  Generalized linear and additive models are very efficient regression tools
but the selection of relevant terms becomes difficult if higher order
interactions are needed. In contrast, tree-based methods also known as
recursive partitioning are explicitly designed to model a specific form of
interaction but with their focus on interaction tend to neglect the main
effects. The method proposed here focusses on the main effects of categorical
predictors by using tree type methods to obtain clusters. In particular when
the predictor has many categories one wants to know which of the categories
have to be distinguished with respect to their effect on the response. The
tree-structured approach allows to detect clusters of categories that share the
same effect while letting other variables, in particular metric variables, have
a linear or additive effect on the response. An algorithm for the fitting is
proposed and various stopping criteria are evaluated. The preferred stopping
criterion is based on $p$-values representing a conditional inference
procedure. In addition, stability of clusters are investigated and the
relevance of variables is investigated by bootstrap methods. Several
applications show the usefulness of tree-structured clustering and a small
simulation study demonstrates that the fitting procedure works well.
