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

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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.