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Paper

Modeling Heterogeneity in Duration Models Box-Steffensmeier, Janet M. Zorn, Christopher Uploaded 07-11-1999 Keywords heterogeneity survival models split-population variance correction frailty random effects Abstract 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.

2

Paper

Covariate Functional Form in Cox Models Keele, Luke Uploaded 10-25-2005 Keywords Cox model event history survival models splines semi-parametric duration models Abstract In most event history models, the effect of a covariate on the hazard is assumed to have a log-linear functional form. For continuous covariates, this assumption is often violated as the effect is highly nonlinear. Assuming a log-linear functional form when the nonlinear form applies causes specification errors leading to erroneous statistical conclusions. Scholars can, instead of ignoring the presence of nonlinear effects, test for such nonlinearity and incorporate it into the model. I review methods to test for and model nonlinear functional forms for covariates in the Cox model. Testing for such nonlinear effects is important since such nonlinearity can appear as nonproportional hazards, but time varying terms will not correct the misspecification. I investigate the consequences of nonlinear function forms using data on international conflicts from 1950-1985. I demonstrate that the conclusions drawn from this data depend on fitting the correct functional form for the covariates.

3

Paper

Stochastic Dependence in Competing Risks Gordon, Sanford C. Uploaded 09-05-2001 Keywords Competing risks duration models survival models event history random effects frailty models unobserved heterogeneity Monte Carlo simulation Congress legislative position-taking cabinet survival numeric integration Markov Chain Monte Carlo Abstract The term "Competing Risks" describes duration models in which spells may terminate via multiple outcomes: The term of a cabinet, for example, may end with or without an election; wars persist until the loss or victory of the aggressor. Analysts typically assume stochastic independence among risks, the duration modeling equivalent of independence of irrelevant alternatives. However, many political examples violate this assumption. I review competing risks as a latent variables approach. After discussing methods for modeling dependence that place restrictions on the nature of association, I introduce a parametric generalized dependent risks model in which inter-risk correlation may be estimated and its significance tested. The method employs risk-specific random effects drawn from a multivariate normal distribution. Estimation is conducted using numerical methods and/or Bayesian simulation. Monte Carlo simulation reveals desirable large sample properties of the estimator. Finally, I examine two applications using data on cabinet survival and legislative position taking.

4

Poster

The Past is Ever-Present: The Dynamic Nature of Intrastate Conflict Jones, Benjamin Uploaded 07-28-2012 Keywords Event history Survival models Multi-state models Civil war Path dependence Abstract Civil wars pose a grave challenge to international stability as they tend to recur frequently over time. Nevertheless, existing theory treats civil wars as independent events. I reconceptualize civil war as a dynamic process, which creates a new statistical challenge – modeling multi-stage processes through a series of transitions within a longitudinal process. To overcome this problem, I introduce a multi-state event history model, which models the entire civil war process as a series of successive stages in which previous outcomes shape subsequent events, and apply it to a dataset of all civil wars from 1950-2004. The results provide strong evidence that previous outcomes exert both a direct, and indirect effect on subsequent transitions, revealing the conditional nature of factors frequently associated with war and peace.