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Quantifying Change Over Time: Interpreting Time-varying Effects In Duration Analyses

  • Constantin Ruhe (a1) (a2)


Duration analyses in political science often model nonproportional hazards through interactions with analysis time. To facilitate their interpretation, methodologists have proposed methods to visualize time-varying coefficients or hazard ratios. While these techniques are a useful, initial postestimation step, I argue that they are insufficient to identify the overall impact of a time-varying effect and may lead to faulty inference when a coefficient changes its sign. I show how even significant changes of a coefficient’s sign do not imply that the overall effect is reversed over time. In order to enable a correct interpretation of time-varying effects in this context, researchers should visualize their results with survivor functions. I outline how survivor functions are calculated for models with time-varying effects and demonstrate the need for such a nuanced interpretation using the prominent finding of a time-varying effect of mediation on interstate conflict. The reanalysis of the data using the proposed visualization methods indicates that the conclusions of earlier mediation research are misleading. The example highlights how survivor functions are an essential tool to clarify the ambiguity inherent in time-varying coefficients in event history models.


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Author’s note: I would like to thank Kyle Beardsley for comments and for providing perfectly documented replication material. I would also like to thank Gerald Schneider, Adam Scharpf, Tobias Böhmelt, Nikolay Marinov, Sebastian Schutte and the participants at the European Network of Conflict Research 2015 Conference in Barcelona for their helpful input, as well as R. Michael Alvarez and the anonymous reviewers for their great feedback and critique which substantively improved this manuscript. I gratefully acknowledge funding by the German Foundation for Peace Research (Deutsche Stiftung Friedensforschung), SP06/06-2015. The replication material is available at

Contributing Editor: R. Michael Alvarez



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Quantifying Change Over Time: Interpreting Time-varying Effects In Duration Analyses

  • Constantin Ruhe (a1) (a2)


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