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.***My research program over the next few years intends to build upon these recent developments and consists in developing new tools to fit mixed effects models to large datasets and/or to datasets obtained through response dependent sampling schemes. This research program innovates in many aspects. In the short term, model selection criteria that are easy to use and compute on multi-core machines will be derived and added to our R package TwoStepCLogit. This will enable the numerous end users in biology, ecology and environmental sciences to use the new methods with their ever growing GIS/GPS databases that record animal movement data. In the medium term, I will adapt our Two-Step method so that it can fit generalized mixed regression models to massive databases where a large number of clients or patients are followed longitudinally (e.g., insurance, marketing, pharmacoepidemiology, twitter and social media data). Industrial partners will likely get involved at this stage and should provide data and internship opportunities for students/postdocs. The advantage of this new method is that it will easily be amenable to highly parallelized computing. In the longer term, we will try to capitalize on the fact that the Two-Step method is based on the EM-algorithm to derive an on-line implementation of the methods (i.e., update the model fit as soon as a new data point comes in). Again, R packages to implement the methods will be made publicly available.*** *** *** **