IDEAS home Printed from https://ideas.repec.org/p/cdl/uctcwp/qt2hr8d4bs.html
   My bibliography  Save this paper

Probit Model Estimation Revisited: Trinomial Models of Household Car Ownership

Author

Listed:
  • Bunch, David S.
  • Kitamura, Ryuichi

Abstract

In this paper we revisit various important issues relating to practical estimation of the multinomial probit model, using an empirical analysis of car ownership as a test case. To provide context, a brief literature review of empirical probit studies is included. Estimates are obtained for a full range of model specifications, including models with random (uncorrelated and correlated) taste variation and/or a general random error structure, and issues of estimability, specification testing, and alternative normalizations for probit models are addressed. Three model trust region algorithms for finding maximum likelihood estimates are compared, and the superiority of a structured quasi-Newton method employing "model switching" over more traditional approaches (Broyden-Fletcher-Goldfarb-Shanno secant update, Berndt-Hall-Hall-Hausman) is demonstrated. The trust region algorithms have reliable convergence properties and provide useful diagnostic information. Finally, a comparison of some probit integral approximation schemes (Clark, and two variants of Mendell-Elston) versus numerical integration is included. There is additional evidence against using Clark's approximation, but a variant of the Mendell-Elston approach appears promising. Numerical problems with variable-ordering techniques (such as separated-split) are demonstrated.

Suggested Citation

  • Bunch, David S. & Kitamura, Ryuichi, 1991. "Probit Model Estimation Revisited: Trinomial Models of Household Car Ownership," University of California Transportation Center, Working Papers qt2hr8d4bs, University of California Transportation Center.
    • Handle: RePEc:cdl:uctcwp:qt2hr8d4bs
    as

    Download full text from publisher

    File URL: https://www.escholarship.org/uc/item/2hr8d4bs.pdf;origin=repeccitec
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Dansie, B. R., 1985. "Parameter estimability in the multinomial probit model," Transportation Research Part B: Methodological, Elsevier, vol. 19(6), pages 526-528, December.
    3. 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.
    4. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665, National Bureau of Economic Research, Inc.
    5. Sparmann, Jürg M. & Daganzo, Carlos F. & Soheily, Mahboubeh, 1983. "Linear probit models: Statistical properties and improved estimation methods," Transportation Research Part B: Methodological, Elsevier, vol. 17(1), pages 67-86, February.
    6. E J Miller & S R Lerman, 1981. "Disaggregate Modelling and Decisions of Retail Firms: A Case Study of Clothing Retailers," Environment and Planning A, , vol. 13(6), pages 729-746, June.
    7. Horowitz, Joel, 1980. "The accuracy of the multinomial logit model as an approximation to the multinomial probit model of travel demand," Transportation Research Part B: Methodological, Elsevier, vol. 14(4), pages 331-341, December.
    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. Randall Filer & Marjorie Honig, 2005. "Endogenous Pensions and Retirement Behavior," CESifo Working Paper Series 1547, CESifo.
    2. Matteo Ricciarelli, 2009. "Investment choice and asset allocation of Italian households: the discrete-continuous approach," Applied Economics, Taylor & Francis Journals, vol. 43(6), pages 651-662.
    3. Victoria Prowse, 2012. "Modeling Employment Dynamics With State Dependence and Unobserved Heterogeneity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 411-431, April.
    4. David S. Bunch, 2014. "Numerical methods for optimization-based model estimation and inference," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 23, pages 565-598, Edward Elgar Publishing.
    5. Rinus Haaijer & Michel Wedel & Marco Vriens & Tom Wansbeek, 1998. "Utility Covariances and Context Effects in Conjoint MNP Models," Marketing Science, INFORMS, vol. 17(3), pages 236-252.

    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. GRAMMIG, Joachim & HUJER, Reinhard & SCHEIDLER, Michael, 2001. "The econometrics of airline network management," LIDAM Discussion Papers CORE 2001055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Natarajan, Ranjini & McCulloch, Charles E. & Kiefer, Nicholas M., 2000. "A Monte Carlo EM method for estimating multinomial probit models," Computational Statistics & Data Analysis, Elsevier, vol. 34(1), pages 33-50, July.
    3. Hanemann, W. Michael & Kanninen, Barbara, 1996. "The Statistical Analysis Of Discrete-Response Cv Data," CUDARE Working Papers 25022, University of California, Berkeley, Department of Agricultural and Resource Economics.
    4. Horowitz, Joel & Keane, Michael & Bolduc, Denis & Divakar, Suresh & Geweke, John & Gonul, Fosun & Hajivassiliou, Vassilis & Koppelman, Frank & Matzkin, Rosa & Rossi, Peter & Ruud, Paul, 1994. "Advances in Random Utility Models," MPRA Paper 53026, University Library of Munich, Germany.
    5. Haaijer, Marinus E., 1996. "Predictions in conjoint choice experiments : the x-factor probit model," Research Report 96B22, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    6. 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.
    7. Bolduc, Denis & Kaci, Mustapha, 1993. "Estimation des modèles probit polytomiques : un survol des techniques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 69(3), pages 161-191, septembre.
    8. 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.
    9. Hajivassiliou, Vassilis A. & Ruud, Paul A., 1986. "Classical estimation methods for LDV models using simulation," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 40, pages 2383-2441, Elsevier.
    10. 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.
    11. Friederike Paetz & Winfried J. Steiner, 2017. "The benefits of incorporating utility dependencies in finite mixture probit models," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 793-819, July.
    12. Heng Z. Chen & Frank Lupi & John P. Hoehn, 1999. "An Empirical Assessment of Multinomial Probit and Logit Models for Recreation Demand," Chapters, in: Joseph A. Herriges & Catherine L. Kling (ed.), Valuing Recreation and the Environment, chapter 5, pages 141-162, Edward Elgar Publishing.
    13. Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-632, November.
    14. Paul Gertler & Roland Sturm & Bruce Davidson, 1994. "Information and the Demand for Supplemental Medicare Insurance," NBER Working Papers 4700, National Bureau of Economic Research, Inc.
    15. Borsch-Supan, Axel & Hajivassiliou, Vassilis A., 1993. "Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models," Journal of Econometrics, Elsevier, vol. 58(3), pages 347-368, August.
    16. Rennings, Klaus & Ziegler, Andreas & Zwick, Thomas, 2001. "Employment changes in environmentally innovative firms," ZEW Discussion Papers 01-46, ZEW - Leibniz Centre for European Economic Research.
    17. Langche Zeng, 2000. "A Heteroscedastic Generalized Extreme Value Discrete Choice Model," Sociological Methods & Research, , vol. 29(1), pages 118-144, August.
    18. Vassilis A. Hajivassiliou, 1993. "Simulating Normal Rectangle Probabilities and Their Derivatives: The Effects of Vectorization," Cowles Foundation Discussion Papers 1049, Cowles Foundation for Research in Economics, Yale University.
    19. 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.
    20. van Soest, A.H.O., 1990. "Essays on micro-econometric models of consumer demand and the labour market," Other publications TiSEM be045d62-a73d-4d7c-a591-f, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    Social and Behavioral Sciences;

    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:cdl:uctcwp:qt2hr8d4bs. 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: Lisa Schiff (email available below). General contact details of provider: https://edirc.repec.org/data/itucbus.html .

    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.