Gaining Insight With Recursive Partitioning Of Generalized Linear Models

Recursive partitioning algorithms separate a feature space into a set of disjoint rectangles.
Then, usually, a constant in every partition is fitted. While this is a simple and
intuitive approach, it may still lack interpretability as to how a specific relationship between dependent and
independent variables may look. Or it may be that a certain model is assumed or of
interest and there is a number of candidate variables that may non-linearily give rise to
different model parameter values.
We present an approach that combines generalized linear models with recursive partitioning
that offers enhanced interpretability of classical trees as well as providing an
explorative way to assess a candidate variable's influence on a parametric model.
This method conducts recursive partitioning of a the generalized linear model by
(1) fitting the model to the data set, (2) testing for parameter instability over a set of
partitioning variables, (3) splitting the data set with respect to the variable associated with
the highest instability. The outcome is a tree where each terminal node is associated with a generalized linear model.
We will show the methods versatility and suitability to gain additional insight
into the relationship of dependent and independent variables by two examples, modelling
voting behaviour and a failure model for debt amortization.