Duration Models and Proportional Hazards in Political Science
Box-Steffensmeier, Janet M.
In recent years political scientists have increasingly
adopted a wide range of techniques for modeling duration data. A key
assumption of all these approaches is that the hazard ratios (i.e.,
the conditional relative risks across substrata) are proportional to
one another, and that this proportionality is maintained over time.
Estimation of proportional hazards (PH) models when in fact
hazards are non-proportional results in coefficient biases and
decreased power of significance tests. In particular, misspecified PH
models will overestimate the impact of variables whose associated
hazards are increasing, while coefficient estimates for covariates in
which the hazards are converging will be biased towards zero. We
investigate the proportionality assumption of two widely used duration
models, the Weibull parametric model and Cox's (1972) semiparametric
approach, in the context of a duration modelof Supreme Court
retirements. We address the potential problems with incorrectly
assuming proportionality, illustrate a range of techniques for testing
the proportionality assumption, and conclude with a number of means
for accurately and efficiently estimating these models in the presence
of non-proportional hazards.
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