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

学者们早就知道，当受试者经历多个事件时，多个事件数据会在分析时引起问题，而不考虑事件之间的相关性。 特别地，还没有关于对重复事件的常见发生进行建模的最佳方式的解决方案，其中受试者经历相同类型的事件超过一次。 本研究项目将导致评估是否两个主要的方法之一，用于重复事件的研究，方差校正或脆弱性，是更好地能够占内主题的相关性。 蒙特卡罗证据将有助于确定是否以及在什么条件下重复事件的替代建模策略是适当的。 接下来，该项目将通过检查标准风险模型的结果来比较脆弱性和多水平脆弱性模型，没有校正聚类，三个单一的脆弱性效应模型允许聚类，最后一个模型基于交叉分类的脆弱性模型，允许所有三个水平的聚类。 最后，本项目将研究异质性分析中缺失数据的处理。 模拟将比较方差校正和脆弱模型与缺失数据的复杂性。 该项目产生的统计工作将有助于解决有关政治动态的辩论，如自由和平，通过评论用于测试这些理论和应用所讨论的模型的不同建模策略的可靠性。 研究期间将使我加深对事件历史模型的理解，并获得蒙特卡罗模拟，贝叶斯分析和计算机编程领域的新技能。重复事件数据的最佳建模策略是一个重要问题。 我们对政治过程的理解，就像在所有研究中一样，取决于我们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是合适的指导，因此，毫不奇怪，我们看到分析师不确定分析数据的最佳方法。 鉴于使用不同的模型和方法所产生的巨大的实质性差异，这是一个跨研究社区感兴趣的问题。 这项研究得到了方法，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.