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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. This paper is a revised version of CWP01/06.

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 CWP20/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:20/06
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    References listed on IDEAS

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    2. Bordley, Robert F., 2011. "An anti-ideal point representation of economic discrete choice models," Economics Letters, Elsevier, vol. 110(1), pages 60-63, January.
    3. 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.
    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. Ardakani, Omid M. & Bordley, Robert F. & Soofi, Ehsan S., 2025. "Expected information of noisy attribute forecasts for probabilistic forecasts," European Journal of Operational Research, Elsevier, vol. 323(3), pages 1013-1023.
    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. 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.
    10. 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.
    11. Matzkin, Rosa L., 2019. "Constructive identification in some nonseparable discrete choice models," Journal of Econometrics, Elsevier, vol. 211(1), pages 83-103.
    12. 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).
    13. Yu, Lili & Zhao, Yichuan, 2024. "Laplace approximated quasi-likelihood method for heteroscedastic survival data," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    14. 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.

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