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Discrete Choice Data with Unobserved Heterogeneity: A Conditional Binary Quantile Model

  • Xiao Lu (a1)

Abstract

In political science, data with heterogeneous units are used in many studies, such as those involving legislative proposals in different policy areas, electoral choices by different types of voters, and government formation in varying party systems. To disentangle decision-making mechanisms by units, traditional discrete choice models focus exclusively on the conditional mean and ignore the heterogeneous effects within a population. This paper proposes a conditional binary quantile model that goes beyond this limitation to analyze discrete response data with varying alternative-specific features. This model offers an in-depth understanding of the relationship between the explanatory and response variables. Compared to conditional mean-based models, the conditional binary quantile model relies on weak distributional assumptions and is more robust to distributional misspecification. The model also relaxes the assumption of the independence of irrelevant alternatives, which is often violated in practice. The method is applied to a range of political studies to show the heterogeneous effects of explanatory variables across the conditional distribution. Substantive interpretations from counterfactual scenarios are used to illustrate how the conditional binary quantile model captures unobserved heterogeneity, which extant models fail to do. The results point to the risk of averaging out the heterogeneous effects across units by conditional mean-based models.

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Footnotes

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Author’s note: This work was supported by the Collaborative Research Center “Political Economy of Reforms” (SFB 884 Project C1: Legislative Reforms and Party Competition), which is funded by the German Research Foundation. The author also acknowledges support by the state of Baden-Württemberg through bwHPC (high-performance computing cluster MISO Production) and the German Research Foundation through grant INST 35/1134-1 FUGG. An earlier version of this paper has been presented in the poster session of the 6th Asian Political Methodology Meeting in Kyoto. I thank Thomas König, James Lo, Jamie Monogan, Jong Hee Park, Richard Traumüller, the Editor-in-Chief, Jeff Gill, and three anonymous reviewers for their very helpful discussions and suggestions. Replication materials for this paper are available (Lu 2019).

Contributing Editor: Jeff Gill

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References

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