Tree-Structured Modelling of Varying Coefficients

Abstract: The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a set of explanatory variables and it is unknown which variables are modified by which covariates. A recursive partitioning strategy is proposed that is able to deal with the complex selection problem. The tree-structured modelling yields for each covariate, which is modified by other variables, a tree that visualizes the modified effects. The performance of the method is investigated in simulations and two applications illustrate its usefulness.