Flexible semiparametric mixed models

In linear mixed models the influence of covariates is restricted to
a strictly parametric form. With the rise of semi- and
nonparametric regression also the mixed model has been expanded to
allow for additive predictors. The common approach uses the
representation of additive models as mixed models. An alternative
approach that is proposed in the present paper is likelihood based
boosting. Boosting originates in the machine learning community
where it has been proposed as a technique to improve classification
procedures by combining estimates with reweighted observations.
Likelihood based boosting is a general method which may be seen as
an extension of L2 boost. In additive mixed models the advantage of
boosting techniques in the form of componentwise boosting is that
it is suitable for high dimensional settings where many influence
variables are present. It allows to fit additive models for many
covariates with implicit selection of relevant variables and
automatic selection of smoothing parameters. Moreover, boosting
techniques may be used to incorporate the subject-specific
variation of smooth influence functions by specifying random slopes
on smooth e ects. This results in flexible semiparametric mixed
models which are appropriate in cases where a simple random
intercept is unable to capture the variation of e ects across
subjects.