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Back to the Future: Modeling Time Dependence in Binary Data

  • David B. Carter (a1) and Curtis S. Signorino (a2)

Since Beck, Katz, and Tucker (1998), the standard method for modeling time dependence in binary data has been to incorporate time dummies or splined time in logistic regressions. Although we agree with the need for modeling time dependence, we demonstrate that time dummies can induce estimation problems due to separation. Splines do not suffer from these problems. However, the complexity of splines has led substantive researchers (1) to use knot values that may be inappropriate for their data and (2) to ignore any substantive discussion concerning temporal dependence. We propose a relatively simple alternative: including t, t 2, and t 3 in the regression. This cubic polynomial approximation is trivial to implement—and, therefore, interpret—and it avoids problems such as quasi-complete separation. Monte Carlo analysis demonstrates that, for the types of hazards one often sees in substantive research, the polynomial approximation always outperforms time dummies and generally performs as well as splines or even more flexible autosmoothing procedures. Due to its simplicity, this method also accommodates nonproportional hazards in a straightforward way. We reanalyze Crowley and Skocpol (2001) using nonproportional hazards and find new empirical support for the historical-institutionalist perspective.

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Authors' note: We thank Daehee Bak, Hein Goemans, Jay Goodliffe, Luke Keele, Eduardo Leoni, Arthur Spirling, Randy Stone, Chris Zorn, and three anonymous reviewers for their comments and suggestions. This article has also benefited from comments provided during seminars at the University of Berkeley, the University of Minnesota, the University of Pittsburgh, and the Watson Center for Conflict and Cooperation, as well as from comments provided during conference presentations at the annual meetings of the Political Methodology Society (2007), Peace Science Society (2007), and the American Political Science Association (2008). We thank Jocelyn Crowley, Theda Skocpol, and Glenn Palmer for generously providing their data. Supplementary materials (Web Appendix) for this article are available on the Political Analysis Web site.

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Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
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