Binary, count and duration data all code discrete events occurring at points in time. Although a single data generation process can produce all of these three data types, the statistical literature is not very helpful in providing methods to estimate parameters of the same process from each. In fact, only single theoretical process exists for which know statistical methods can estimate the same parameters - and it is generally used only for count and duration data. The result is that seemingly trivial decisions abut which level of data to use can have important consequences for substantive interpretations. We describe the theoretical event process for which results exist, based on time independence. We also derive a set of models for a time-dependent process and compare their predictions to those of a commonly used model. Any hope of understanding and avoiding the more serious problems of aggregation bias in events data is contingent on first deriving a much wider arsenal of statistical models and theoretical processes that are not constrained by the particular forms of data that happen to be available. We discuss these issues and suggest an agenda for political methodologists interested in this very large class of aggregation problems.
King, Alt, Burns, and Laver (1990) proposed and estimated a unified model in which cabinet durations depended on seven explanatory variables reflecting features of the cabinets and the bargaining environments in which they formed, along with a stochastic component in which the risk of a cabinet falling was treated as a constant across its tenure. Two recent research reports take issue with one aspect of this model. Warwick and Easton replicate the earlier findings for explanatory variables but claim that the stochastic risk should be seen as rising, and at a rate which varies, across the life of the cabinet. Bienen and van de Walle, using data on the duration of leaders, allege that random risk is falling. We continue in our goal of unifying this literature by providing further estimates with both cabinet and leader duration data that confirm the original explanatory variables’ effects, showing that leaders’ durations are affected by many of the same factors that affect the durability of the cabinets they lead, demonstrating that cabinets have stochastic risk of ending that is indeed constant across the theoretically most interesting range of durations, and suggesting that stochastic risk for leaders in countries with cabinet government is, if not constant, more likely to rise than fall.