Inference for seemingly unrelated linear mixed models

Linear mixed models and data generated from repeated measurements have found substantial applications in many disciplines. This paper considers the estimation problem of fixed effects and variance components in the system of two seemingly unrelated linear mixed models. We first propose the covariance adjustment estimator of the fixed effects and then construct consistent estimators of its unknown parameters and further study the small sample performance of the two-stage estimator. It is shown that the proposed two-stage covariance adjustment estimator is preferred and feasible based on its theoretical properties and some numerical illustrations. Finally, we investigate the effects of covariance adjustment on the variance components by plugging the two-stage estimator into the restricted log-likelihood of the variance components, and the results imply that seemingly unrelated linear mixed models may only improve the estimation of the fixed effects.& COPY; 2023 Elsevier B.V. All rights reserved.