A Statistical Evaluation of Repeated Events Models with an Application to the Study of the Democratic Peace

学者们早就知道，当受试者经历不止一个事件时，多个事件数据在分析时如果不考虑事件之间的相关性就会产生问题。特别是，还没有关于对重复事件的共同发生进行建模的最佳方法的解决方案，在这种情况下，受试者多次经历相同类型的事件。这项研究项目将评估研究重复事件的两种主要方法中的哪一种更能解释受试者内部的相关性，即方差校正或脆弱。蒙特卡罗证据将有助于确定重复事件的替代建模策略是否以及在什么条件下是合适的。下一步，该项目将比较脆弱性模型和多级脆弱性模型，方法是检查没有对集群进行校正的标准风险模型、允许集群的三个单一脆弱性效应模型的结果，以及最后一个基于交叉分类脆弱性模型的模型，该模型允许按所有三个等级进行集群。最后，该项目将调查异质性分析中缺失数据的处理。模拟将重新运行，比较方差修正和脆弱模型与丢失数据的复杂性。这个项目产生的统计工作将通过评论用于测试这些理论的不同建模策略的可靠性并应用所讨论的模型来帮助解决关于政治动态的辩论，例如自由和平。研究期将使我加深对事件历史模型的理解，并在蒙特卡洛模拟、贝叶斯分析和计算机编程领域获得新的技能。重复事件数据的最佳建模策略是一个重要的问题。我们对政治进程的理解，就像在所有研究中一样，取决于我们可以从模型中得出的推论的质量。目前几乎没有关于哪种方法或模型合适的指导，因此，毫不奇怪，我们看到分析师不确定分析数据的最佳方式。考虑到使用不同的模型和方法会产生巨大的实质性差异，这将是整个研究界感兴趣的问题。这项研究得到了方法学、测量和统计计划以及职业中期方法学机会奖学金公告下的统计和概率计划的支持。

Scholars have long known that multiple events data, which occur when subjects experience more than one event, cause a problem when analyzed without taking into consideration the correlation among the events. In particular, there has not been a solution about the best way to model the common occurrence of repeated events, where the subject experiences the same type of event more than once. This research project will result in an assessment of whether one of the two main approaches for the study of repeated events, variance corrected or frailty, is better able to account for within-subject correlation. Monte Carlo evidence will help determine whether and under what conditions alternative modeling strategies for repeated events are appropriate. Next, the project will compare frailty and multi-level frailty models by examining the results of a standard hazard model with no correction for clustering, three single frailty effect models to allow for clustering, and finally a model based on a cross-classified frailty model that allows for clustering by all three levels. Finally, the project will investigate the treatment of missing data in analyses of heterogeneity. Simulations will be rerun comparing variance corrected and frailty models with the complication of missing data. The statistical work resulting from this project will help resolve debates about political dynamics, such as the liberal peace, by commenting on the reliability of the different modeling strategies used to test those theories and applying the models discussed. The fellowship period will allow me to deepen my understanding of event history models and acquire new skills in the areas of Monte Carlo simulations, Bayesian analysis, and computer programming.The question as to the best modeling strategy for repeated events data is an important one. Our understanding of political processes, as in all studies, depends on the quality of the inferences we can draw from our models. There is currently little guidance about which approach or model is appropriate and so, not surprisingly, we see analysts unsure of the best way to analyze their data. Given the dramatic substantive differences that result from using the different models and approaches, this is a problem that will be of interest across research communities. This research is supported by the Methodology, Measurement, and Statistics Program and the Statistics and Probability Program under the Mid-Career Methodological Opportunities Fellowship Announcement.