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

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

    Using maximum likelihood estimation for discrete choice modeling of small datasets causes two problems. The rst 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 rst-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 ndings on data from a stated choice study on various forms of employee compensation.

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    File URL: https://www.uantwerpen.be/images/uantwerpen/container1244/files/TEW%20-%20Onderzoek/Working%20Papers/RPS/2013/RPS-2013-013.pdf
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    Bibliographic Info

    Paper provided by University of Antwerp, Faculty of Applied Economics in its series Working Papers with number 2013013.

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    Length: 38 pages
    Date of creation: Aug 2013
    Date of revision:
    Handle: RePEc:ant:wpaper:2013013

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    Postal: Prinsstraat 13, B-2000 Antwerpen
    Web page: https://www.uantwerp.be/en/faculties/applied-economic-sciences/
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    Related research

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

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    References

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    1. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, November.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
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