Modeling Heterogeneity in Duration Models
Box-Steffensmeier, Janet M.
As increasing numbers of political scientists have turned to event history models to
analyze duration data, there has been growing awareness of the issue of heterogeneity:
instances in which subpopulations in the data vary in ways not captured by the systematic
components of standard duration models. We discuss the general issue of heterogeneity,
and offer techniques for dealing with it under various conditions. One special case of
heterogeneity arises when the population under study consists of one or more subpopulations
which will never experience the event of interest. Split-population, or "cure" models,
account for this heterogeneity by permitting separate analysis of the determinants of
whether an event will occur and the timing of that event, using mixture distributions.
We use the split-population model to reveal additional insights into the strategies of
political action committees' allocation decisions, and compare split-population and
standard duration models of Congressional responses to Supreme Court decisions.
We then go on to explore the general issue of heterogeneity in survival data by
considering two broad classes of models for dealing with the lack of independence among
failure times: variance correction models and "frailty" (or random effects) duration models.
The former address heterogeneity by adjusting the variance matrix of the estimates to allow
for correct inference in the presence of that heterogeneity, while the latter approach
treats heterogeneity as an unobservable, random, multiplicative factor acting on the
baseline hazard function. Both types of models allow us to deal with heterogeneity that
results, for example, from correlation at multiple levels of data, or from repeated events
within units of analysis. We illustrate these models using data on international conflicts.
In sum, we explore the issue of heterogeneity in event history models from a variety
of perspectives, using a host of examples from contemporary political science. Our techniques
and findings will therefore be of substantial interest to both political methodologists and
others engaged in empirical work across a range of subfields.
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