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.

翻译：提出了一种新颖的数据驱动方法，用于线性混合模型（LMMs）中固定效应与随机效应的先验参数联合选择。该方法有助于估计复杂的随机效应结构以及潜在的高维数据。尽管贝叶斯框架需要指定信息性先验参数，但此类值往往无法先验获取——尤其是针对随机效应协方差。所提出的方法通过经验贝叶斯框架自动化这一选择过程，该框架利用高效的拉普拉斯近似最大化边际似然。数值模拟表明，该方法能显著提升参数估计精度与预测性能。最后，通过实际空气污染与健康数据集的案例展示，该方法如何支持使用更复杂且统计上更合理的模型以改进预测结果。