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An argument for preferring Firth bias-adjusted estimates in aggregate and individual-level discrete choice modeling


  • KESSELS, Roselinde
  • JONES, Bradley
  • GOOS, Peter


Using maximum likelihood estimation for discrete choice modeling of small datasets causes two problems. The first problem is that the data often exhibit separation, in which case the maximum likelihood estimates do not exist. Also, provided they exist, the maximum likelihood estimates are biased. In this paper, we show how to adapt Firth's bias-adjustment method for use in discrete choice modeling. This approach removes the first-order bias of the estimates, and it also deals with the separation issue. An additional advantage of the bias adjustment is that it is usually accompanied by a reduction in the variance. Using a large-scale simulation study, we identify the situations where Firth's bias-adjustment method is most useful in avoiding the problem of separation as well as removing the bias and reducing the variance. As a special case, we apply the bias-adjustment approach to discrete choice data from individuals, making it possible to construct an empirical distribution of the respondents' preferences without imposing any a priori population distribution. For both research purposes, we base our findings on data from a stated choice study on various forms of employee compensation.

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  • KESSELS, Roselinde & JONES, Bradley & GOOS, Peter, 2013. "An argument for preferring Firth bias-adjusted estimates in aggregate and individual-level discrete choice modeling," Working Papers 2013013, University of Antwerp, Faculty of Applied Economics.
  • Handle: RePEc:ant:wpaper:2013013

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    References listed on IDEAS

    1. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, March.
    2. Kessels, Roselinde & Jones, Bradley & Goos, Peter & Vandebroek, Martina, 2009. "An Efficient Algorithm for Constructing Bayesian Optimal Choice Designs," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 279-291.
    3. Kessels, Roselinde & Goos, Peter & Vandebroek, Martina, 2008. "Optimal designs for conjoint experiments," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2369-2387, January.
    4. 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.
    5. Peter J. Lenk & Wayne S. DeSarbo & Paul E. Green & Martin R. Young, 1996. "Hierarchical Bayes Conjoint Analysis: Recovery of Partworth Heterogeneity from Reduced Experimental Designs," Marketing Science, INFORMS, vol. 15(2), pages 173-191.
    6. Theodoros Evgeniou & Massimiliano Pontil & Olivier Toubia, 2007. "A Convex Optimization Approach to Modeling Consumer Heterogeneity in Conjoint Estimation," Marketing Science, INFORMS, vol. 26(6), pages 805-818, 11-12.
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    Cited by:

    1. KUPFER, Franziska & KESSELS, Roselinde & GOOS, Peter & VAN DE VOORDE, Eddy & VERHETSEL, Ann, 2013. "A discrete choice approach for analysing the airport choice for freighter operations in Europe," Working Papers 2013028, University of Antwerp, Faculty of Applied Economics.
    2. Kupfer, Franziska & Kessels, Roselinde & Goos, Peter & Van de Voorde, Eddy & Verhetsel, Ann, 2016. "The origin–destination airport choice for all-cargo aircraft operations in Europe," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 87(C), pages 53-74.

    More about this item


    Discrete choice modeling; Firth's bias adjustment; Penalized maximum likelihood; Individual-level estimates; Data separation;

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