  Gradient boosting from the field of statistical learning is widely known as a
powerful framework for estimation and selection of predictor effects in various
regression models by adapting concepts from classification theory. Current
boosting approaches also offer methods accounting for random effects and thus
enable prediction of mixed models for longitudinal and clustered data. However,
these approaches include several flaws resulting in unbalanced effect selection
with falsely induced shrinkage and a low convergence rate on the one hand and
biased estimates of the random effects on the other hand. We therefore propose
a new boosting algorithm which explicitly accounts for the random structure by
excluding it from the selection procedure, properly correcting the random
effects estimates and in addition providing likelihood-based estimation of the
random effects variance structure. The new algorithm offers an organic and
unbiased fitting approach, which is shown via simulations and data examples.
