A boosting approach to 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 non-parametric 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 explanatory 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 effects. This results in flexible semiparametric mixed models which are appropriate in cases where a simple random intercept is unable to capture the variation of effects across subjects.