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Separation and rare events

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  • Beiser-McGrath, Liam F.

Abstract

When separation is a problem in binary dependent variable models, many researchers use Firth's penalized maximum likelihood in order to obtain finite estimates (Firth, 1993; Zorn, 2005; Rainey, 2016). In this paper, I show that this approach can lead to inferences in the opposite direction of the separation when the number of observations are sufficiently large and both the dependent and independent variables are rare events. As large datasets with rare events are frequently used in political science, such as dyadic data measuring interstate relations, a lack of awareness of this problem may lead to inferential issues. Simulations and an empirical illustration show that the use of independent weakly-informative prior distributions centered at zero, for example, the Cauchy prior suggested by Gelman et al. (2008), can avoid this issue. More generally, the results caution researchers to be aware of how the choice of prior interacts with the structure of their data, when estimating models in the presence of separation.

Suggested Citation

  • Beiser-McGrath, Liam F., 2020. "Separation and rare events," LSE Research Online Documents on Economics 117222, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:117222
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    File URL: http://eprints.lse.ac.uk/117222/
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    References listed on IDEAS

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    1. Gary Clyde Hufbauer & Jeffrey J. Schott & Kimberly Ann Elliott, 2007. "Economic Sanctions Reconsidered, 3rd edition (hardcover)," Peterson Institute Press: All Books, Peterson Institute for International Economics, number 4075, January.
    2. Zorn, Christopher, 2005. "A Solution to Separation in Binary Response Models," Political Analysis, Cambridge University Press, vol. 13(2), pages 157-170, April.
    3. Rainey, Carlisle, 2016. "Dealing with Separation in Logistic Regression Models," Political Analysis, Cambridge University Press, vol. 24(3), pages 339-355, July.
    4. Cook, Scott J. & Hays, Jude C. & Franzese, Robert J., 2020. "Fixed effects in rare events data: a penalized maximum likelihood solution," Political Science Research and Methods, Cambridge University Press, vol. 8(1), pages 92-105, January.
    5. Gary Clyde Hufbauer & Jeffrey J. Schott & Kimberly Ann Elliott, 1990. "Economic Sanctions Reconsidered: 2nd Edition," Peterson Institute Press: All Books, Peterson Institute for International Economics, number 82, January.
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    More about this item

    Keywords

    Bayesian; categorical data analysis; discrete choice models;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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