An alternative REML estimation of covariance matrices in linear mixed models

We propose a data-driven procedure for modeling covariance matrices in linear mixed-effects models with minimal distributional assumption on the random effects. It is based on elimination of the random effects using a transformation of the response variable. The approach makes it possible for the first time to disentangle the covariance matrices and model them separately. The performance of the proposed method is assessed via simulations and real data.