomial probit models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3697-3708, March.
    22. Brownstone, David & Train, Kenneth, 1999. "Forecasting new product penetration with flexible substitution patterns," University of California Transportation Center, Working Papers qt1j6814b3, University of California Transportation Center.
    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. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    3. Prateek Bansal & Vahid Keshavarzzadeh & Angelo Guevara & Shanjun Li & Ricardo A Daziano, 2022. "Designed quadrature to approximate integrals in maximum simulated likelihood estimation [Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariat," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 301-321.
    4. Batram, Manuel & Bauer, Dietmar, 2019. "On consistency of the MACML approach to discrete choice modelling," Journal of choice modelling, Elsevier, vol. 30(C), pages 1-16.
    5. Laurent GOMEZ, 2024. "La mobilité quotidienne des immigrés en France," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 59, pages 79-107.
    6. Blake, Miranda R. & Dubey, Subodh & Swait, Joffre & Lancsar, Emily & Ghijben, Peter, 2020. "An integrated modelling approach examining the influence of goals, habit and learning on choice using visual attention data," Journal of Business Research, Elsevier, vol. 117(C), pages 44-57.
    7. 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.
    8. 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.
    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. Kerem Tuzcuoglu, 2019. "Composite Likelihood Estimation of an Autoregressive Panel Probit Model with Random Effects," Staff Working Papers 19-16, Bank of Canada.
    11. Rodrigues, Filipe, 2022. "Scaling Bayesian inference of mixed multinomial logit models to large datasets," Transportation Research Part B: Methodological, Elsevier, vol. 158(C), pages 1-17.
    12. Biswas, Mehek & Bhat, Chandra R. & Ghosh, Sulagna & Pinjari, Abdul Rawoof, 2024. "Choice models with stochastic variables and random coefficients," Journal of choice modelling, Elsevier, vol. 51(C).
    13. Ke Wang & Xin Ye, 2021. "Development of alternative stochastic frontier models for estimating time-space prism vertices," Transportation, Springer, vol. 48(2), pages 773-807, April.
    14. Stéphanie Souche, 2023. "Which transport modes do people use for travelling to coworking spaces (CWSs)?," Post-Print halshs-04010016, HAL.
    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. 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.
    17. Daniel Rodenburger, 2024. "Refining analytic approximation based estimation of mixed multinomial probit models by parameter selection," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(4), pages 411-425, May.
    18. 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.
    19. Bhat, Chandra R., 2018. "New matrix-based methods for the analytic evaluation of the multivariate cumulative normal distribution function," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 238-256.
    20. Becker, Felix & Danaf, Mazen & Song, Xiang & Atasoy, Bilge & Ben-Akiva, Moshe, 2018. "Bayesian estimator for Logit Mixtures with inter- and intra-consumer heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 1-17.
    21. 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. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    2. Bhat, Chandra R., 2018. "New matrix-based methods for the analytic evaluation of the multivariate cumulative normal distribution function," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 238-256.
    3. Prateek Bansal & Vahid Keshavarzzadeh & Angelo Guevara & Shanjun Li & Ricardo A Daziano, 2022. "Designed quadrature to approximate integrals in maximum simulated likelihood estimation [Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariat," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 301-321.
    4. Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    5. Ziegler Andreas, 2010. "Z-Tests in Multinomial Probit Models under Simulated Maximum Likelihood Estimation: Some Small Sample Properties," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(5), pages 630-652, October.
    6. Campbell, Danny & Hutchinson, W. George & Scarpa, Riccardo, 2006. "Using Discrete Choice Experiments to Derive Individual-Specific WTP Estimates for Landscape Improvements under Agri-Environmental Schemes: Evidence from the Rural Environment Protection Scheme in Irel," Sustainability Indicators and Environmental Valuation Working Papers 12220, Fondazione Eni Enrico Mattei (FEEM).
    7. Ricardo A. Daziano & Martin Achtnicht, 2014. "Forecasting Adoption of Ultra-Low-Emission Vehicles Using Bayes Estimates of a Multinomial Probit Model and the GHK Simulator," Transportation Science, INFORMS, vol. 48(4), pages 671-683, November.
    8. Bliemer, Michiel C.J. & Rose, John M., 2010. "Construction of experimental designs for mixed logit models allowing for correlation across choice observations," Transportation Research Part B: Methodological, Elsevier, vol. 44(6), pages 720-734, July.
    9. 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.
    10. Haghani, Milad & Bliemer, Michiel C.J. & Hensher, David A., 2021. "The landscape of econometric discrete choice modelling research," Journal of choice modelling, Elsevier, vol. 40(C).
    11. Sándor, Zsolt & Train, Kenneth, 2004. "Quasi-random simulation of discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 313-327, May.
    12. Campbell, Danny, 2007. "Combining mixed logit models and random effects models to identify the determinants of willingness to pay for rural landscape improvements," 81st Annual Conference, April 2-4, 2007, Reading University, UK 7975, Agricultural Economics Society.
    13. Danny Campbell & George Hutchinson & Riccardo Scarpa, 2006. "Using mixed logit models to derive individual-specific WTP estimates for landscape improvements under agri-environmental schemes: evidence from the Rural Environment Protection Scheme in Ireland," Working Papers 0607, Rural Economy and Development Programme,Teagasc.
    14. Karthik K. Srinivasan & Hani S. Mahmassani, 2005. "A Dynamic Kernel Logit Model for the Analysis of Longitudinal Discrete Choice Data: Properties and Computational Assessment," Transportation Science, INFORMS, vol. 39(2), pages 160-181, May.
    15. Bhat, Chandra & Zhao, Huimin, 2002. "The spatial analysis of activity stop generation," Transportation Research Part B: Methodological, Elsevier, vol. 36(6), pages 557-575, July.
    16. Danny Campbell & George Hutchinson & Riccardo Scarpa, 2006. "Integrating landscape improvement indices and discrete choice experiments: evidence from the Rural Environment Protection Scheme in Ireland," Working Papers 0609, Rural Economy and Development Programme,Teagasc.
    17. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
    18. Solomon Tarfasa & Roy Brouwer, 2013. "Estimation of the public benefits of urban water supply improvements in Ethiopia: a choice experiment," Applied Economics, Taylor & Francis Journals, vol. 45(9), pages 1099-1108, March.
    19. Stephane Hess & John W. Polak, 2004. "An analysis of parking behaviour using discrete choice models calibrated on SP datasets," ERSA conference papers ersa04p60, European Regional Science Association.
    20. Ida, Takanori & Goto, Rei, 2009. "Interdependency among addictive behaviours and time/risk preferences: Discrete choice model analysis of smoking, drinking, and gambling," Journal of Economic Psychology, Elsevier, vol. 30(4), pages 608-621, August.

    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:eejocm:v:23:y:2017:i:c:p:9-20. 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.journals.elsevier.com/journal-of-choice-modelling .

    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.