<p>Biased ridge regression estimation has recently been extended to linear mixed models, enabling more efficient estimation of the fixed effects. Empirical studies on penalizing the systematic component have suggested corresponding improvements in the efficiency of the predicted random effects as well. In this article, we demonstrate that further improvement is possible. We adopt a previously proposed modified stochastic constraint to formulate an augmented linear mixed model. Analytical derivations based on mean squared error comparisons demonstrate the superiority of our approach when evaluating total estimation and prediction efficiency. Simulation studies confirm the improved performance of our method compared to competing approaches, and a real dataset is analyzed to illustrate its practical application.</p>