Inference and computational methods for mixed models with large or complex data

混合效应模型在统计学应用的许多领域都很有用。通过考虑实验单元内的相关性，它们产生的推断和预测比不利用数据内的这种结构的方法更准确和有效。它们还可以保护估计免受未观察变量引起的偏差。这些特性使它们对许多现代用途具有吸引力。例如，它们可以用来从GPS项圈产生的数据中推断动物运动的决定因素，考虑到汽车传感器收集的近连续时间数据来计算保险费，使用行政卫生数据库制定个性化医疗策略，或者了解社交媒体中“事件”之间的关联。尽管混合效应模型已经被研究了几十年，但它们仍然是许多正在进行的研究的焦点，因为需要进一步的发展使它们更适合上述类型的现代任务。事实上，作为我之前NSERC发现基金的一部分，我们开发了一种两步方法，用于将混合模型拟合到复杂响应依赖的二进制数据中，当数据由中等数量的非常大的集群组成时，这种方法非常高效。

Mixed effects models are useful in many fields of application of statistics. By taking the within-experimental-unit correlation into account, they yield inferences and predictions that are more accurate and efficient than methods that do not exploit this structure within the data. They can also protect the estimations against bias induced by unobserved variables. These properties make them attractive for many modern uses. For instance, they can be used to infer on the determinants of animal movement from data generated by GPS collars, to compute insurance premiums that take into account the near continuous-time data gathered by automobile sensors, to develop personalized medicine strategies using administrative health databases or to understand the associations between "events" in social media. Even though mixed effects models have been investigated for decades, they are still the focus of much ongoing research because further developments are required to make them better suited for modern tasks of the type described above. Indeed as part of my previous NSERC Discovery Grant we developped a Two-Step method to fit mixed models to complex response dependent binary data that is highly efficient when the data consist of a moderate number of very large clusters.