  Boosting techniques from the field of statistical learning have grown to be a
popular tool for estimating and selecting predictor effects in various
regression models and can roughly be separated in two general approaches,
namely gradient boosting and likelihood-based boosting. An extensive framework
has been proposed in order to fit generalised mixed models based on boosting,
however for the case of cluster-constant covariates likelihood-based boosting
approaches tend to mischoose variables in the selection step leading to wrong
estimates. We propose an improved boosting algorithm for linear mixed models
where the random effects are properly weighted, disentangled from the fixed
effects updating scheme and corrected for correlations with cluster-constant
covariates in order to improve quality of estimates and in addition reduce the
computational effort. The method outperforms current state-of-the-art
approaches from boosting and maximum likelihood inference which is shown via
simulations and various data examples.
