🤖 AI Summary
This study addresses the challenge of specifying prior parameters for both fixed and random effects in linear mixed models when dealing with high-dimensional data or complex covariance structures. The authors propose a data-driven joint shrinkage approach that, within an empirical Bayes framework, employs Laplace approximation to efficiently maximize the marginal likelihood and automatically select prior parameters for both effect types. This method represents the first to jointly and adaptively estimate priors for fixed and random effects, overcoming the limitations of conventional approaches that rely on manual specification. Numerical experiments demonstrate that the proposed method significantly outperforms existing techniques in terms of parameter estimation accuracy and predictive performance. Its effectiveness in modeling complex random-effect structures is further validated through application to real-world data on air pollution and health outcomes.
📝 Abstract
A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well as potentially high-dimensional data. Although Bayesian frameworks require the specification of informative prior parameters, such values are often unavailable a priori - especially for random-effect covariances. The proposed method automates this selection through an Empirical Bayes framework, which maximizes the marginal likelihood using an efficient Laplace approximation. Numerical simulations demonstrate that this methodology significantly enhances parameter estimation accuracy and predictive performance. Finally, an application to a real-world air pollution and health dataset illustrates how the method enables the use of more sophisticated and statistically appropriate models to improve predictive outcomes.