Interpreting Duration Models, the Redux

– “Getting Time Right: Using Cox Models and Probabilities to Interpret Binary Panel Data” (with Benjamin T. Jones) – working paper
– “Different Words, Same Song: Advice for Substantively Interpreting Duration Models” (with Benjamin T. Jones) – 2019, PS: Political Science & Politics {paper abstract}
– “mstatecox in Stata: A Package for Simulating Transition Probabilities from Semi-Parametric Multi-State Survival Models” (with Benjamin T. Jones) – 2018, Stata Journal {paper abstract}

“Getting Time Right”

Abstract
Logit and probit (L/P) models are a mainstay of binary time-series cross-sectional analyses (BTSCS). Researchers include cubic splines or time polynomials to acknowledge the temporal element inherent in these data. However, L/P models cannot easily acknowledge 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. In addition, we offer a new interpretation technique for Cox models—transition probabilities—to make their model results more easily interpretable. We use applications from judicial politics and interstate conflict to demonstrate our points.

“Different Words, Same Song”

Abstract
Duration models’ use in political science continues to grow, more than a decade after Box-Steffensmeier and Jones (2004). However, several common misconceptions about the models still persist. To improve scholars’ use and interpretation of duration models, we point out that duration models are a type of regression model, and therefore follow the same rules as other, more commonly used regression models. We offer four guiding maxims to this end. We survey the various duration model interpretation strategies and group them into four categories, which is an important organizational exercise that does not appear elsewhere. We then discuss these strategies’ strengths and weaknesses, noting that all are correct from a technical perspective, but some strategies make more sense than others for non-technical reasons, which ultimately informs best practices.

“mstatecox in Stata”

Abstract
Multi-state duration models are a valuable tool used in multiple fields to examine how subjects move through a series of discrete phases/stages. The models themselves may be estimated using common statistical software, but their broader adoption has been limited due to a lack of software to substantively interpret their results. Transition probabilities are the common post-estimation quantity for interpreting multi-state duration model results. De Wreede, Fiocco, and Putter’s mstate package provides R with the functionality to estimate these quantities from semi-parametric multi-state models, yet no Stata equivalent exists for semi-parametric models. We introduce a new set of Stata commands to meet this need. Our mstatecox suite calculates transition probabilities from semi-parametric multi-state duration models via simulation. It can accommodate any configuration of stages, and also has the ability to accommodate time-interacted covariates. We demonstrate our package’s functionality using de Wreede, Fiocco, and Putter’s (2011) European Registry of Blood and Marrow Transplantation example dataset from R-mstate.