IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/01-06.html
   My bibliography  Save this paper

Using a Laplace approximation to estimate the random coefficients logit model by non-linear least squares

Author

Listed:
  • Matthew C. Harding

    (Institute for Fiscal Studies and Stanford University)

  • Jerry Hausman

    (Institute for Fiscal Studies and MIT)

Abstract

Current methods of estimating the random coefficients logit model employ simulations of the distribution of the taste parameters through pseudo-random sequences. These methods suffer from difficulties in estimating correlations between parameters and computational limitations such as the curse of dimensionality. This paper provides a solution to these problems by approximating the integral expression of the expected choice probability using a multivariate extension of the Laplace approximation. Simulation results reveal that our method performs very well, both in terms of accuracy and computational time.

Suggested Citation

  • Matthew C. Harding & Jerry Hausman, 2006. "Using a Laplace approximation to estimate the random coefficients logit model by non-linear least squares," CeMMAP working papers CWP01/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:01/06
    as

    Download full text from publisher

    File URL: http://cemmap.ifs.org.uk/wps/cwp0601.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    3. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, September.
    4. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, September.
    5. David Hensher & William Greene, 2003. "The Mixed Logit model: The state of practice," Transportation, Springer, vol. 30(2), pages 133-176, May.
    6. 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.
    7. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    8. Hess, Stephane & Polak, John W., 2005. "Mixed logit modelling of airport choice in multi-airport regions," Journal of Air Transport Management, Elsevier, vol. 11(2), pages 59-68.
    9. Beggs, S. & Cardell, S. & Hausman, J., 1981. "Assessing the potential demand for electric cars," Journal of Econometrics, Elsevier, vol. 17(1), pages 1-19, September.
    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. Bordley, Robert F., 2011. "An anti-ideal point representation of economic discrete choice models," Economics Letters, Elsevier, vol. 110(1), pages 60-63, January.
    2. Bhat, Chandra R., 2012. "Recent developments in discrete choice model formulation, estimation, and inference," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 273-275.
    3. Moon, Hyungsik Roger & Shum, Matthew & Weidner, Martin, 2018. "Estimation of random coefficients logit demand models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 613-644.
    4. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
    5. Czajkowski, Mikołaj & Budziński, Wiktor, 2019. "Simulation error in maximum likelihood estimation of discrete choice models," Journal of choice modelling, Elsevier, vol. 31(C), pages 73-85.
    6. Salanié, Bernard & Wolak, Frank, 2018. "Fast, “Robust†, and Approximately Correct: Estimating Mixed Demand Systems," CEPR Discussion Papers 13236, C.E.P.R. Discussion Papers.
    7. Bernard Salanie & Frank A. Wolak, 2018. "Fast, "robust", and approximately correct: estimating mixed demand systems," CeMMAP working papers CWP64/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Matzkin, Rosa L., 2012. "Identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 166(1), pages 106-115.
    9. Cherchi, Elisabetta & Guevara, Cristian Angelo, 2012. "A Monte Carlo experiment to analyze the curse of dimensionality in estimating random coefficients models with a full variance–covariance matrix," Transportation Research Part B: Methodological, Elsevier, vol. 46(2), pages 321-332.
    10. Matzkin, Rosa L., 2019. "Constructive identification in some nonseparable discrete choice models," Journal of Econometrics, Elsevier, vol. 211(1), pages 83-103.
    11. Zenga, Mariangela & Mazzoleni, Marcella & Mariani, Paolo & Marletta, Andrea, 2021. "The risk of inappropriateness: An analysis of the hospitalisations in the Italian geriatric wards," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    12. Yu, Lili & Zhao, Yichuan, 2024. "Laplace approximated quasi-likelihood method for heteroscedastic survival data," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).

    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. 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).
    2. 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.
    3. Siikamaki, Juha & Layton, David F., 2007. "Discrete choice survey experiments: A comparison using flexible methods," Journal of Environmental Economics and Management, Elsevier, vol. 53(1), pages 122-139, January.
    4. Daniel Ackerberg, 2009. "A new use of importance sampling to reduce computational burden in simulation estimation," Quantitative Marketing and Economics (QME), Springer, vol. 7(4), pages 343-376, December.
    5. Laura Mørch Andersen, 2013. "Obtaining reliable Likelihood Ratio tests from simulated likelihood functions," IFRO Working Paper 2013/1, University of Copenhagen, Department of Food and Resource Economics.
    6. Cordera, Rubén & Luigi dell’Olio, & Sipone, Silvia & Moura, José Luis, 2024. "Modeling airport choice for a multi-airport area using a random parameter logit model," Research in Transportation Economics, Elsevier, vol. 104(C).
    7. Xu, Min & Meng, Qiang & Liu, Kai & Yamamoto, Toshiyuki, 2017. "Joint charging mode and location choice model for battery electric vehicle users," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 68-86.
    8. Bijan J. Borah, 2006. "A mixed logit model of health care provider choice: analysis of NSS data for rural India," Health Economics, John Wiley & Sons, Ltd., vol. 15(9), pages 915-932, September.
    9. Paleti, Rajesh, 2018. "Generalized multinomial probit Model: Accommodating constrained random parameters," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 248-262.
    10. Frick, Bernd & Barros, Carlos Pestana & Prinz, Joachim, 2010. "Analysing head coach dismissals in the German "Bundesliga" with a mixed logit approach," European Journal of Operational Research, Elsevier, vol. 200(1), pages 151-159, January.
    11. Faure, Corinne & Guetlein, Marie-Charlotte & Schleich, Joachim & Tu, Gengyang & Whitmarsh, Lorraine & Whittle, Colin, 2022. "Household acceptability of energy efficiency policies in the European Union: Policy characteristics trade-offs and the role of trust in government and environmental identity," Ecological Economics, Elsevier, vol. 192(C).
    12. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    13. Steve Berry & Oliver B. Linton & Ariel Pakes, 2004. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 613-654.
    14. Bernard Fortin & Nicolas Jacquemet & Bruce Shearer, 2008. "Policy Analysis in Health-Services Market: Accounting for Quality and Quantity," Annals of Economics and Statistics, GENES, issue 91-92, pages 293-319.
    15. Steven T. Berry & Philip A. Haile, 2021. "Foundations of Demand Estimation," Cowles Foundation Discussion Papers 2301, Cowles Foundation for Research in Economics, Yale University.
    16. Basu, Debasis & Hunt, John Douglas, 2012. "Valuing of attributes influencing the attractiveness of suburban train service in Mumbai city: A stated preference approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(9), pages 1465-1476.
    17. Falco, Paolo & Maloney, William F. & Rijkers, Bob & Sarrias, Mauricio, 2015. "Heterogeneity in subjective wellbeing: An application to occupational allocation in Africa," Journal of Economic Behavior & Organization, Elsevier, vol. 111(C), pages 137-153.
    18. Deka, Devajyoti & Carnegie, Jon, 2021. "Predicting transit mode choice of New Jersey workers commuting to New York City from a stated preference survey," Journal of Transport Geography, Elsevier, vol. 91(C).
    19. 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.
    20. Useche, Pilar & Barham, Bradford & Foltz, Jeremy, 2006. "A Trait Specific Model of GM Crop Adoption by Minnesota and Wisconsin Corn Farmers," Working Papers 201525, University of Wisconsin-Madison, Department of Agricultural and Applied Economics, Food System Research Group.

    More about this item

    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:ifs:cemmap:01/06. 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: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/cmifsuk.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.