Political scientists commonly use Grambsch and Therneau’s (1994, Biometrika 81, 515–526) ubiquitous Schoenfeld-based test to diagnose proportional hazard violations in Cox duration models. However, some statistical packages have changed how they implement the test’s calculation. The traditional implementation makes a simplifying assumption about the test’s variance–covariance matrix, while the newer implementation does not. Recent work suggests the test’s performance differs, depending on its implementation. I use Monte Carlo simulations to more thoroughly investigate whether the test’s implementation affects its performance. Surprisingly, I find the newer implementation performs very poorly with correlated covariates, with a false positive rate far above 5%. By contrast, the traditional implementation has no such issues in the same situations. This shocking finding raises new, complex questions for researchers moving forward. It appears to suggest, for now, researchers should favor the traditional implementation in situations where its simplifying assumption is likely met, but researchers must also be mindful that this implementation’s false positive rate can be high in misspecified models.

Keele (2010, Political Analysis 18:189–205) emphasizes that the incumbent test for detecting proportional hazard (PH) violations in Cox duration models can be adversely affected by misspecified covariate functional form(s). In this note, I reevaluate Keele’s evidence by running a full set of Monte Carlo simulations using the original article’s illustrative data-generating processes (DGPs). I make use of the updated PH test calculation available in R’s survival package starting with v3.0-10. Importantly, I find the updated PH test calculation performs better for Keele’s DGPs, suggesting its scope conditions are distinct and worth further investigating. I also uncover some evidence for the traditional calculation suggesting it, too, may have additional scope conditions that could impact practitioners’ interpretation of Keele (2010). On the whole, while we should always be attentive to model misspecification, my results suggest we should also become more attentive to how frequently the PH test’s performance is affected in practice, and that the answer may depend on the calculation’s implementation.

Logit and probit (L/P) models are a mainstay of binary time-series cross-sectional (BTSCS) analyses. Researchers include cubic splines or time polynomials to acknowledge the temporal element inherent in these data. However, L/P models cannot easily accommodate three other aspects of the data’s temporality: whether covariate effects are conditional on time, whether the process of interest is causally complex, and whether our functional form assumption regarding time’s effect is correct. Failing to account for any of these issues amounts to misspecification bias, threatening our inferences’ validity. We argue scholars should consider using Cox duration models when analyzing BTSCS data, as they create fewer opportunities for such misspecification bias, while also having the ability to assess the same hypotheses as L/P. We use Monte Carlo simulations to bring new evidence to light showing Cox models perform just as well—and sometimes better—than logit models in a basic BTSCS setting, and perform considerably better in more complex BTSCS situations. In addition, we highlight a new interpretation technique for Cox models—transition probabilities—to make Cox model results more readily interpretable. We use an application from interstate conflict to demonstrate our points.

This article provides an accessible introduction to the phenomenon of monotone likelihood in duration modeling of political events. Monotone likelihood arises when covariate values are monotonic when ordered according to failure time, causing parameter estimates to diverge toward infinity. Within political science duration model applications, this problem leads to misinterpretation, model misspecification and omitted variable biases, among other issues. Using a combination of mathematical exposition, Monte Carlo simulations and empirical applications, this article illustrates the advantages of Firth's penalized maximum-likelihood estimation in resolving the methodological complications underlying monotone likelihood. The results identify the conditions under which monotone likelihood is most acute and provide guidance for political scientists applying duration modeling techniques in their empirical research.

We develop a new Bayesian split population survival model for the analysis of survival data with misclassified event failures. Within political science survival data, right-censored survival cases are often erroneously misclassified as failure cases due to measurement error. Treating these cases as failure events within survival analyses will underestimate the duration of some events. This will bias coefficient estimates, especially in situations where such misclassification is associated with covariates of interest. Our split population survival estimator addresses this challenge by using a system of two equations to explicitly model the misclassification of failure events alongside a parametric survival process of interest. After deriving this model, we use Bayesian estimation via slice sampling to evaluate its performance with simulated data, and in several political science applications. We find that our proposed “misclassified failure” survival model allows researchers to accurately account for misclassified failure events within the contexts of civil war duration and democratic survival.

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.

The Cox proportional hazards model is a commonly used method for duration analysis in political science. Typical quantities of interest used to communicate results come from the hazard function (for example, hazard ratios or percentage changes in the hazard rate). These quantities are substantively vague, difficult for many audiences to understand and incongruent with researchers’ substantive focus on duration. We propose methods for computing expected durations and marginal changes in duration for a specified change in a covariate from the Cox model. These duration-based quantities closely match researchers’ theoretical interests and are easily understood by most readers. We demonstrate the substantive improvements in interpretation of Cox model results afforded by the methods with reanalyses of articles from three subfields of political science.

A partir des données de l'enquête SINE 98 de l'INSEE, une étude économétrique de la survie des entreprises culturelles fait apparaître les résultats suivants. Premièrement, le pourcentage d'entreprises qui meurent chaque année n'est pas stable au cours du temps et diffère selon le secteur considéré (arts visuels, spectacle vivant, patrimoine, édition, audiovisuel ou produits culturels). Le risque artisanal est très fort les trois ou quatre premières années alors que le risque industriel apparaît une fois ces premières années passées. Deuxièmement, le taux de survie des entreprises culturelles est très sensible à leur regroupement géographique. Si la proximité d'entreprises ayant la même activité est néfaste à la survie des entreprises culturelles, une forte concentration d'activités culturelles variées est très fortement bénéfique à leur survie. L'effet de synergie l'emporte sur l'effet de concurrence. Il donne un fondement à la productivité des regroupements d'entreprises culturelles qualifiés de pôle de compétitivité culturel ou de district culturel.