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Title: Simultaneous shrinkage of the linear mixed model's fixed and random effects using empirical Bayes Authors:  Matteo Amestoy - Amsterdam University Medical Centers (Netherlands) [presenting]
Mark van de Wiel - Amsterdam University Medical Centers (Netherlands)
Wessel van Wieringen - Amsterdam University Medical Centers (Austria)
Abstract: Estimation of linear mixed models (LMM) from high dimensional data or studies with an imbalanced design requires regularization to prevent over-fitting. However, standard LMM solvers do not facilitate shrinkage, while Bayesian hierarchical model implementations require fully parametric specification of the priors. The choice of the distributional form of these priors is guided by mathematical convenience. But an informed choice of the prior's parameter, especially for the covariance matrix of the random effects, is usually not at hand. We propose to select the hyperparameters in a data-driven fashion. Hereto we present an empirical Bayes (EB) method for the joint estimation of the parameters of a prior on the fixed effects and on the covariance matrix of the random effects. In our EB procedure, we maximize the marginal likelihood of the model using a Laplace approximation, where the model's maximum a posteriori is estimated with an expectation-maximization algorithm. We extensively compare the performance of our proposed method to standard LMM algorithms in simulation. Various scenarios show that our method improves the accuracy of the estimates and increases the prediction power of the LMM. Overall, estimation of the LMM from high-dimensional data benefits from the use of EB methods for data-driven regularization.